# Operations & Supply Chain Management: Principles and Practice

Fotios Petropoulos, Henk Akkermans, O. Zeynep Aksin, Imran Ali, Mohamed Zied Babai, Ana Barbosa-Povoa, Olga Battaïa, Maria Besiou, Nils Boysen, Stephen Brammer, et al.

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Fotios Petropoulos, Henk Akkermans, O. Zeynep Aksin, Imran Ali, Mohamed Zied Babai, et al. Operations & Supply Chain Management: Principles and Practice. International Journal of Production Research, 2025, pp.1-184. 10.1080/00207543.2025.2555531. hal-05375064

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**Operations & supply chain management:**
**principles and practice**

Fotios Petropoulos, Henk Akkermans, O. Zeynep Aksin, Imran Ali, Mohamed Zied Babai, Ana Barbosa-Povoa, Olga Battaïa, Maria Besiou, Nils Boysen, Stephen Brammer, Alistair Brandon-Jones, Dirk Briskorn, Tyson R. Browning, Paul Buijs, Piera Centobelli, Andrea Chiarini, Paul Cousins, Elizabeth A. Cudney, Andrew Davies, Steven J. Day, René de Koster, Rommert Dekker, Juliano Denicol, Mélanie Despeisse, Stephen M. Disney, Alexandre Dolgui, Linh Duong, Malek El-Qallali, Behnam Fahimnia, Fatemeh Fakhredin, Stanley B. Gershwin, Salar Ghamat, Vaggelis Giannikas, Christoph H. Glock, Janet Godsell, Kannan Govindan, Claire Hannibal, Anders Haug, Tomislav Hernaus, Juliana Hsuan, Dmitry Ivanov, Marianne Jahre, Björn Johansson, Madan Shankar Kalidoss, Argyris Kanellopoulos, Devika Kannan, Elif Karul, Konstantinos V. Katsikopoulos, Ayse Begüm Kilic-Ararat, Rainer Kolisch, Maximilian Koppenberg, Maneesh Kumar, Yong-Hong Kuo, Andrew Kusiak, Michael A. Lewis, Stanley Frederick W. T. Lim, Veronique Limère, Jiyin Liu, Omid Maghazei, Matija Marić, Joern Meissner, Miranda Meuwissen, Pietro Micheli, Samudaya Nanayakkara, Bengü Nur Özdemir, Thanos Papadopoulos, Stephen Pavelin, Srinath Perera, Wendy Phillips, Dennis Prak, Hubert Pun, Sharfah Ahmad Qazi, Usha Ramanathan, Gerald Reiner, Ewout Reitsma, Jens K. Roehrich, Nada R. Sanders, Joseph Sarkis, Nico André Schmid, Christoph G. Schmidt, Andreas Schroeder, Kostas Selviaridis, Stefan Seuring, Chuan Shi, Byung-Gak Son, Martin Spring, Brian Squire, Wendy van der Valk, Dirk Pieter van Donk, Geert-Jan van Houtum, Miriam Wilhelm, Finn Wynstra & Ting Zheng

**To cite this article:** Fotios Petropoulos, Henk Akkermans, O. Zeynep Aksin, Imran Ali, Mohamed Zied Babai, Ana Barbosa-Povoa, Olga Battaïa, Maria Besiou, Nils Boysen, Stephen Brammer, Alistair Brandon-Jones, Dirk Briskorn, Tyson R. Browning, Paul Buijs, Piera Centobelli, Andrea Chiarini, Paul Cousins, Elizabeth A. Cudney, Andrew Davies, Steven J. Day, René de Koster, Rommert Dekker, Juliano Denicol, Mélanie Despeisse, Stephen M. Disney, Alexandre Dolgui, Linh Duong, Malek El-Qallali, Behnam Fahimnia, Fatemeh Fakhredin, Stanley B. Gershwin, Salar Ghamat, Vaggelis Giannikas, Christoph H. Glock, Janet Godsell, Kannan Govindan, Claire Hannibal, Anders Haug, Tomislav Hernaus, Juliana Hsuan, Dmitry Ivanov, Marianne Jahre, Björn Johansson, Madan Shankar Kalidoss, Argyris Kanellopoulos, Devika Kannan, Elif Karul, Konstantinos V. Katsikopoulos, Ayse Begüm Kilic-Ararat, Rainer Kolisch, Maximilian Koppenberg, Maneesh Kumar, Yong-Hong Kuo, Andrew Kusiak, Michael A. Lewis, Stanley Frederick W. T. Lim, Veronique Limère, Jiyin Liu, Omid Maghazei, Matija Marić, Joern Meissner, Miranda Meuwissen, Pietro Micheli, Samudaya Nanayakkara, Bengü Nur Özdemir, Thanos Papadopoulos, Stephen Pavelin, Srinath Perera, Wendy Phillips, Dennis Prak, Hubert Pun, Sharfah Ahmad Qazi, Usha Ramanathan, Gerald Reiner, Ewout Reitsma, Jens K. Roehrich, Nada R. Sanders, Joseph Sarkis, Nico André Schmid, Christoph G. Schmidt, Andreas Schroeder, Kostas Selviaridis, Stefan Seuring, Chuan Shi, Byung-Gak Son, Martin Spring, Brian Squire, Wendy van der Valk, Dirk Pieter van Donk, Geert-Jan van Houtum, Miriam Wilhelm, Finn
To link to this article: https://doi.org/10.1080/00207543.2025.2555531

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Operations & supply chain management: principles and practice

Fotios Petropoulos<sup>1, a</sup>, Henk Akkermans<sup>b</sup>, O. Zeynep Aksin<sup>c</sup>, Imran Ali<sup>d</sup>, Mohamed Zied Babaie<sup>e</sup>, Ana Barbosa-Povoá<sup>f</sup>, Olga Battaia<sup>e</sup>, Maria Besiou<sup>g</sup>, Nils Boysen<sup>h</sup>, Stephen Brammer<sup>a</sup>, Alistair Brandon-Jones<sup>a</sup>, Dirk Briskorn<sup>i</sup>, Tyson R. Browning<sup>j</sup>, Paul Buijs<sup>k</sup>, Piera Centobelli<sup>l</sup>, Andrea Chiarini<sup>1, m</sup>, Paul Cousins<sup>n</sup>, Elizabeth A. Cudney<sup>1, o</sup>, Andrew Davies<sup>p</sup>, Steven J. Day<sup>q</sup>, René de Koster<sup>r</sup>, Rommert Dekker<sup>s</sup>, Juliano Denicol<sup>t</sup>, Mélanie Despeisse<sup>1, u</sup>, Stephen M. Disney<sup>1, v</sup>, Alexandre Dolgui<sup>1, w</sup>, Linh Duong<sup>1, x</sup>, Malek El-Qallali<sup>y</sup>, Behnam Fahimnia<sup>z</sup>, Fatemeh Fakhredin<sup>aa</sup>, Stanley B. Gershwin<sup>bb</sup>, Salar Ghamat<sup>cc</sup>, Vaggelis Giannikas<sup>1, a</sup>, Christoph H. Glock<sup>1, dd</sup>, Janet Godsell<sup>ee</sup>, Kannan Govindan<sup>ff</sup>, Claire Hannibal<sup>gg</sup>, Anders Haugh<sup>hh</sup>, Tomislav Hernaus<sup>ii</sup>, Juliana Hsuan<sup>jj</sup>, Dmitry Ivanov<sup>1, kk</sup>, Marianne Jahre<sup>g</sup>, Björn Johansson<sup>u</sup>, Madan Shankar Kalidoss<sup>ll</sup>, Argyris Kanellopoulos<sup>mm</sup>, Devika Kannan<sup>ff</sup>, Elif Karul<sup>c</sup>, Konstantinos V. Katsikopoulos<sup>nn</sup>, Ayse Begüm Kilic-Ararat<sup>a</sup>, Rainer Kolisch<sup>oo</sup>, Maximilian Koppenberg<sup>pp</sup>, Maneesh Kumar<sup>1, qq</sup>, Yong-Hong Kuo<sup>1, rr</sup>, Andrew Kusiak<sup>ss</sup>, Michael A. Lewis<sup>a</sup>, Stanley Frederick W. T. Lim<sup>tt</sup>, Veronique Limère<sup>uu</sup>, Jiyin Liu<sup>ee</sup>, Omid Maghazei<sup>a</sup>, Matija Maric<sup>ii</sup>, Joern Meissner<sup>aa</sup>, Miranda Meuwissen<sup>pp</sup>, Pietro Micheli<sup>vv</sup>, Samudaya Nanayakkara<sup>ww</sup>, Bengü Nur Özdemir<sup>xx</sup>, Thanos Papadopoulos<sup>yy</sup>, Stephen Pavelin<sup>a</sup>, Srinath Perera<sup>ww</sup>, Wendy Phillips<sup>x</sup>, Dennis Prak<sup>zz</sup>, Hubert Pun<sup>aaa</sup>, Sharfah Ahmad Qazi<sup>bbb</sup>, Usha Ramanathan<sup>ccc</sup>, Gerald Reiner<sup>1,ddd</sup>, Ewout Reitsma<sup>eee</sup>, Jens K. Roehrich<sup>a</sup>, Nada R. Sanders<sup>fff</sup>, Joseph Sarkis<sup>ggg</sup>, Nico André Schmid<sup>hhh</sup>, Christoph G. Schmidt<sup>a</sup>, Andreas Schroeder<sup>iii</sup>, Kostas Selviaridis<sup>iii</sup>, Stefan Seuring<sup>1,bbb</sup>, Chuan Shijij<sup>ii</sup>, Byung-Gak Son<sup>kkk</sup>, Martin Spring<sup>iii</sup>, Brian Squire<sup>ll</sup>, Wendy van der Valk<sup>b</sup>, Dirk Pieter van Donk<sup>k</sup>, Geert-Jan van Houtum<sup>mmm</sup>, Miriam Wilhelm<sup>nnn</sup>, Finn Wynstra<sup>ooo</sup> and Ting Zheng<sup>1, dd</sup>

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<footnote><sup>a</sup>School of Management, University of Bath, Bath, UK; <sup>b</sup>Department of Information Systems & Operations Management, Tilburg School of Economics and Management, Tilburg University, Tilburg, Netherlands; <sup>c</sup>College of Administrative Sciences and Economics, Koc University, Istanbul, Turkey; <sup>d</sup>School of Business and Law, Central Queensland University, Melbourne, Australia; <sup>e</sup>Kedge Business School, Bordeaux, France; <sup>f</sup>Center for Management Studies, Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal; <sup>g</sup>Kühne Logistics University, Hamburg, Germany; <sup>h</sup>Lehrstuhl für Operations Management, Friedrich-Schiller-Universität Jena, Jena, Thuringia, Germany; <sup>i</sup>Bergische Universität Wuppertal, Wuppertal, Germany; <sup>j</sup>Neeley School of Business, Texas Christian University, Fort Worth, TX, USA; <sup>k</sup>Department of Operations, University of Groningen, Groningen, Netherlands; <sup>l</sup>Department of Industrial Engineering, University of Naples “Federico II”, Naples, Italy; <sup>m</sup>Department of Management, University of Verona, Verona, Italy; <sup>n</sup>Management School, University of Liverpool, Liverpool, UK; <sup>o</sup>John E. Simon School of Business, Maryville University of Saint Louis, Town and Country, Missouri, USA; <sup>p</sup>Science Policy Research Unit, University of Sussex Business School, Brighton, UK; <sup>q</sup>School of Management, Zhejiang University, Hangzhou, People’s Republic of China; <sup>r</sup>Rotterdam School of Management, Erasmus University, Rotterdam, The Netherlands; <sup>s</sup>Erasmus School of Economics, Erasmus University, Rotterdam, Netherlands; <sup>t</sup>Bartlett School of Sustainable Construction, The Bartlett Faculty of the Built Environment, University College London, London, UK; <sup>u</sup>Department of Industrial and Material Sciences, Chalmers University of Technology, Gothenburg, Sweden; <sup>v</sup>Center for Simulation, Analytics, and Modelling, University of Exeter Business School, Exeter, UK; <sup>w</sup>LS2N-CNRS, IMT Atlantique, Nantes, France; <sup>x</sup>College of Business and Law, University of the West of England, Bristol, UK; <sup>y</sup>Rabdan Academy, Abu Dhabi, UAE; <sup>z</sup>Institute of Transport and Logistics Studies, The University of Sydney Business School, Sydney, Australia; <sup>aa</sup>Kühne Logistics University, Hamburg, Germany; <sup>bb</sup>Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA; <sup>cc</sup>Lazaridis School of Business and Economics, Wilfrid Laurier University, Waterloo, Ontario, Canada; <sup>dd</sup>Technical University of Darmstadt, Darmstadt, Germany; <sup>ee</sup>Loughborough Business School, Loughborough University, Loughborough, UK; <sup>ff</sup>Adelaide Business School, University of Adelaide, Adelaide, Australia; <sup>gg</sup>Robert Gordon University, Aberdeen, UK; <sup>hh</sup>Department of Business and Sustainability, University of Southern Denmark, Kolding, Denmark; <sup>ii</sup>Faculty of Economics and Business, University of Zagreb, Zagreb, Croatia; <sup>jj</sup>Department of Operations Management, Copenhagen Business School, Copenhagen, Denmark; <sup>kk</sup>Berlin School of Economics and Law, Department of Business Administration, Berlin, Germany; <sup>ll</sup>Department of Technology and Innovation, University of Southern Denmark, Kolding, Denmark; <sup>mm</sup>Operations Research & Logistics Group, Wageningen University and Research, Wageningen, Netherlands; <sup>nn</sup>Department of Decision Analytics and Risk, University of Southampton Business School, Southampton, UK; <sup>oo</sup>TUM School of Management, Technical University of Munich, Munich, Germany; <sup>pp</sup>Wageningen University and Research, Wageningen, Netherlands; <sup>qq</sup>Cardiff Business School, Cardiff University, Cardiff, UK; <sup>rr</sup>Department of Data and Systems Engineering, The University of Hong Kong, Pokfulam, Hong Kong; <sup>ss</sup>Department of Industrial and Systems Engineering, University of Iowa, Iowa City, Iowa, USA; <sup>tt</sup>Eli Broad College of Business, Michigan State University, East Lansing, Michigan, USA; <sup>uu</sup>Department of Business Informatics and Operations Management, Ghent University, Ghent, Belgium; <sup>vv</sup>Warwick Business School, University of Warwick, Warwick, UK; <sup>ww</sup>Centre for Smart Modern Construction, School of Engineering, Design and Built Environment, Western Sydney University, Kingswood, Australia; <sup>xx</sup>University of Wisconsin-Whitewater, Whitewater, Wisconsin, USA; <sup>yy</sup>Department of Analytics, Operations and Systems, Kent Business School, University of Kent, Kent, UK; <sup>zz</sup>Department of Industrial Engineering and Business Information Systems, University of Twente, Enschede, Netherlands; <sup>aaa</sup>Ivey Business School, Western University, London, Ontario, Canada; <sup>bbb</sup>Faculty of Economics and Management, University of Kassel, Kassel, Germany; <sup>ccc</sup>Department of Management, College of Business Administration, University of Sharjah, Sharjah, United Arab Emirates; <sup>ddd</sup>Vienna University of Economics and Business, Vienna, Austria; <sup>eee</sup>Department of Supply Chain and Operations Management, School of Engineering, Jönköping University, Jönköping, Sweden; <sup>fff</sup>Northeastern University, Boston, MA, USA; <sup>ggg</sup>Business School, Worcester Polytechnic Institute, Worcester, MA, USA; <sup>hhh</sup>IESEG School of Management, University of Lille, Lille, France; <sup>iii</sup>Lancaster University Management School, Lancaster University, Lancaster, UK; <sup>iii</sup>School of Data Science, The Chinese University of Hong Kong, Shenzhen, People’s Republic of China; <sup>kkk</sup>Bayes Business School, City University London, London, UK; <sup>iii</sup>University of Bristol Business School, University of Bristol, Bristol, UK; <sup>mmm</sup>Department of Industrial Engineering and Innovation Sciences, Eindhoven University of Technology, Eindhoven, The Netherlands; <sup>nnn</sup>Department of Information Systems and Operations Management, Vienna University of Economics and Business, Vienna, Austria; <sup>ooo</sup>Department of Technology and Operations Management, Rotterdam School of Management, Erasmus University, Rotterdam, Netherlands</footnote>
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### ABSTRACT

Operations and Supply Chain Management (OSCM) has continually evolved, incorporating a broad array of strategies, frameworks, and technologies to address complex challenges across industries. This encyclopedic article provides a comprehensive overview of contemporary strategies, tools, methods, principles, and best practices that define the field's cutting-edge advancements. It also explores the diverse environments where OSCM principles have been effectively implemented. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners.

### ARTICLE

**HISTORY** Received 25

February 2025; Accepted 25

August 2025

**KEYWORDS** Review;

encyclopedia; theory;

practice; principles; strategy

## 1. Introduction¹

Thousands of years of civilisation has seen modern humans evolve from hunter-gatherers to agrarian societies to city-states and nations. Operations management (OM) and supply chain management (SCM) principles have been ingrained in each of these stages. OM and SCM principles and practices existed even before scientific explanations and theories were established to help us understand and improve them. Practices included managing production, transportation, storage, and distribution – in many cases as part of historical documents.

Here is an example. A popular western Judeo-Christian bible story – also appearing in the Torah and the Qur'an – is of Joseph, son of Jacob. In the book of Genesis (41–47). The story focuses on Joseph's management of grains during his time in Egypt. He was appointed the senior administrator in what is likely the Egyptian department of agriculture and commerce. Joseph planned (forecasted) for seven years of surplus and seven years of famine – trying level supply and demand during peak and trough times. This was an empire-wide effort to ensure efficient grain production (harvesting), delivery, storage, production, financial transactions, and meticulous recordkeeping of thousands of farms and schedules. Inventory management was necessary to provide food and prevent spoilage. Human resources management was needed throughout the process. Joseph didn't necessarily have textbooks with formalised and scientific tools and techniques (as presented in this compendium paper) – but the concepts and practices did exist before we gave them their names.

This story – whether fact or fictional – exemplifies a period where centralised and mass production concepts were practised. It also exemplifies a long history of operations and supply chain management principles. These principles were important enough to appear in religious and historical documents and literature.

Sometimes we lose perspective and believe that pre-modern practices were not as complex as today. Clearly planning for and feeding a whole empire over decades, even in agrarian societies, showed that significant complexities existed in early civilisations. OM and SCM have

been ingrained in society for thousands of years and the practices have been intertwined with civilisation and modernity progression.

Many operations and supply chain textbooks provide a review of the historical nature of operations and supply chain management (e.g. Gupta and Starr 2014; Stevenson 2020). In fact, many introductory OM and SCM textbooks include the historical evolution of operations and supply chain principles in their first two chapters.

General business history books also have similar outlines. Pre-industrial management principles from the Middle East, Asia, and Africa and the role of the Church and Feudalism are all part of this business history (e.g. Wilson et al. 2021).

In the book, *A World Lit Only by Fire* (Manchester 1993), business and trade helped further the growth of the Renaissance and the University system. Where languages, law, and business became central to a time period where global supply chains started to function.

Modern business history – after the industrial revolution commences – has management advances in fixating on productivity and efficiency improvements. OM and SCM textbooks include economic principal milestones such as Adam Smith's division of labour allowing greater specialisation with resultant work efficiency; steam power and the industrial revolution (technology); and parts and materials standardisation (processes and designs) including the cotton gin and military weaponry. These principles and tools contributed to productivity. Then scientific principles emerged (Frederick Winslow Taylor) – and the initial stages of just-in-time and supply chain (vertical) integration (Henry Ford). These were the formalisation stages.

During the past century science, mathematics, economics, and technology were interspersed. Society knew how to build stable bridges even before theoretical science and mathematics emerged to support and improve practice. To help develop innovations and replicate success theory and practice supported each other. Eventually, modern operations research tools and computerisation resulted in optimisation and greater automated control within OM.
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Prior to the 1970's most operations were considered as shop floor concerns, and sometimes included inter-organisational management of multi-echelon inventory. Operations was primarily focussed on short-term and tactical planning and management concerns – usually focussing on efficiencies and cost management. Even-tually, operations became strategic (Skinner 1969). As a strategy, operations can help organisations differen-tiate themselves and build competitive advantage. This strategic perspective grew during the 1970's and 1980's as various global competitiveness issues arose – moving away from mass production to other principles and more nuanced operations perspectives.

Many of us lived and remember a time when operations management was positioned as management sciences and operations research. But operations and its strategic content is more complex than specific mathematical principles can capture – wicked problems could not be solved just by single mathematical models and tools (Churchman 1967). Thus, more qualitative management and business perspectives were introduced. For example, Total Quality Management – which included analytical models – also introduced managerial, culture, and qualitative principles such as *continuous improvement*. This period also portended World Class Manufacturing (Flynn, Schroeder, and Flynn 1999) and Operational Excellence (Oakland, Oakland, and Turner 2020).

In the later 1980's the term 'supply chain management' was introduced. The adoption and diffusion of the concept started to take hold in the 1990's with initial programmes and textbooks on supply chain management – an outgrowth of purchasing, logistics, transportation, operations, and marketing – began to enter the academic lexicon (Mentzer et al. 2001).

During these periods – as exemplified by a historical perspective on sustainability (Sarkis and Zhu 2018) and sustainable development goals (SDGs; Sarkis and Ibrahim 2022) within the *International Journal of Production Research* – the focus was mainly on economic and business optimisation. Supply chain management was mostly focussed on the traditional topics, many of which are covered in this paper.

As the strategic focus expanded and business-societal interactions became more pronounced, the OM-SCM research evolved. Broader and non-traditional manufacturing production concerns further emerged. Issues such as humanitarian operations, triple-bottom-line sustainability, and healthcare operations entered the research literature during the early 2000's into the 2020's. Highly integrated, smarter, multiple stakeholder technologies also transpired. Multiple stakeholder perspectives and engaged transdisciplinary involvement in research opened new doors for OM and SCM scholars to

step through, into fields that that traditionalists may not have envisioned such as of medical, biological conservation, philosophy ethics, and feminist theory fields.

External pressures and interventions meant that OM and SCM needed greater resilience, decarbonisation, equity, and circularity – at global and local levels. OM and SCM research catalysts were no longer intra-organisational worries, but societal shifts and concerns. In many cases we went from addressing current problems to prospective and real problems.

Traditional optimisation, operational efficiencies, and productivity remain concerns; but strategic and external environmental and institutional issues are significantly influencing OM and SCM research and application. Oftentimes scholars are a step ahead of practice – preemptively providing prospective OM and SCM solutions for industry. Exploring solutions that can benefit society, an important dimension of responsible research.

In this scholarly compendium we examine current and emergent OM and SCM topics. OM topics are initially introduced. Perspectives on twenty OM themes are covered by leading global scholars. SCM topics are then overviewed by another set of leading scholars. Eleven SCM sections provide a comprehensive view with state-of-the-art insights presented. Broader society, environment, global economics, and institutional concerns span both OM-SCM. These OM-SCM spanning themes are more prevalent in practice and in theory.

The earlier sections of this paper focus on conceptual and academic perspectives. But, as the saying goes, the 'proof of the pudding is in the eating' – the last major section considers various applications from traditional manufacturing and production applications, to agriculture, healthcare, and humanitarian operations applications. The broad variety of applications represent how the various theories and conceptualisations can help us understand, manage, and support diverse contexts beyond the shopfloor. These broad applications are evidence that OM and SCM are maturing and more societally important. OM-SCM has become part of the popular discourse – especially after the interconnected global web of material, information, financial, and capital flows were disrupted during the COVID crisis.

This compendium covers a wide range of topics with scholars from throughout the world. Many are leading scholars who have lived through some of the most significant changes in our field occurring over the past five decades. Some are junior scholars whose perspectives are insightful and needed to guide us into the future. Each topic (section and sub-section) provides what the author of that section believes are important topical elements and with thoughts for future directions. Many also provide some recommendations on further reading that they
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feel can help both novice and advanced researchers and practitioners.

We hope that you enjoy this broad compendium of the OM-SCM field. We believe it can be a valuable reference resource but realise it is a snapshot in time of where we have been, where we are, and the road ahead.

## 2. Operations management

### 2.1. Operations strategy²

The study of Operations Strategy (OS) began with Skinner's (1969) seminal argument that corporate strategy should be aligned with business unit strategies and, in turn, functional (e.g. operations) strategies (Ward and Duray 2000). This process should ensure that all levels of strategy are coherent and support strategic objectives. Today, there are many definitions of OS but in their best-selling textbook (Slack and Lewis 2024) describe it as the 'total pattern of decisions that shape the long-term capabilities of any type of operation'. This captures the systemic character of OS, combining structure and function, or more pragmatically, the 'what' (how big, where, what suppliers, etc.) and 'how' of operations capabilities being reconciled with (market) requirements. The specific mechanisms for this reconciliation give rise to alternative OS models.

The first and arguably most influential model is that of 'cumulative' capability building, an approach strongly linked to lean/quality concepts (discussed at length in other sections in this paper). Although exact trajectories (e.g. quality first, then reliability, flexibility, and cost efficiency, etc.) remain the subject of debate (Narasimhan and Schoenherr 2013; Sarmiento, Wheylan, and Thürer 2018; Singh et al. 2015), the sequence of building capabilities does matter (Rosenzweig and Roth 2004). The second model is the idea of 'trade-offs', which observes that, in simple terms, if one thing increases, another must decrease (Boyer and Lewis 2002). For instance, a warehouse can carry a few large or many small items. Of course, the concept of a trade-off suggests strategic choices made with complete knowledge of the dis/function of each setup. Interestingly, most of the evidence of firm performance used to underpin the cumulative capabilities logic came from measured improvement within individual plants over time (to lead their competitors in almost every dimension of performance). In contrast, trade-off data came from comparisons across plants at a given time. This may suggest that the two approaches are not in conflict (Schmenner and Swink 1998). The third model is to be focussed; an OS concentrating on a limited set of tasks will likely generate more productive outcomes. Beyond Skinner's (1974) original focussed

factory, there are also well-known examples of focus in healthcare systems around the world, including the Shouldice Hernia Hospital in Canada (taught in virtually every business school), the Aravind Eye Clinic in India and Coxa Hospital for Joint Replacement in Finland. OS research generally (Ketokivi and Jokinen 2006) supports the benefits of focus (Huckman and Zinner 2008; Tsikriktsis 2007), and there is a strong logic for the benefits, such as the static economies of scale that appear as either reductions in average cost via amortising of fixed investments or improvements in average quality from learning, depth of know-how, etc. There may also be benefits in 'related spillovers'; Fong Boh, Slaughter, and Espinosa (2007), for example, found that software team productivity was more strongly impacted by the group's average experience with related activities than the average experience with the focal activity.

Regardless of the specific approach to OS, measurement and metrics are crucial, providing the foundation for operational control and organisational learning (Sitkin, Sutcliffe, and Schroeder 1994). The relationship between strategy and performance measurement is well-documented, with effective measurement systems enhancing strategic alignment at various levels of the organisation (Micheli and Manzoni 2010). Interestingly, the idea of programmatic strategic alignment shares similarities with the concept of Hoshin Kanri, the planning process that involves multi-directional communication (Witcher and Butterworth 2001).

As well as this emphasis on the process of OS, and although scholars have referred to them in different ways, including 'decision areas', 'policy areas', 'sub-strategies' or 'tasks', a great deal of research explores aspects of OS content. From consideration of the (dis)economic scale of capacity and its increments to the timing of any changes (Olhager, Rudberg, and Wikner 2001) to the set of broad and long-term decisions governing how the operation is improved on a continuing basis (e.g. Six Sigma: Linderman et al. 2003), any elements of an operating model that involves more significant decisions (i.e. more existential, capital intensive/complex investments, etc.) with considerable lead-times are of interest to OS researchers. For example, consider the process management triangle (Klassen and Menor 2007), a heuristic for understanding an implied trade-off relationship between capacity utilisation, variability in terms of input and processing characteristics, and inventory. These interactions suggest generic guidelines for OS decisions. If an operation has high levels of utilisation (a busy factory), it will generate a backlog in the presence of any meaningful variability (such as product variety). A specific capacity strategy for such a situation would be to drive down variability by, for instance, focussing on particular product
<figure><img src="image_17.png" /></figure>

types, only allowing scheduled demand, etc. Alternatively, if additional capacity can be added, the impact of variability can be significantly reduced, meaning that the system is responsive (low/no backlog) but at the 'cost' of low absolute levels of utilisation and high relative costs. Recognition of the balance between costs and flexibility/responsiveness – and echoing the (Schmenner and Swink 1998) argument that trade-off and cumulative capability can be complementary approaches – just reflecting different aspects of performance improvement over time – the balance of cost and flexibility is also central to discussions of mass customisation, where firms like BMW have had great success using modular architectures to deliver customised products efficiently (Kortmann et al. 2014).

Other decisions, such as make-versus-buy (MvB), which sets the boundaries for internal and external resources and capabilities (McIvor 2005), have also long been an OS priority. This decision has evolved from its transactional cost economics roots to include OS considerations like protecting and developing resources and managing supply risks. This decision area also highlights how OS has evolved in an era of global business ecosystems (e.g. Adner 2017), the sharing economy (Benjafar and Hu 2020) and a rapidly evolving set of digital infrastructures (Choi et al. 2022). Consequently, the evolution of OS in many industries has shifted away from internal resource management to the dynamic management of external assets. This transformation necessitates re-evaluating traditional operating strategies and MvB's issues. Maghazei, Lewis, and Netland (2022), for example, explored the acquisition of emerging operational technologies and drones and observed a dynamic interaction between an ecosystem keen to hype a solution and a more tentative market pull from companies. Likewise, Giustiziero et al. (2023) noted how many digital firms are both very narrow in scope and very large scale, concluding this reflects different economics of MvB in contemporary digital technology ecosystems. This increasingly underscores the importance of managing relationships with partners, competitors, and customers. OS has always stressed that the health of a firm's supply network influences its performance. Still, this shift to 'hyper specialisation' requires OS to more pro-actively consider ecosystem health alongside internal capabilities (Iansiti and Levien 2004). Indeed, many operational technologies are perhaps better characterised by a relational rather than entitative ontology? As Faraj and Leonardi (2022, 777) argued when describing how autonomous vehicles rely on GPS, AI, or connection to a charging network,

[s]ome of these relations may be performed within the firm, but many are performed involving a diverse set of external actors via constant real-time data flows. Thus,

no entity within this network of relations is meaningful outside the scope of the relations that constitute it'.

This relational framing has potentially profound implications for OS. For example, traditional internal performance metrics must also be complemented by measures of ecosystem health, such as structure, predictability, and vulnerability.

OS's evolution means it is now more global (Gray and Massimino 2014) and technologically enabled (Choi et al. 2022). There has been a corresponding supply chain turn, and sustainability (Longoni and Cagliano 2015) is now increasingly (but perhaps insufficiently) a significant concern. There has also been a fuller incorporation of regulatory and other governance concerns (Fan et al. 2022). At its core, effective OS is still concerned with the alignment between different levels and functions. Cumulative capabilities, trade-offs, and focus remain critical logics, albeit today, we have an increased understanding of the influence of behavioural factors (Fahimnia et al. 2019) – from overconfidence, where individuals believe they know more than they do, to anchoring decisions on otherwise irrelevant past experiences and then making insufficient adjustments to these anchored estimates – in considering how the OS process works.

## 2.2. Capacity management³

Capacity management is a crucial aspect of strategic planning in businesses, focussing on optimising resource use to achieve maximum efficiency and productivity. Slack, Chambers, and Johnston (2010) emphasise the importance of aligning capacity with demand to ensure operational efficiency. In essence, capacity management ensures that an organisation has the right amount and mixture of resources at the right time to meet current and future demands. Done correctly, it optimally allocates resources to meet customer demand both efficiently and effectively (Chopra and Meindl 2021). It involves a deep understanding of the organisation's capabilities, allowing for a proactive approach in aligning those capabilities with business needs. Hopp and Spearman (2012) describe capacity management as balancing supply and demand, a process that includes identifying the resources needed, measuring current capacity, and making necessary adjustments to meet customer needs without overextending resources.

Research shows that effective capacity management not only reduces costs but also enhances supply chain performance by improving lead times and service levels (Axsäter 2015). In a dynamic market, the ability to respond quickly to fluctuations in demand is paramount.
<figure><img src="image_18.png" /></figure>

Thus, a well-executed capacity management strategy provides businesses with the agility needed to adapt to changing circumstances (Fabbe-Costes and Jahre 2008). For instance, firms that utilise advanced analytics and real-time data can make informed decisions regarding capacity adjustments, leading to significant competitive advantages (Aghezzaf 2005).

Moreover, the integration of capacity management with supply chain strategies enhances overall performance. As noted by Montgomery and Runger (2020), organisations that align their capacity planning with supply chain logistics can achieve optimal performance and resource utilisation. Consequently, effective capacity management contributes to better service levels, customer satisfaction, and profitability (Blanchard 2021).

## Steps involved in capacity management

In the business context, capacity management involves several steps:

**Demand Forecasting:** The process begins with accurately predicting customer demand. Babai, Boylan, and Rostami-Tabar (2022) stress that accurate demand forecasting is crucial in aligning supply with anticipated customer needs, thus reducing underutilisation and overutilisation of resources. This involves predicting future product or service requirements using historical data, market analysis, and trend forecasting. According to Syntetos, Boylan, and Disney (2009), incorporating advanced forecasting methods can significantly improve the accuracy of demand predictions, leading to better capacity planning outcomes.

**Capacity Evaluation:** Once demand is forecasted, businesses need to evaluate their current capacity. Syntetos, Boylan, and Disney (2009) argue that continuous evaluation of capacity and capabilities is essential for improving operational performance and resilience in the face of market fluctuations. This step assesses processes, people, and technology to identify gaps between current capacity and future demand. Additionally, Nia, Awasthi, and Bhuiyan (2021) highlight the importance of utilising simulation models to assess capacity in complex systems, allowing for a deeper understanding of potential bottlenecks.

**Capacity Adjustment:** Wu, Erkoc, and Karabuk (2005) highlight that timely capacity adjustments can mitigate risks and enhance responsiveness to changing market conditions. After evaluating demand and capacity, businesses may need to adjust resources by expanding, building new facilities, or introducing advanced technologies. The implementation of flexible capacity strategies, as discussed by Law and Kelton (2007), can provide firms with the ability to scale operations up or down based on fluctuating demand.

**Performance Monitoring:** Continuous performance monitoring ensures that capacity adjustments result in desired outcomes. Regularly reviewing key performance indicators (KPIs) helps businesses determine whether their capacity management strategies are effective. According to Shumsky and Zhang (2009), utilising dashboard reporting tools can facilitate real-time monitoring and improve decision-making processes related to capacity management. Moreover, leveraging advanced techniques such as Bayesian networks can enhance performance monitoring by modelling the relationships between various performance metrics, allowing organisations to identify potential issues before they escalate (Maleki and Cruz-Machado 2013). This proactive approach not only supports more informed decision-making but also fosters a culture of continuous improvement within the supply chain, leading to enhanced operational efficiency (Maleki and Cruz-Machado 2013).

## Scientific methods used in capacity management

* Little's Law provides insights into the relationship between work-in-progress inventory, throughput, and lead time (Hopp and Spearman 2012).

* Queuing theory is instrumental in analysing process flows and managing wait times in service systems (Gross and Harris 2011).

* Optimisation models are critical tools for efficiently allocating resources to minimise operational costs while meeting demand (Varian 2014).

* Simulation techniques can help in understanding complex systems and predicting the impacts of capacity adjustments (Fabbe-Costes and Jahre 2008).

## Extended strategies for capacity management

**Outsourcing:** Outsourcing can improve flexibility and allow businesses to focus on core competencies, making it a cost-effective strategy for managing capacity variations (Quinn 1999). This strategy enables organisations to adapt their capacity in line with market demands without significant capital investments. By outsourcing certain functions, companies can leverage specialised expertise and resources, which enhances their responsiveness to fluctuations in demand (Lee, Jeong, and Moon 2002). This strategic decision not only minimises fixed costs but also facilitates advanced planning and scheduling, thereby improving overall supply chain performance (Lee, Jeong, and Moon 2002).

**Collaboration and Alliances:** Collaboration between organisations can help capitalise on each other's strengths, achieve economies of scale, and efficiently manage complex supply chains (Tan, Lyman, and Wisner 2002). Joint ventures or partnerships can lead to shared resources, enhancing overall capacity. According to Simatupang and
<figure><img src="image_19.png" /></figure>

Sridharan (2008), effective collaboration design can significantly improve supply chain performance by facilitating better communication and information sharing among partners. This increased level of collaboration allows organisations to respond more swiftly to market changes and align their strategies, ultimately leading to enhanced operational efficiency and customer satisfaction.

**Subcontracting:** Subcontracting helps firms manage capacity limitations while focussing on their core strengths (Heikkilä 2002). By leveraging external expertise and resources, companies can remain agile and responsive to market changes. Dainty, Briscoe, and Millett (2001) highlight that subcontracting not only allows firms to access specialised skills and technology but also fosters collaborative relationships that can enhance overall supply chain performance. This approach enables firms to adapt to demand fluctuations more effectively and optimise their resource allocation, leading to improved project outcomes and customer satisfaction.

## The impact of capacity management

Effective capacity management significantly reduces operational costs and enhances customer satisfaction, enabling businesses to balance costs and customer demand, thereby boosting loyalty and competitiveness (Slack, Chambers, and Johnston 2010). Additionally, it plays a crucial role in building resilience to market disruptions (Kochan and Nowicki 2018). Research by Aghezzaf (2005) indicates that organisations proactively managing their capacity are better equipped to handle unexpected challenges. Furthermore, Sazvar et al. (2021) emphasise that integrating sustainability into capacity planning enhances an organisation's ability to respond to uncertainties, particularly in critical supply chains like vaccines, underscoring the strategic importance of capacity management.

## Conclusion

In conclusion, capacity management is a critical business function that involves the strategic allocation of resources to meet current and future demand. It encompasses various processes, including demand forecasting, capacity evaluation, adjustment, and performance monitoring, which collectively contribute to a business's operational efficiency and effectiveness (Slack, Chambers, and Johnston 2010). By employing scientific principles and data-driven techniques, organisations can enhance their decision-making processes and optimise resource utilisation, ensuring long-term sustainability and growth (Varian 2014).

The integration of capacity management with supply chain strategies amplifies its importance, as businesses

that align their capacity planning with supply chain logistics can achieve superior performance and customer satisfaction (Blanchard 2021). Additionally, the adoption of outsourcing, collaboration, and subcontracting strategies further strengthens capacity management efforts by leveraging external expertise, sharing resources, and fostering flexibility (Dainty, Briscoe, and Millett 2001; Lee, Jeong, and Moon 2002; Tan, Lyman, and Wisner 2002).

In a rapidly changing business environment, effective capacity management not only reduces operational costs but also enhances resilience against market disruptions, enabling organisations to respond swiftly to fluctuations in demand and maintain competitive advantage (Aghezzaf 2005; Kochan and Nowicki 2018). As such, the significance of robust capacity management strategies cannot be overstated, as they play a vital role in achieving organisational goals and ensuring customer loyalty.

## 2.3. Inventory management⁴

Inventory management involves a set of policies and controls designed to monitor the levels of inventory – including raw materials, components, and finished products – across various locations within the supply chain, such as warehouses and production systems (Nahmias 2009). The goal is to maintain the right quantity of products to meet demand while minimising holding costs and preventing stockouts (Cachon and Terwiesch 2023). From a practical standpoint, inventory management should address three main questions:

(1) Where to stock the product?

(2) When to place the order to replenish the stock?

(3) How much to order to replenish the stock?

The inventory management research originated with the Economic Order Quantity (EOQ) model (Harris 1990), which optimised inventory levels for single-item, single-echelon systems under the assumption of constant demand. This model established the concept of economies of scale in inventory management. By the 1950s, advancements were made for military applications, focussing on inventory systems with stochastic demand and extending to multi-item and multi-echelon systems.

### Single-echelon single-item inventory systems

The early EOQ model, assuming constant demand, was refined by Wilson (1934), to minimise total costs under linear inventory holding and ordering costs. Extensions included allowances for non-linear costs, imperfect items, shortages costs, etc. (Rosenberg 1979; Salameh
<figure><img src="image_20.png" /></figure>

and Jaber 2000). In the 1950s, time-varying deterministic demand models emerged, considering finite time horizons and applying dynamic programming, the most well-known one being Wagner and Whitin (1958). A considerable literature was then developed to propose near-optimal solutions for this problem, often referred to as the lot sizing problem (Silver and Meal 1973, particularly). An overview of this literature is provided by Glock, Grosse, and Ries (2014).

The literature was also extended in the 1950s to consider inventory systems subject to uncertainty. Inventory control policies were then developed to deal with stochastic demand where both backordering and lost sales cases are considered. The optimality of periodic review order-up-to policies was proved in the former case (Arrow, Karlin, and Scarf 1958). However, recognising the limitations of backordering in retail settings, later studies shifted focus to lost-sales models, which better reflect customer behaviour during stockouts (Buchanan and Love 1985; Zipkin 2008). These models are analysed to optimise reorder points and order-up-to levels under different assumptions of lead time and demand distributions (Johansen and Thorstenson 1993) and under service-level-driven systems (Federgruen and Zipkin 1984).

Regarding demand modelling and forecasting in stochastic inventory systems, parametric and non-parametric approaches are used. In the former, a demand distribution is assumed, and a forecasting method is used to estimate the moments of the distribution. Distributions such as Normal, Poisson, Gamma and Negative Binomial have dominated the inventory literature for fast and slow moving items with a strong empirical evidence (Syntetos, Babai, and Altay 2012; Syntetos and Boylan 2006; Turrini and Meissner 2019). In this case there is a plethora of forecasting methods that have been developed ranging from simple time series techniques to machine learning (ML) methods. In the non-parametric approach, no assumption is made for the demand distribution, which can be empirically determined using bootstrapping methods (Hasni et al. 2019a, 2019b). More information on forecasting approaches is provided in Section 4.6. Prak, Teunter, and Syntetos (2017) address the issue of correlated forecast errors when calculating inventory parameters. Goltsos et al. (2022) classify the various levels of interaction and integration between the forecasting and inventory control literature.

## Multi-item systems

Most warehouses store a variety of heterogeneous SKUs. Jointly controlling these leads to new dynamics and decisions. Firstly, classification serves to manage all SKUs efficiently. Secondly, customers face the entire assortment, giving rise to new definitions of service and demand

substitution between SKUs. Finally, there may be cost benefits of jointly replenishing different SKUs.

In order to efficiently divide management effort over thousands of SKUs, these are typically divided into groups (Silver, Pyke, and Thomas 2016). The most commonly used division is into three groups – A, B, and C – based on demand value (volume multiplied by price). This so-called ABC classification can be extended to an ABC-XYZ classification by adding a measure of demand regularity. XYZ classifications are often based on the coefficient of variation, whereas this does not necessarily align with forecast accuracy. Occasionally, classifications are also based on other measures, such as supply risk, lead time, or criticality (e.g. Flores and Whybark 1987).

Service targets are typically determined at a higher level than that of the individual SKU. Assortment-level service requirements are usually translated to the SKU level by setting the same target service level for all SKUs in a group. Teunter, Babai, and Syntetos (2010); Teunter, Syntetos, and Babai (2017) show that this is suboptimal and suggest a cost-based approach to determine SKU-level fill rate targets. van Donselaar, Broekmeulen, and de Kok (2021) determine reorder levels for a given assortment fill rate. The so-called order fill rate (Song 1998) acknowledges that customer orders may consist of multiple SKUs which must all be on stock to fulfil the order.

Particularly in retail settings (Section 5.8), a customer may buy a different product than originally intended. The product may not be in the assortment (assortment-based substitution, e.g. Smith and Agrawal 2000) or out of stock (stockout-based substitution, e.g. Netes sine and Rudi 2003). It is typically assumed that a customer switches to their second-choice option with a certain probability and otherwise leaves, but more complex structures with multiple alternatives also exist. Joint optimisation of inventories under substitution is notoriously difficult, and for a comprehensive review we refer to Nagpal, Chanda, and Seth (2021).

In practice there may be (usually fixed order) cost advantages when SKUs are replenished together, giving rise to the joint replenishment problem (JRP). Even for deterministic demand, the JRP is *NP*-hard. Silver (1976) created an efficient heuristic that chooses the replenishment intervals of all other SKUs as multiples of some base interval. For the considerably different stochastic JRP, so-called can-order policies have been proposed (e.g. Federgruen, Groenevelt, and Tijms 1984). Below a certain inventory position threshold an SKU must be ordered, and below another, higher threshold, an SKU may be added to an existing order. Creemers and Boute (2022) show that can-order policies perform well.
<figure><img src="image_21.png" /></figure>

## Multi-echelon systems

In the 1960s, research on multi-echelon inventory systems started by dealing mainly with repairable spare parts inventory systems in military settings. A pivotal development was the Multi-Echelon Technique for Recoverable Item Control (METRIC) model by Sherbrooke (1968) that considers a single repair depot replenishing multiple stock points. The METRIC model assumes unlimited repair shop capacity, Poisson-distributed demand that can be backordered and a base stock inventory control policy. Extensions of METRIC have relaxed these assumptions to improve model realism, by considering limited repair capacity (Díaz and Fu 1997), compound Poisson demand distributions (Costantino et al. 2017; Graves 1985), lateral transshipments (Lee 1987) and lost sales cases (Kouki, Arts, and Babai 2024). Service restrictions and their impact on multi-echelon inventory systems under the METRIC framework have been examined by Topan, Bayındır, and Tan (2017) and Dreyfuss and Giat (2018). These studies investigate how limiting the availability of certain services affects overall inventory management and service levels. A discussion of maintenance aspects in OM is given in Section 2.20.

METRIC-type models as described above deal with distribution (or divergent) systems, but multi-tier inventory systems may exhibit various structures. In assembly (or convergent) systems – common in manufacturing settings (Section 5.6) – multiple upstream stock locations converge towards fewer downstream stock locations. Raw materials or components typically have lower value than end products and may therefore be cheaper to keep in stock (upstream). After Schmidt and Nahmias (1985) examined the optimal policy in a finite-horizon, two-location assembly system under stochastic demand, Rosling (1989) studied a more general and infinite-horizon system, and showed equivalence with a serial system (Clark and Scarf 1960), for which exact (Federgruen and Zipkin 1984) and approximate (van Houtum and Zijm 1991) solution procedures exist. Extensions exist, e.g. towards supplier uncertainty (DeCroix 2013).

Most work discussed so far uses a stochastic service approach: each stock location keeps a safety stock so that a service level target is achieved. Stock-outs do occur and delay downstream replenishments, which complicates the analysis. Simpson (1958) described the guaranteed service approach: demand is assumed to be bounded, and every location keeps a safety stock so that a given service time to the downstream location is always guaranteed. Although bounded demand is a strong assumption, Simpson (1958) gives a possible interpretation for the bound being the maximum accepted demand. Graves and Willems (2003) contrast and illustrate the stochastic

and guaranteed service approach and highlight the latter as a simple approach to tackle complex supply chains. Information asymmetries in multi-tier supply chains lead to increased upstream order variability, a phenomenon known as the bullwhip effect (see Section 3.8).

To the reader searching for detailed information on inventory models and their applications, we recommend Zipkin (2000), Axsäter (2015), and Silver, Pyke, and Thomas (2016) as three excellent examples of comprehensive inventory management textbooks.

## 2.4. Warehousing⁵

The fundamental purpose of warehousing, defined as the intermediate storage of goods in a dedicated facility, is to decouple the time and place of production or supply from the time and place of consumption between successive supply chain stages (Bartholdi and Hackman 2019).

By decoupling the *time*, stockpiling goods can facilitate the matching of supply and demand (Section 2.3). Demand peaks served from stock can avoid costly excess capacities needed for just-in-time production that remain idle during the off-peak season. Warehouses can also stockpile excess supply (e.g. during harvest) to serve a stable demand. In addition to mastering predictable supply and demand peaks caused by repetitive seasonalties, inventories also protect against unpredictable events (e.g. excess wind energy and social commerce sales hype). This effect gains significance if the warehouse is also used for value-adding services (that is, late customisation of products) to reduce the impact of uncertain demand through risk pooling (Section 4.10). Furthermore, decoupling the timing of production and consumption can also protect against price fluctuations of purchased goods (Section 2.19). For instance, warehouses can hold back products from the market to await price increases and store an enlarged procurement lot to realise quantity discounts.

By decoupling the *place* of production and consumption, warehousing adds flexibility to transportation processes, as a high frequency of delivery to customers (and the corresponding delivery sizes) can be accommodated more easily by a close-by warehouse, rather than by remote manufacturers (Section 3.10). On the service side, storing products in warehouses close to customers reduces delivery times and prevents split deliveries from different production sites. Instead of servicing less-than-truckload customer demands with half-empty vehicles (or at low frequency) directly from a faraway production site, a warehouse can be supplied in full truckloads, bundling the demand of multiple close-by customers. The handling of returns in a nearby warehouse
<figure><img src="image_22.png" /></figure>

promises further reductions in transportation costs. Ack-
erman (2012) provides an in-depth discussion on the
purposes of warehousing.

The basic process steps of warehousing are receiv-
ing, storage, order picking, shipping, and return han-
dling (Gu, Goetschalckx, and McGinnis 2007). Although
virtually every warehouse performs these basic pro-
cess steps, their specific execution varies significantly
between warehousing systems. Each system consists of
hardware (that is, storage devices (racks), material han-
dling systems (Section 2.5), and picking tools (pick-
by-voice devices)), and processes defining the work-
flow along the hardware (Boysen, De Koster, and Wei-
dinger 2019). Warehousing systems can be categorised
into picker-to-parts and parts-to-picker systems, based
on how Stock Keeping Units (SKUs) and pickers come
together (Boysen and De Koster 2025). In picker-to-parts
systems, pickers move to the storage locations of the
demanded SKUs. Conversely, in parts-to-picker systems,
SKUs are brought to pick stations with stationary pickers
using a material handling system. Picker-to-parts sys-
tems, which rely primarily on a human workforce, offer
high flexibility but incur significant wage costs. On the
other hand, parts-to-picker systems use fixed machin-
ery, which, while less flexible, involves a higher invest-
ment but reduces operational expenses and can increase
order throughput. In recent years, significant advance-
ments in robotics have impacted the warehousing sector
(Azadeh, De Koster, and Roy 2019). Instead of relying
on fixed, inflexible hardware like conveyors, lifts, and
cranes, the use of more flexible Autonomous Mobile
Robots (AMRs) has introduced a third category. These
robots can operate in systems that are much more flex-
ible than traditional parts-to-picker and picker-to-parts
systems. Hence, we define a third class of warehousing
systems based on AMR usage. We discuss each of these
three classes of warehousing systems in the following
sections.

Figure 1 gives an impression of a warehouse system consisting of a picker-to-parts and two different parts-to-picker systems: a miniload crane-based Automated Storage and Retrieval System and a system with shelf-moving robots.

Picker-to-parts systems

*System setup:* In picker-to-parts systems, pickers move toward the SKUs’ storage locations to retrieve the requested number of products defined on their (nowadays electronic) pick lists. The pickers are equipped with either a manual cart or drive on a motorised cart. The SKUs are stored in racks, typically arranged to the left and right of parallel picking aisles connected by cross aisles (according to Gue and Meller 2009, other, flying-V

or fishbone-shaped rack orientations may be beneficial
in unit load retrieval operations, i.e. without order pick-
ing). Picking tours start and end at a depot where the
picked goods are collected and prepared for shipping.
Often, there is just a single central depot, but some ware-
houses also apply decentralised systems with multiple
access points to a conveyor system that connects the
depot (Schiffer et al. 2022).

Especially in e-commerce, where customers order just a few items per order (Boysen, De Koster, and Weidinger 2019), picking in an order-by-order manner produces excessive unproductive travel back and forth to the depot. Therefore, many warehouses apply batching and zoning to streamline their order fulfilment processes. To increase pick density per tour, batching groups multiple customer orders into extended pick lists, and zoning partitions the warehouse into smaller zones, each with a dedicated workforce. There is parallel and progressive (or sequential) zoning (De Koster, Le-Duc, and Roodbergen 2007). The former promises a significant speedup because all zones start order picking on the same order set in parallel. In progressive zoning, a dedicated order bin is sent from zone to zone (typically by a conveyor), which prolongs completion times but avoids extra order consolidation. The latter is the price for batching and parallel zoning: an extra consolidation stage, often based on loop conveyors (Boysen et al. 2019), must sort the collected products by order.

*Decision tasks:* During layout design (Section 2.12), decisions on the structure of the warehouse must be made. This includes the choice of the number of picking and cross aisles and the positioning of the depot. If zoning is applied, the number of zones and their locations must be fixed. Boysen and De Koster (2025) provide a recent literature review of these decisions. On a subsequent level, storage assignment decides the specific storage positions where each SKU is stored. Next to the classical storage policies for unit-load storage (i.e. random, closest-open-location, dedicated, full-turnover, class-based, and family grouping storage, see De Koster, Le-Duc, and Roodbergen 2007), there is also scattered storage, which has established foremost in e-commerce. Scattered storage breaks up the homogeneous pallets and distributes the individual pieces per SKU over the storage racks. For hardly predictable pick lists, scattered storage increases the chance that – whatever it is that is ordered jointly – somewhere it is stored close together and can be picked without excessive picker travel (Boysen, De Koster, and Weidinger 2019), albeit at the expense of extra replenishment effort. On an operational level, if batching is applied, the order pool must be partitioned into pick lists, each assembled on a separate picker tour (see Boysen and De Koster 2025). Finally, picker routing
<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /><figcaption>**Figure 1.** Warehouse with a picker-to-parts and two parts-to-picker systems.</figcaption></figure>

decides on the picker's tour through the warehouse for a given pick list (Masae, Glock, and Grosse 2020, provide an in-depth survey on the manifold picker routing literature).

Some papers discuss integrated modelling and solution of decision problems in picker-to-parts systems (for a survey, see Van Gils et al. 2018). Next to integrated optimisation, the recent literature has started to emphasise the importance of human factors in system design; factors that consider human limitations and capabilities (Grosse, Glock, and Neumann 2017). These factors can be included in the planning process and focus on the well-being of human operators. Grosse et al. (2015) and De Lombaert et al. (2023) review the literature and sketch opportunities. In addition, incentive systems, goal setting, public performance feedback, gamification, and picker personality traits appear to impact performance and, in many cases, also well-being (e.g. De Vries, De Koster, and Stam 2016).

## Parts-to-picker systems

**System setup:** Parts-to-picker systems eliminate unproductive picker travel by delivering SKUs to workstations with stationary pickers: humans or automated devices (e.g. a robot arm with a vacuum gripper). The main hardware elements are an Automated Storage and Retrieval System (ASRS) where the goods are stored (often as unit

loads) and retrieved, the picking workstations for product unit picking, and a conveying system connecting them. The traditional ASRS is a crane-operated (high-bay) rack filled with pallets or bins (Roodbergen and Vis 2009), but there are also (horizontal and vertical) carousels, vertical lift modules, puzzle-based storage systems, deep-lane ASRSs, and shuttle-based storage systems (Azadeh, De Koster, and Roy 2019). Workstations range from simple racks for order bins to ergonomic stations, adaptable in height with automated bin exchange and weighing mechanism to reduce picking errors (Boysen et al. 2019).

**Decision tasks:** During layout design, a suitable ASRS type must be identified and dimensioned, along with enough workstations for the targeted workload (Boysen and De Koster 2025). When deciding on the storage positions of the SKUs within the ASRS, basically the same policies are applied as already discussed for picker-to-parts systems (see above and Roodbergen and Vis 2009). Finally, order processing must coordinate the storage and retrieval of bins from the ASRS with the picking process at the picking workstations (Boysen, Schwerdfeger, and Stephan 2023).

## Robotised systems

Driven by technological progress, like in the fields of sensors, real-time control, autonomous driving, and
<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /><figcaption>**Figure 2.** Overview of decisions at different hierarchical levels in (a) picker-to-parts and (b) parts-to-picker and robotised systems.</figcaption></figure>

robotisation, AMRs have become more and more successful in recent years (Fragapane et al. 2021). Other than their famous predecessors, Automated Guided Vehicles (AGVs), AMRs are not bound to predefined paths; computer vision allows flexible adaptation to a changing environment. In picker-to-parts systems, AMRs that also pick, such as the Toru robot of Magazino, can substitute human pickers, at least for a restricted product assortment (e.g. shoeboxes; Boysen and De Koster 2025). For non-standard products, transport AMRs accompany human pickers through the warehouse and relieve them of the burden of transporting the picked products back to the depot (Azadeh et al. 2025; Löffler, Boysen, and Schneider 2022). The most famous AMRs of parts-to-picker systems are (probably) shelf-moving (KIVA) robots. They drive under a rack (also denoted as inventory pod), lift it, and deliver the pod to a stationary picker (Weidinger, Boysen, and Briskorn 2018). Other AMR representatives are storage grid-supported (Autostore) robots (Azadeh, De Koster, and Roy 2019), rack-climbing (Exotec) robots (Chen, De Koster, and Gong 2022), and multi-tote (Quicktron, Haipick) AMRs (Qin et al. 2024) delivering bins autonomously from storage locations. Finally, there are also AMRs for order consolidation (Zou et al. 2021). Equipped with a tiltable tray or small conveyor tablet, they can distribute goods between sorting destinations. The different decisions in picker-to-parts and parts-to-picker (including robotised) systems are summarised in Figure 2.

## Conclusion

To decouple the time and place of production from the time and place of consumption, warehouses have always been an essential part of supply chains. However, e-commerce and omnichannel retailing (Section 5.8) have transformed them from a marginal element to a mission-critical supply chain stage. Hence, it seems reasonable to project that warehousing will remain a vivid field of research in the foreseeable future.

## 2.5. Material handling⁶

Material handling represents a fundamental part of operations management in any organisation or supply chain, comprising the processing of physical products in the form of parts, components, or final products within facilities such as factories, distribution centres, warehouses, cross docks, and container ports. It can be described as the activities whereby material is physically relocated from one position to another within the same facility. The objective is providing goods at the right time, in the right quantity, and to the right location where they can be retrieved for processing. This intralogistic transportation process may include additional activities such as searching, inspection, packaging, and (un)loading and can be found in several sectors such as manufacturing (Kusiak 2018, also Section 5.6), warehousing (Azadeh, De Koster, and Roy 2019, also Section 2.4), construction (Prasad, Zavadskas, and Chakraborty 2015, also Section 5.2), container terminal operations (Carlo, Vis, and Roodbergen 2014), and healthcare (Bhosekar et al. 2023, also Section 5.4).

Manual material handling operations require significant physical and cognitive effort (Soufi, David, and Yahouni 2021) but can be supported by the implementation of appropriate material handling equipment (MHE). According to Tompkins et al. (2010), MHE can be classified into four types: (i) containers and unitising equipment, such as pallets, totes, and cylinders; (ii) material transport equipment, such as conveyors and industrial vehicles; (iii) storage and retrieval equipment, such as racks or carousels; (iv) automatic data collection and communication equipment such as tags or vision technology. MHE ranges from manual to fully automated and highly autonomous solutions such as autonomous mobile robots (AMR), also called autonomous intelligent vehicles (AIV) (Fragapane et al. 2021; Hellmann et al. 2019), and autonomous vehicle storage and retrieval systems (AVS/RS) (Marchet et al. 2013). Material handling typically incurs a high investment cost for automated solutions or a high labour cost for manual solutions (Tompkins et al. 2010) and effective and efficient material handling is instrumental for the operational performance of a system.

Operations managers are primarily concerned with the design and operation of material handling systems. Their design investigates both ideal facility (Gue and Kim 2007) and process layout (Schmid and Limère 2019) to facilitate smooth and efficient material flow while minimising handling requirements. This encompasses the selection of appropriate material handling equipment (MHE) under economic (Moretti et al. 2021), human-centric (ergonomics, safety, well-being) (Finnsgård et al.
<figure><img src="image_27.png" /></figure>

2011; Hanson et al. 2018), environmental (Erkayaoğlu and Demirel 2016), or service-level (Bhosekar et al. 2021) considerations. The operation of material handling systems, on the other hand, applies principles from control theory and scheduling approaches to ensure effectiveness.

## Designing material handling systems: equipment selection

For MHE selection, frequently, the products to be handled and its packaging reduce the amount of practically feasible material handling equipment. Therefore, best practice examples are often used in the industry whereas the analytical hierarchy process is the predominant academic method to determine MHE (Chakraborty and Banik 2006; Chan, Ip, and Lau 2001). Life-cycle analysis approaches can be found to assess the environmental aspects of different MHE alternatives (Erkayaoğlu and Demirel 2016). It should be noted that structured MHE selection processes are typically adjusted for the specific environment in which the equipment will be used, e.g. in warehousing (Azadeh, De Koster, and Roy 2019), hospitals (Bhosekar et al. 2023), or construction (Prasad, Zavadskas, and Chakraborty 2015). In most environments, one may find an array of choices spanning from labour-intensive to highly automated options as shown, e.g. by Adenipekun, Limère, and Schmid (2022) who optimise the vehicle type selection in an assembly system from an economic perspective. The final choice may be taken when considering facility layout or process design.

## Designing material handling systems: facility layout and process design

Facility design (see Section 2.12 for more detail) concerns the placement of spaces and equipments in a facility. Therefore, it is interlinked with the selection of material handling equipment. In process-oriented facilities, where flow units follow different routes through the facility, efficient facility layout reduces the demand for material handling trips and the corresponding investments in MHE. Simplistic design improvement approaches such as CRAFT have been replaced by optimisation-based approaches that consider changes in demand over time (Montreuil and Venkatadri 1991) or even allow for facility redesign McKendall and Hakobyan (2010). In contrast, flow lines and manufacturing cells require less material handling (King 1980). Therefore, their layout does not necessarily account for material handling considerations. Flow lines may also be designed for increased flexibility where products do not follow rigid routes but instead are transported by AGVs to resources with slack capacities using autonomous vehicles (Hottenrott and Grunow 2019).

The design of operational processes and alternatives impacts material handling and frequently minimises material handling efforts. One such example can be found at high variety mixed-model assembly lines (see Section 2.13) where part supply often requires significant material handling efforts. The assembly line feeding problem (ALFP), as initially proposed by Bozer and McGinnis (1992), investigates increasingly more feeding process alternatives and aspects of the feeding process. Initially, these considerations focussed strongly on the available storage space and fewer process alternatives (Caputo and Pelagagge 2008; Limère et al. 2012), more recent work considers additional aspects such as facility layout and aims to minimise material handling efforts (Schmid, Montreuil, and Limère 2022; Schmid, Montreuil, and Limère 2024). Another example for process alternatives can be found in order-picking operations in which zone picking may be applied in picker-to-parts systems (see Section 2.4). If no zoning is applied, pickers may have to walk longer decreasing their picking efficiency. In contrast, zoning avoids excessive walking but often requires some material handling equipment to transport items from one zone to the next or for final consolidation (i.e. progressive versus parallel zoning; De Koster, Le-Duc, and Roodbergen 2007).

In summary, the combination of a facility's layout, the process choice, and MHE selection determines the efficiency of the material handling system design (see also Dallari, Marchet, and Melacini 2009).

## Operation of material handling systems

After having defined material handling systems by selecting, quantifying, and positioning the equipment those systems go into operation. We refer the reader also to Sections 2.11 and 2.15 where production control and scheduling are discussed more generally. Specifically for material handling, as stated above, an important objective is to provide the right good at the right time and place. To this end, one may either define certain control rules according to which systems operate or one may use real-time information and schedule activities to optimise some objective such as total or maximum tardiness. Control rules could be as simple as First-Come-First-Serve or more sophisticated. In the FCFS approach, the job that is finished first will be transported to its succeeding station, irrespective of that station's availability. More advanced control rules can be found in Klaas et al. (2016), using a simulation to derive decision rules for the effective operation of an automated storage and retrieval system. In addition, their proposed approach adapts dynamically when the system's status (utilisation or demand patterns) are evolving away from the simulation's parameters. In other environments such
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as assembly, manufacturing, or hospitals, material handling is frequently conducted along so-called milk runs (also called mizusumashi), which define a route that is followed periodically for replenishment. Emde and Boysen (2012) provide an approach to define milk runs and their periodicity.

Scheduling approaches provide an alternative to control approaches. In some systems, demand may be known with certainty for multiple days in advance, allowing to schedule the part replenishment such that no material shortage occurs as described by Boysen and Bock (2011). Milk runs may also be combined with a scheduling approach that determines optimised but variable deliveries frequencies, which may lead to reduced inventories at the point of consumption (Emde and Gendreau 2017). Furthermore, scheduling may allow a more flexible use of material handling equipment, possibly reducing the demand for MHE.

The use of AMR technology impacts scheduling and control of material handling systems significantly. These vehicles no longer need to follow predetermined paths or schedules but operate autonomously. Fragapane et al. (2021) give a detailed overview of how specific technological developments impact traditional planning and control decision areas.

Despite large amounts of research focussing on technical improvements and automation efforts, humans remain relevant to material handling in many enterprises (Glock et al. 2021). Evidently, human-centric aspects, especially worker safety, well-being, and ergonomics, are of high relevance for operations managers in such enterprises. This relevance is even more pronounced when the workforce is ageing (Calzavara et al. 2020). According to Denis et al. (2020) training for material handling workers frequently does not deliver to its goals of reduced disease and accidents. They identify a multitude of considerations for improving such training. Importantly, they state that training should address a wider range of situations and prepare operators to identify the appropriate action in their situation but also demands for additional practice during the training. Increasingly, a combination of humans and robots is operating material handling systems. Determining an effective combination, e.g. by allocating tasks to either humans or robots (Boudella, Sahin, and Dallery 2018), seems relevant.

## Conclusion

For a general overview on material handling activities and equipment, we refer to Tompkins et al. (2010), Stephens (2019), and Kay (2012). From a process point of view, different assembly line feeding policies and the related decision-making approaches are presented by Schmid and Limère (2019). Regarding planning and

control of autonomous MHE, the review article of Fragapane et al. (2021) gives a thorough overview and a research agenda, while for manual material handling the use of assistive devices is treated in detail in Glock et al. (2021). Finally, we believe material handling systems should be flexible and robust to variable product mixes and volumes. Klaas et al. (2016) provide an excellent example for the adaptation of operating and control principles of an AS/RS when demand changes and may serve as an example for future work.

## 2.6. Buffer allocation⁷

Koenigsberg (1959) highlighted three challenges in the design of production lines: selecting the set of machines in the line, determining the locations of buffers, and deciding on the sizes of buffers. The third challenge is the buffer allocation problem (BAP). Efficient production line design is important in high-volume manufacturing industries.

This section explores the concepts, mathematical modelling, and recent advancements in solving the BAP. For a more comprehensive description of the topic, see the latest review articles, such as Demir, Tunali, and Eliiyi (2014), Weiss, Schwarz, and Stolletz (2019), and Koyuncuoğlu (2024).

## Concepts

A production line is a set of *K* machines connected in series and separated by *K*−1 buffers. Material flows from upstream inventory to the first machine for an operation, then to the first buffer where it waits, to the second machine, and so on, until it passes through the final machine and then goes to downstream inventory. There are two quantities associated with a buffer: its size and the time-varying inventory level (or buffer level or work-in-process or WIP) (Figure 3).

Machines interfere with each other when material flow is disrupted by machine failures. Failures can cause neighbouring machines to be idle. If the buffer before a machine is empty, the machine will be starved and not able to work; if the buffer after it is full, the machine will be blocked and also not able to work.

The most important performance measures are the production rate or throughput, the number of items produced in a given time period divided by the length of the time period; and the average amount of inventory in each buffer. Increasing buffer sizes increases production rate. The cost of increasing buffer sizes includes the cost of the buffers and the space they occupy, the cost of holding inventory, and the increased time the parts stay in the line. The BAP seeks the buffer sizes that maximise the net benefit.
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<figure><img src="image_30.png" /><figcaption>Figure 3. A Production Line Example.</figcaption></figure>

The current BAP research literature optimises analytical models of lines. It consists of two streams: one in which machines are reliable with random processing times, and one in which they are unreliable. In the first stream, each machine is modelled as an M/G/c/K queue. In the second, machines are unreliable and can fail and be repaired at random times. These models are characterised by their machines' behaviour:

* The deterministic model: Machines' operation times are equal, deterministic, and constant; material is discrete. In most of the literature, machine failures and repairs follow geometric distributions.

* The exponential model: Each machine's operation, up and down times are continuous and follow exponential distributions. Material is discrete.

* The continuous model: Each machine's operation, up and down times are continuous. Material is treated as a continuous fluid.

Machines can have single or multiple failure modes (e.g. Levantesi, Matta, and Tolio 1999, 2003; Tolio, Matta, and Gershwin 2002).

The machine models are simple representations of reality and the evaluation of models of lines is most often approximate. The challenge is to create models of machines and lines that are close enough to reality to be useful and to develop algorithms to predict and optimise the performance of the lines. Much of the analysis has been extended to assembly/disassembly systems, as well as constant WIP (or CONWIP) loop systems.

## Mathematical modelling

BAP is an optimisation problem where the goal is to determine the optimal buffer sizes $N_i$ for a given set of machines, subject to constraints on system parameters. Over the years, researchers have explored a variety of objective functions and constraints.

**Problem Formulation.** One classical approach minimises the total buffer size while satisfying a production rate constraint:

$$ \begin{array}{ll} \min_{\mathbf{N}} & \displaystyle\sum_{i=1}^{K-1} N_i \\ \text{Primal subject to} & \mathbb{E}[P(\mathbf{N})] \geq P^* \\ & N_i \geq 0, \end{array} \quad (1) $$

where $N_i$ represents the size of the $i$th buffer, $\mathbb{E}[P(\mathbf{N})]$ represents the average production rate as a function of buffer sizes $\mathbf{N} = [N_1, \dots, N_{K-1}]'$, and $P^*$ is the target production rate. This is the primal problem. It is difficult to solve directly because it has a $(K-1)$-dimensional nonlinear constraint.

To solve (1), Gershwin and Schor (2000) propose the following dual problem. It maximises the expected production rate for a given total buffer size $N_{\text{Total}}$:

$$ \begin{array}{ll} \displaystyle\max_{\mathbf{N}} & \mathbb{E}[P(\mathbf{N})] \\ \text{Dual subject to} & \displaystyle\sum_{i=1}^{K-1} N_i = N_{\text{Total}} \\ & N_i \geq 0. \end{array} \quad (2) $$

They solve the primal by finding the value of $N_{\text{Total}}$ such that $\mathbb{E}[P(\mathbf{N})]$ in (2) is equal to $P^*$ in (1). This is easier than solving (1) directly because (2) has only linear constraints. The value of $N_{\text{Total}}$ is found by a one-dimensional search.

As the literature has expanded, the focus has shifted to more general forms, which encompass various other performance metrics beyond buffer size and throughput. These problems all have special cases of the following objective function (Weiss, Schwarz, and Stolletz 2019):

$$ \max_{\mathbf{N}} a \mathbb{E}[P(\mathbf{N})] - \sum_{i=1}^{K-1} b_i N_i - \sum_{i=1}^{K-1} c_i \bar{n}_i - d \mathbb{E}[LT(\mathbf{N})] - e \mathbb{E}[WT(\mathbf{N})], \quad (3) $$

where $\bar{n}_i$ is the average inventory level of the $i$th buffer, and $\mathbb{E}[LT(\mathbf{N})]$ and $\mathbb{E}[WT(\mathbf{N})]$ represent the average lead time and average waiting time of customer orders. For instance, Yuzukirmizi and Smith (2008) include the lead time in their objective function.

**Performance Evaluation.** For these systems, the high dimensionality and the nonlinear interactions among machines and buffers make exact solutions impossible for long lines. The usual approach is to use small systems as building blocks and develop approximate numerical methods to evaluate the performance of long lines. For reliable machines, the basic models are M/M/1/K and M/G/1/K queues (e.g. Smith and Cruz 2005); for unreliable machines, the basic models are the two-machine one-buffer line models based on Markov chains
<figure><img src="image_31.png" /></figure>

(e.g. Gershwin 1994; Tan and Gershwin 2011; Tolio and Ratti 2018). These small systems have exact or approximate closed-form solutions. Exact numerical solutions for a variety of small system structures, including production lines, can be calculated by iterated matrix multiplication using the method of Tan (2002) to generate the matrices.

For long lines, the generalised expansion method (Cruz, Duarte, and van Woensel 2008; Kerbachea and Smith 1987) is proposed for systems with reliable machines, while decomposition and aggregation are prevailing methods to deal with unreliable machines. The decomposition method (Dallery, David, and Xie 1988; Gershwin 1987), and its extensions (e.g. Levantesi, Matta, and Tolio 2003; Tolio and Matta 1998) enabled the evaluation of different models of long lines with unreliable machines. It approximates a K-machine $K-1$-buffer system with $K-1$ two-machine one-buffer systems. Decomposition aims to find parameters for these two-machine systems so that, for each buffer, the material flow behaviour in the two-machine line closely matches that in the original line. The goal is for an observer of the flow of parts into and out of a buffer in a real production line can be convinced that he is observing the flow of parts in a fictitious two-machine line. The aggregation method (Jacobs and Meerkov 1995; Li and Meerkov 2007; Lim, Meerkov, and Top 1990) combines all the two-machine one-buffer subsystems into a single aggregated machine. It consists of a forward aggregation which merges the first subline from the start towards the end and a backward aggregation which merges the last subline into a single machine from the end towards the beginning. This is repeated until the throughput converges. Simulation is another tool for the performance evaluation of large-scale production systems. It is flexible and can be accurate but it is time-consuming (Helber et al. 2011).

**Optimisation techniques.** Gradient methods (Helber 2001; Shi and Gershwin 2009) use decomposition to calculate gradients via forward difference, followed by a line search to locate the next optimal point. Although buffer sizes $N_i$s are integers, treating them as continuous variables allows gradient calculation. The optimal continuous solution is then rounded to integers (Han and Park 2002). Meta-heuristic methods treat buffer sizes as integers. Examples include genetic algorithms (Dolgui et al. 2002), tabu search (Demir, Tunali, and Løkketangen 2011), simulated annealing (Spinellis, Papadopoulos, and Smith 2000), and degraded ceiling (Nahas, Ait-Kadi, and Nourelfath 2006). Hybrid algorithms that combine multiple meta-heuristics include Shi and Men (2003), Dolgui, Eremeev, and Sigaev (2007) and Kose and Kilincci (2015). Mathematical programming techniques

include the dynamic programming which breaks the problem into smaller subproblems (Diamantidis and Papadopoulos 2004). Colledani and Tolio (2005) linearise decomposition equations, converting the problem into a mixed-integer linear programming problem.

## Recent advancements

Production line design involves considerations beyond buffer allocation. Traina and Gershwin (2013) address the problem of simultaneously selecting machines and determining buffer sizes for profit maximisation. Kiesmuller and Sachs (2020) optimise buffer capacity and spare parts inventory.

Many factories have very long production lines, particularly for automobile manufacturing. Shi and Gershwin (2016) describe a method that divides a long line into several short lines, optimises them separately, and combines their buffer distributions. Xi et al. (2019) decompose long series-parallel unbalanced production lines into decoupled subsystems.

Machine learning can be instrumental in developing more complex machine models. Helber, Kellenbrink, and Südbeck (2024) integrate an artificial neural network to replace the traditional Markov chain model in the context of two-machine lines, where the machines have significantly more than the typical two states.

## Concluding remarks

In modern manufacturing systems, the decreasing product lifetimes necessitate frequent factory reconfigurations or replacements, limiting the time available to learn and improve these systems. As a result, intuition derived from research and from careful, systematic observation of real factories becomes increasingly vital (Gershwin 2017). Academic research provides theoretical insights and models and offers valuable tools and methodologies that can be directly applied to improve industrial processes. Works such as Lim, Meerkov, and Top (1990), Burman, Gershwin, and Suyematsu (1998), Liberopoulos and Tsarouhas (2002), Patchong, Lemoine, and Kern (2003), Colledani et al. (2010), Matta, Pezzoni, and Semeraro (2012), and Li (2013) demonstrate how theoretical advancements in buffer allocation can be effectively applied to real-world production systems. For instance, these studies address practical challenges in industries such as electronics, food processing, automotive manufacturing, and continuous improvement in production lines, showcasing how operations research and engineering methods optimise throughput, reduce costs, and enhance system reliability.
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## 2.7. Process design⁸

Process design is broadly speaking developing and choosing tasks, either to be executed by equipment, machines or people (alone or combined) and arrange them to produce a product or service for the organisations customers. More specifically, according to Ellram, Tate, and Carter (2007) process design concerns the methods used to manufacture products, including the manufacturing strategies employed (e.g. make-to-order, assemble-to-order, make-to-stock, or just-in-time), production facilities (e.g. number, location, capacity, or specialisation), and equipment (e.g. general-purpose equipment vs. specialised equipment). As a consequence, there is a close relation with the design of a product. Hence, for some processes such as chemical ones, a specific process design will be only able to produce one specific product. Given the above link with a product and customer, it is quite natural that process design should aim to meet the specific operations management performance criteria associated with the product and the customer being quality, speed, dependability, flexibility and cost (see, for example, Slack and Brandon-Jones 2019). Following the developments around process design, two additions can be made. Firstly, as an additional important performance measure sustainability is considered (e.g. Elkington 2002; World Commission on Environment and Development 1987). Second, while in the past product design, and process design would be considered as related but sequential processes, recent insights have argued for a concurrent approach, that argues that product, process and supply chain should be design together (e.g. Browning et al. 2023; Ellram, Tate, and Carter 2007; Fine, Golany, and Naseraldin 2005).

While process design might be considered as a predominantly engineering related activity, it is also related to the design of organisational and information processes. The choices made in process design being it in the physical, organisational or information design, impact operations management and supply chain management. An important contribution to the understanding of process design that links product characteristics to the process is to consider volume and variety of products. This is originally based on the work of Hayes and Wheelwright (1979). The idea behind the product-process matrix is to distinguish on one axis variety and volume and on the other process tasks and process flow. In general, the idea is that high (low) variety and low (high) volume are going together on the one axis, while diverse/complex (vs repeated/divided) process task and intermittent (vs continuous) process flow do the same on the other. Together, for manufacturing it results into five basic process types project, jobbing, batch, mass

and continuous processes. We will shortly discuss these below.

* Project processes can be characterised by offering large scale, unique projects, often with a duration of several years, that are highly complex, with a considerable amount of freedom for the professional workers to shape their work. Managerial challenges relate to material handling, scheduling tasks and shifting bottlenecks.

* Jobbing processes have also a wide variety of products with low volume, but products have more in common and usually share resources with each other. Also, products might be manufactured again, unlike project processes, although many jobs remain unique. Complexity is high, but usually the size of the product is smaller. Still, workers need considerable skills although uncertainty, as associated with project, is less. Managerial challenges are similar to the ones in projects.

* Batch processes have some characteristics in common with jobbing, but products show less variety and are produced in batches of more than one product at a time. For very small batch sizes these processes show much similarity with jobbing, but are still different as batches of the same products will be produced regularly. Batch processes might also have just a few products that are produced in relatively large numbers. Then the use of resources might be more in a fixed order, rather than more random as in jobbing/small batches. Typical managerial challenges are the balance of different types of resources, being flexible and specifically if repetition increases maintaining workforce motivation.

* Mass processes can be characterised by large volumes of a narrow range. Here narrow range needs to be interpreted from a production point of view as products might be different in some issues e.g. their colour, which does not affect the manufacturing process. The repetitive nature of work is high and predictable. To maintain speed managers should be sure to safeguard materials, they face huge capital investments and both mass and continuous process come with increased levels of vertical integration.

* Continuous processes are in fact similar to mass processes, with an even higher volume and even less variety (can be just one product), with products that are often not countable in figures but rather litres or tons. Production can be continuous 24/7, only stopping for large maintenance activities (sometimes once in several years). This process type is dominated by large investments in technology, limited manpower that mainly performs control and/or maintenance
<figure><img src="image_33.png" /></figure>

tasks rather than operational ones, and a high level of automation, including control.

The product-process matrix has been influential as it depicts clearly the specific managerial challenges for different types of operations. However, new technologies such as advanced manufacturing technology might be able to influence the range a specific product design can be used for and stretch its potential range of products (e.g. Das and Narasimhan 2001). Also, Helkiö and Tenhiälä (2013) have argued that the product-process matrix is somewhat simplistic and static, which makes it less useful for the dynamic changes in volume and product variety that many companies face. Similar concerns have been launched regarding contemporary developments as Industry 4.0 (Tortorella et al. 2022) or additive manufacturing (Eyers et al. 2022).

While in the above the focus is rather on the internal processes and their arrangements, the related concept of Customer Order Decoupling Point (CODP) has similarly used variety and volume of a product to decide on how products are delivered to the market in terms of specificity, delivery lead time and dependability. As such it links process characteristics (as manufacturing lead time and product characteristics) with external ones related to the customer (market demand and delivery time) while also considering information flows in a company (and associated planning processes) and between customer and manufacturer (related to the ordering process). The CODP can be defined as ‘the point at which product becomes earmarked for a particular customer. Downstream of this order penetration (OP) point, customer orders drive the systems that control materials flow; upstream, forecast and plans do the driving’ (Sharman 1984, 75). Based on a balance between market characteristics (e.g. specificity of demand, delivery speed) and manufacturing characteristics (e.g. costs of goods, processing time) five distinct position of the CODP have been distinguished in the literature: make to stock (MTS), assemble to order (ATO), make to order (MTO), purchase and make to order (PMTO), and engineer to order (ETO). While the first one directly delivers a product form inventory upon arrival of an order, the last one starts engineering and purchasing once an order arrives. Hence there is a huge difference in delivery leadtime, but also in product specificity and the number of activities performed after ordering. Olhager and Van Donk (2024) provide an extensive overview of the developments in the research on CODP. The positing of the CODP has consequences for a variety of operations and supply chain management issues. Some examples of subjects that have been explored include the links with various aspects of the supply chain; for example information

system (Giesberts and Van der Tang 1992; Olhager 2010), supply chain resilience (Dittfeld, Van Donk, and van Huet 2022) and supply chain integration (Van Donk and Van Doorne 2016), internal related aspects such as capacity planning and scheduling (Soman, Van Donk, and Gaalman 2007) and stock-keeping unit classification (Van Kampen and Van Donk 2014) and wider aspects as operations strategy (Olhager 2003). Similar to process design studies the CODP concept has been mainly studied as a static concept, while the dynamics of it are of great relevance given changes that organisations encounter in product portfolio, customer base, technology and information systems.

Process design has connections with many aspects of operations management. Some obvious cross references are operations strategy (Section 2.1) and facility layout (Section 2.12), while the different process types each have their own specific characteristics regarding planning (Section 2.14), production and control (Section 2.11), job design (Section 2.8) and almost all other operations management related aspects. The CODP has strong connections with buffer allocation (Section 2.6), but also with a number of supply chain management related aspects as network design (Section 3.3), outsourcing (Section 3.4) and forecasting (Section 4.6).

## 2.8. Work design⁹

While managers are accountable for organisational goals and collective performance targets, employees are responsible for executing their tasks and roles. Managerial decisions about who does what in organisations are impactful and represent ongoing challenges. They should be carefully planned rather than left to chance. As a microstructural and motivational concern, work design allocates resources, assigns roles and tasks to organisational members, intrinsically (de)motivates job incumbents, and ensures coordinated workforce efforts to achieve desired individual, group, and organisational outcomes (Morgeson and Campion 2003). This multi-layered process entails (i) setting, dividing, and grouping tasks, (ii) integrating tasks between and within organisational levels, and (iii) setting authority, responsibility, roles, and interactions of employees inside and outside their organisation. Work is carried out by people as well as machines. Therefore, it is important to emphasise that work design primarily focuses on human work, while scheduling deals with task and resource allocation—often including machine operation, not just human labour (see Section 2.15).

The theory and research on work design are extensive, especially in the field of industrial and organisational psychology. However, the study of work organisation
<figure><img src="image_34.png" /></figure>

issues extends beyond this discipline, encompassing areas such as organisational design, operations management, human resource management, sociology of work, and organisational behaviour. While disciplinary boundaries do exist, they are often blurred in practice, highlighting the interdisciplinary nature of work design. The managerial dilemmas about allocating and integrating work throughout an organisation cannot be resolved using a single lens; instead, designing and organising intertwined jobs must align with goals and strategy, structural and process design, and several HRM functions.

Within the context of operations management and supply chain management, work design is inextricably linked in a cause-and-effect relationship particularly with operations strategy (Section 2.1), buffer management (Section 2.6), process design (Section 2.7), operations excellence (Section 2.9), facility layout (Section 2.12), scheduling (Section 2.15), digitalisation (Section 3.2), outsourcing (Section 3.4), technology management (Section 4.8), and performance measurement (Section 4.9).

It is vital to distinguish work design from job analysis to avoid confusion and misunderstanding. Job or work analysis is necessary to identify, understand, and describe work within an organisation. It serves as a baseline for the majority of HRM functions, with HR experts using job analysis when creating job descriptions for workforce planning, performance management, compensation management, and job evaluation. On the other hand, work design primarily focuses on the differentiation and integration of work within an organisation, representing a non-monetary tool for motivating employees and an optimisation tool for designing the microstructure of organisations.

Depending on desired outcomes, we can distinguish among five main work design perspectives: motivational, mechanistic, biological, perceptual/motor, and socio-technical systems (Campion and Thayer 1985; Rousseau 1977). The *motivational perspective* aims to design meaningful jobs and promote motivation and job satisfaction (Lysova et al. 2019). The *mechanistic perspective* is oriented toward efficiency, while the biological perspective minimises physical stress and strain (Campion and Thayer 1985). The *perceptual/motor perspective* is oriented toward human mental capabilities and limitations, primarily about the attention and concentration requirements of jobs (Campion 1988). Finally, the *socio-technical systems perspective* considers social and technological factors, particularly emphasising the interactions between work groups and their environment (Rousseau 1977). The comprehensive and interdisciplinary nature of work design (Campion 1988) highlights the importance of

this workplace phenomenon. If individualised and optimised, work design may lead to positive outcomes (Humphrey, Nahrgang, and Morgeson 2007), such as increased motivation, enhanced efficiency and extra work effort, reduced stress, and a fit between job requirements and employees' capabilities (i.e. a person-job fit).

The two most common traditional approaches to work design are mechanistic and motivational. The *mechanistic approach* stems from Adam Smith and proponents of Scientific Management. Organising principles such as division of labour and specialisation were (and still are) crucial for improving productivity and job performance, which consequently brought the need for changing jobs by simplifying them. It is well documented that the principles of the mechanistic approach are successfully implemented even today and have garnered much attention in operations management. On the other hand, the *motivational approach* gained most of the attention in industrial and organisational psychology, organisational behaviour, and management domains. It is rooted in theories and models such as the job characteristics model (Hackman and Oldham 1976) and job demands-resources theory (Bakker, Demerouti, and Sanz-Vergel 2023). Both theories suggest that modifying work characteristics can enhance employee attitudes and motivation.

Jobs can be described and compared using work characteristics, that is, objective, stable, and universally measurable job properties (Hackman and Oldham 1979). Demerouti et al. (2001) distinguished between job demands (e.g. workload, time pressure) and job resources (e.g. autonomy, supervisor support), each type having different roles in the health impairment and motivational processes. We can also differentiate among four work design dimensions (Morgeson and Humphrey 2006): task, knowledge, social, and contextual. *Task characteristics* relate to the nature and variety of tasks involved in a specific job (e.g. task variety, task significance, task identity). *Knowledge characteristics* pertain to the types of knowledge, skills, and abilities required from an individual based on the tasks performed in the job (e.g. information processing, problem-solving, skill variety). *Social characteristics* describe the nature and intensity of relationships with others in a specific job (e.g. task interdependence, co-worker support, interaction outside the organisation). Finally, *contextual characteristics* describe physical and other aspects of the job (e.g. ergonomics, equipment use, physical demands).

Going beyond the multiple facets of work design, an informed reader should know that organisational requirements change fast, making jobs obsolete shortly after they are designed. Thus, an essential organisational task is to monitor and redesign employees' jobs. In most cases, managers are the ones who re-think and re-assign
<figure><img src="image_35.png" /></figure>

workplace duties for subordinates. *Managerial redesign* means that direct supervisors can give specific employ-ees more autonomy over decision-making or reduce the number of tasks they have performed until now. Recently, proactive approaches to work redesign have emerged. For instance, *job crafting* is the concept of employees proactively customising and altering different aspects of their work (Berg, Dutton, and Wrzesniewski 2013). Employees can autonomously (and under the radar) pur-sue new resources or demands (approach crafting) or practice avoidance crafting by reducing demands (Zhang and Parker 2019). *Idiosyncratic deals* (i-deals) represent another proactive approach to work redesign. These personalised work arrangements negotiated between employees and supervisors (Rousseau 2005) increase flexibility, improve morale, and boost employee loyalty. An example would be when a high performer requires shortened work days for education or personal mat-ters, and her direct supervisor wholeheartedly grants this request for a specific time. Finally, *algorithmic man-agement* entails algorithms allocating tasks and duties to employees instead of managers. Although futuristic, this approach (i.e. ‘using a computational formula that autonomously makes decisions based on statistical mod-els or decision rules without explicit human intervention’; Parent-Rocheleau and Parker 2022) has already been applied (e.g. ridesharing, delivery services) with negative consequences for work design (decreased job resources and increased job demands).

Content-wise, each job can be redesigned using the four most common work redesign techniques: job enrichment, job enlargement, job rotation, and job simplification. *Job enrichment* is an attempt to make the job more enjoyable for job incumbents by introduc-ing new tasks and responsibilities (Cimini, Lagorio, and Gaiardelli 2023). The idea behind such a technique is to offer learning and growth opportunities and training for employees with potential KSAs so that they can perform in more ambitious jobs. Job enrichment is particularly effective for employees with passive or low-stress jobs. *Job enlargement* involves adding new tasks that are similar to the existing ones. This strategy does not imply adding new responsibilities. It is more appropriate if organisa-tions need to allocate specific tasks to employees who are already competent in that area and lack the ambi-tion or KSAs to occupy more responsible job positions. *Job simplification* implies reducing tasks and duties an employee is expected to perform. While it boosts effi-ciency, it is also an effective method for alleviating the strain on employees in highly stressful roles, helping to prevent burnout and maintain work engagement. Finally, *job rotation* entails switching people between different tasks or jobs. It is primarily used to prevent boredom

and reduce injuries and exhaustion, but it also helps build KSAs and an understanding of organisational processes.

Since work design is especially prominent in the dig-ital era, it remains to be seen how the nature of work (i.e. employee tasks and roles) will change. Technological advancement, the introduction of collaborative robots, and the use of AI and algorithmic management create uncertainty and new avenues in work design (Huang, Rust, and Maksimovic 2019; Ötting et al. 2022; Parker and Grote 2022; Rogiers and Collings 2024). The exist-ing knowledge of work design (e.g. Parker, Morgeson, and Johns 2017; Parker and Wall 1998) will not become obsolete yet needs to be upgraded. We witness two very different streams in the literature. The first one pre-dicts that automation would be used to complement human efforts by focussing on manual routinised tasks, which would lead to fewer low-skilled manual jobs but also increase the number of high-skilled jobs for oper-ators with more decision-making autonomy, coordina-tion, planning, and job complexity (Cagliano et al. 2019; Vereycken, Ramioul, and Hermans 2021). The second scenario predicts that technologies such as automation will lead to manufacturing controlled by cyber-physical systems, which will consequently change the nature of jobs for the worse by giving operators less autonomy, simplified tasks, and more organisational procedures (Cagliano et al. 2019; Vereycken, Ramioul, and Her-mans 2021; Waschull et al. 2020). Instead of rolling a die, managers should continue to upskill or cross-skill themselves and their workforce and apply work redesign strategies to meet the changing business and work requirements.

## 2.9. Operations excellence¹⁰

Organisations increasingly pursue Operational Excel-lence (OPEX) to gain a competitive edge by implement-ing business improvement initiatives like Total Quality Management (TQM), Lean, Six Sigma, and Lean Six Sigma (LSS). These approaches focus on improving pro-cesses, reducing inefficiencies, and enhancing customer satisfaction across industries (Antony et al. 2023; Shah and Ward 2007; Sunder and Linderman 2024; Womack and Jones 2003). While Lean and Six Sigma method-ologies have been applied beyond manufacturing to sec-tors like healthcare and finance (Browning and de Tre-ville 2021, for example), a narrow focus on efficiency limits long-term growth. A more holistic, systems-based view that includes social dimensions is essential for sus-tainable improvement (Browning and de Treville 2021). While some researchers view LSS as a strategic approach (Arnheiter and Maleyeff 2005; George 2002), many regard it as one of the most effective frameworks within
<figure><img src="image_36.png" /></figure>

operational excellence (Antony et al. 2023; Chiarini 2011; Jaeger, Matyas, and Sihn 2014).

While improvement methodologies like Lean and Six Sigma are essential, they alone are insufficient to sustain a competitive advantage (Sunder and Linderman 2024). A narrow focus on efficiency limits a firm's ability to explore broader opportunities (Chiarini and Kumar 2021; Tor-torella et al. 2022). Researchers emphasise the need for a more holistic, systems-based view of OPEX that incorporates social factors for sustainable improvement (Browning and de Treville 2021). Just as Lean and Six Sigma have evolved in definition (Browning and de Treville 2021; Cusumano et al. 2021; Hopp and Spearman 2021; Kumar et al. 2008; Kumar, Antony, and Tiwari 2011), OPEX also requires a broader, more integrated perspective, as outlined in Table 1.

The key themes of OPEX emphasise process improvement, systematic approaches, continuous learning, and the crucial role of culture and people. Successful organisations constantly refine their processes to reduce inefficiencies and sustain improvement through structured methodologies like Lean and Six Sigma (Sousa and Voss 2001; Treacy and Wiersema 1995). A strong culture of continuous learning and people development is critical for long-term success (Found, Samuel, and Lyons 2017; Spear 2010). OPEX initiatives must align with organisational goals and drive behaviours that support strategic objectives, ensuring processes, tools, and culture are integrated effectively (Edgeman 2019).

Quality awards like the Malcolm Baldrige National Quality Award (MBNQA) and the European Foundation for Quality Management (EFQM) recognise operational excellence using defined scoring systems (Jaeger, Matyas, and Sihn 2014). These frameworks guide organisations toward business excellence through self-assessment. However, their applicability to small and medium-sized enterprises (SMEs) is debated, as the significant preparation and execution efforts required are challenging for SMEs with limited time and resources (Rusjan 2005).

Agility is also considered an indicator of OPEX in a dynamic and unstable market environment (Carvalho et al. 2019, 2021; Vinodh et al. 2010). The semblance between high performance and maintaining agility when operating in a changing external environment is also defined as operational excellence, which can only be realised through the effective integration of social and technical aspects with a focus on cultivating organisational culture and agility (Carvalho et al. 2019, 2021). This approach to operational excellence not only enables organisations to stay resilient and responsive to evolving market demands (Saleh and Watson 2017) but also fosters the development of technical capabilities and a

<table><caption>**Table 1.** Defining operational excellence.</caption><thead><tr><td>Authors</td><td>Definition of Operational Excellence</td></tr></thead><tbody><tr><td>Treacy and Wiersema (1995)</td><td>Operational Excellence is the <strong>strategy</strong> for organisations striving to <strong>deliver a combination of quality, price, ease of purchase, and service</strong> that surpasses that of any other organisation in their market or industry.</td></tr><tr><td>Dahlgaard and Dahlgaard (1999)</td><td>Operational Excellence is defined in terms of 4Ps: (i) excellent <strong>people</strong>, who establish, (ii) excellent <strong>partnerships</strong> (with suppliers, customers and society) in order to achieve, (iii) excellent <strong>processes</strong> (key business processes and management processes) to produce, and (iv) excellent <strong>products</strong>, which are able to delight the customers.</td></tr><tr><td>Sousa and Voss (2001)</td><td>Describe OPEX as a set of <strong>mutually reinforcing principles</strong> (e.g. continuous improvement and process management) alongside tools and techniques (e.g. control charts and Pareto diagrams).</td></tr><tr><td>Bigelow (2002)</td><td>OPEX represents a <strong>structured and systematic approach to enhancing business and operational processes</strong> to drive successful strategy implementation.</td></tr><tr><td>Hammer (2004, 85)</td><td>The term operational excellence, or operational improvement, 'refers to <strong>achieving high performance via existing modes of operation</strong>: ensuring that work is done as it ought to be to reduce errors, costs and delays but without fundamentally changing how that work gets accomplished'.</td></tr><tr><td>Spear (2010)</td><td>OPEX is all about using a <strong>systematic problem-solving approach to keep learning and improving</strong> within the company's internal and external environment.</td></tr><tr><td>Carvalho et al. (2019)</td><td>Operational Excellence should not be considered <strong>an approach to driving change</strong>, but rather as <strong>a means of providing tools and a framework</strong> for individuals within the organisation to implement it.</td></tr><tr><td>Found, Samuel, and Lyons (2017)</td><td>The Boston Scientific Strategic Operational Excellence Model aligns vision with results through products, technologies, and partnerships, emphasising skills development and a culture of improvement. It employs interconnected tools, systems, and metrics, driven by strategy, values, leadership, and change management. The model is dynamic, incorporating continuous improvement and a systems approach to Operational Excellence.</td></tr><tr><td>Edgeman (2019)</td><td>The Shingo Institute defines Operational Excellence through five key concepts for the Shingo Prize: (i) OPEX focuses on results and behaviours, (ii) Ideal behaviours stem from guiding principles, (iii) Principles are the foundation for a sustainable culture, (iv) Aligning management systems fosters ideal behaviours, and (v) Tools like Lean and Six Sigma are enablers that should be strategically integrated to drive behaviours and achieve results.</td></tr><tr><td>Browning and de Treville (2021)</td><td>When aiming for operational excellence, it is super important to see operations as processes and systems, especially at higher levels in organisations. It is also crucial to consider this same mindset when defining value. This means looking beyond just value-added actions and considering their network of interactions as well.</td></tr></tbody></table>

supportive cultural orientation that sustains operational excellence over time (Carvalho et al. 2019, 2021).
<figure><img src="image_37.png" /></figure>

The integration of operational excellence practices, such as Lean, with Industry 4.0 base technologies (e.g. cloud computing, IoT, big data, and machine learning), enables end-to-end supply chain collaboration and improved performance (Chiarini and Kumar 2021; Frank, Dalenogare, and Ayala 2019; Tortorella et al. 2022). Early research highlighted the synergy between Lean and I4.0, giving rise to concepts like Lean 4.0 and Digital Lean (Buer, Strandhagen, and Chan 2018; Kolberg, Knobloch, and Zühlke 2017). Combining these frameworks is expected to deliver superior results compared to using them in isolation, offering companies a powerful tool for boosting efficiency and effectiveness (Chiarini and Kumar 2021; Januszek et al. 2023). However, companies must approach digital transformation with caution, focussing on developing capabilities for real-time data processing and informed decision-making, rather than overinvesting in costly technologies (Gremyr et al. 2022; Gupta et al. 2023; Koenig, Found, and Kumar 2019; Koenig et al. 2020). Koenig, Found, and Kumar (2019); Koenig et al. (2020) and Gupta et al. (2023) demonstrated the value of frugal innovation in airport operations, showing that targeted, real-time monitoring of critical quality factors can be more effective than a complete technological overhaul. The majority of literature fails to emphasise the role of softer aspects such as the role of the leadership team and the impact on employees to embrace the technology, which are critical for managing digitalisation induced changes in the workplace (Januszek et al. 2023; Tortorella et al. 2021, 2020; van Dun and Kumar 2023).

The first step in operational excellence (OPEX) is understanding value from the customer's perspective, balancing both efficiency and effectiveness (Browning and de Treville 2021). A reductionist approach that separates value-added from non-value-added activities limits improvement potential. Value depends on the quality of inputs – products, processes, and information – used to create it. Browning (2003). Focusing solely on cost reduction risks neglecting quality and customer satisfaction, leading to suboptimal outcomes (Hines et al. 2008). Sustainable improvement requires balancing efficiency and effectiveness; overemphasising efficiency promotes short-term thinking and negative behaviours (Chiarini and Kumar 2021, 2022).

Researchers consistently highlight the importance of softer, socio-cultural factors as critical to the success of OPEX initiatives, particularly in embedding a culture of continuous improvement within organisations and their supply chains (Antony et al. 2023; Arumugam et al. 2024; Cusumano et al. 2021; Found et al. 2018; Hines et al. 2008; Tortorella et al. 2021). For example, Hines et al. (2008) used the iceberg model to emphasise

that beneath-the-surface factors such as strategy alignment, leadership, behaviour, and employee engagement are essential for sustaining continuous improvement. However, these often get overlooked in favour of tools, techniques, and technology, despite their fundamental role in driving long-term success. Antony et al. (2023) further highlighted key soft factors such as employee involvement, training, leadership, and communication as essential for successful OPEX implementation. Additionally, van Dun and Kumar (2023) showed that transformational leadership and emotional intelligence play a critical role in navigating digitalisation changes.

Based on Table 1 and the scope of OPEX, we define Operational Excellence as the strategic pursuit of improving end-to-end processes (from customer order to delivery) through a combination of people development, systematic problem-solving, technology and continuous learning. It focuses on aligning organisational culture, behaviours, and tools with strategic goals to create sustainable improvement, efficiency, and value creation. Operationally excellent organisations are built on a foundation of well-defined principles, empowered people, and a culture of continuous improvement. For deeper insights on OPEX, see works by Found et al. (2018), Chiarini and Kumar (2021, 2022), Tortorella et al. (2020, 2021, 2022), and Sunder and Linderman (2024). For critiques and future research on Lean and OPEX, refer to Hopp and Spearman (2021), Cusumano et al. (2021), and Browning and de Treville (2021).

## 2.10. Quality management¹¹

Quality Management plays a central role in operation management. It has evolved from a relatively routine activity focussed largely on error prevention to an integrative organisational philosophy that seeks to deliver operations improvement and enhanced customer satisfaction.

There are two key perspectives on the term ‘quality’. Dominant in early quality management discourse is the *product-based approach*, where quality reflects differences in measurable attributes of the product (Garvin 1984). Taking this approach, quality is achieved by meeting customer expectations through the consistent conformance to a predetermined set of specifications. The idea of ‘consistent’ implies quality management is used to design and run processes in such a way that ensure product or service conformance. In contrast to this relatively objective and mechanistic view of quality, the *customer’s view of quality* explicitly acknowledges that expectations are shaped by individual needs and experiences (Slack and Brandon-Jones 2024). As such, customers will inevitably perceive the same product or
<figure><img src="image_38.png" /></figure>

service in different ways. Furthermore, when they are not
able to assess the ‘technical’ specification of a product
or service, customers adopt surrogate measures to assess
quality.

In seeking to combine these alternative views of qual-
ity, the disconfirmation perspective (or gap perspective)
has emerged as the dominant orthodoxy (Berry 2004;
Cadotte, Woodruff, and Jenkins 1987; Oliver 1980). This
treats quality as a function of the gap between the
customer’s expectations of the product or service and
their perception of its performance. Disconfirmation is
positive when performance exceeds expectations and
negative when it falls short of expectations (Ganesh,
Arnold, and Reynolds 2000). Within the disconfirma-
tion process, both assimilation effects and contrast effects
(Oliver 1999) play a significant role. Assimilation effects
speak to the way that previously held expectations anchor
quality assessments and are particularly important when
there is performance ambiguity (Ganesh, Arnold, and
Reynolds 2000). Contrast effects concern the magnifi-
cation of quality assessment whereby customers have
a propensity to over-emphasise the scale of their pos-
itive or negative performance assessments (Brandon-
Jones 2006).

In operationalising quality, the ‘Nordic’ perspective (Grönroos 1984) defines quality dimensions in global terms. Technical quality refers to what a customer receives, whilst functional quality is concerned with how the product or service is delivered. Rust and Oliver (1994) build on this perspective with their three-component model including service product, service delivery, and service environment. In contrast, the ‘American’ perspective applies terms to describe the various aspects of the service encounter (e.g. reliability, responsiveness, assurance, empathy, and tangibles) and has been applied extensively through applications of the SERVQUAL scale (Parasuraman, Zeithaml, and Berry 1988).

The ‘sand cone’ model or cumulative capability per-
spective (Ferdows and De Meyer 1990) provides a useful
view on the role of quality in driving operations improve-
ment. The model states that quality should be the pri-
ority for any organisation as it forms the foundation
upon which other aspects of performance – dependabil-
ity, speed, flexibility and cost – can be layered cumula-
tively (rather than sequentially). Only when a minimum
quality threshold has been reached can the operation
move onto improving dependability. To achieve improve-
ments to dependability, requires further improvements to
quality. In turn, once a sufficient level of dependability
has been achieved, the focus can shift towards improving
speed, then flexibility, and finally cost of the operation.
All the time, attention on the ‘lower layers’ of the Sand
cone must be maintained.

Quality management has evolved significantly over
the last hundred years. In the late 1800's, the focus of
quality management (though the term was not really
established) was essentially on enabling the transition
towards mechanised industrial systems and production
volume. As such, when present, quality management
predominantly involved inspection to monitor product
quality (Watson 2019) and to identify defects. The shift
in focus towards productivity at the turn of the 20th cen-
tury resulted in a subtle shift of emphasis away from
simply identifying defects and towards collecting data
to identify sources of variation in products and pro-
cesses, often using statistical process control (Chiarini
and Kumar 2022). Furthermore, there was an increase in
the number of dedicated individuals tasked with assuring
product quality and the establishment of formal quality
functions within organisations (Sousa and Voss 2002).

During the third industrial revolution, customers
began demanding higher product and service quality
in response to greater per capita income (Chiarini and
Kumar 2022). This necessitated a move beyond defect
detection and rejection to a focus on defect prevention.
This period witnessed growing attention on quality man-
agement and the flourishing of Total Quality Manage-
ment (TQM) as well as the related improvement philoso-
phy of Lean (see Sections 2.9 and 4.2). Based on the core
writings of Philip Crosby, W. Edwards Deming, Joseph
Juran and Kaoru Ishikawa, TQM gained huge traction
across many business sectors during the 1980s and 1990s
(Hackman and Wageman 1995; Sousa and Voss 2002).
Whilst the popularity of TQM has declined in the last
twenty years, its general precepts and principles remain
the dominant mode of quality management in contem-
porary organisations (Slack and Brandon-Jones 2024).
In some ways, TQM merely codified the way in which
quality-related practices had progressed up to the 1980s.
Yet it also extended the established ideas of inspection,
quality control and quality assurance with a more strate-
gic orientation to become ‘an integrative management
philosophy aimed at the continuous improvement of per-
formance’ (Ebrahimi and Sadeghi 2013). Here, the *voice
of the customer* (also referred to a *customer centricity*)
and *supplier involvement* were increasingly recognised as
key elements of quality management (Flynn, Schroeder,
and Sakakibara 1994). The recognition that everyone
within the organisation is an internal customer receiv-
ing products and services largely from internal suppliers
reinforced the idea that any errors within the organisa-
tion ultimately impact on the end customer (Slack and
Brandon-Jones 2024; Sousa and Voss 2002).

Quality management considers key *costs of quality* – prevention costs, appraisal costs, internal failure costs and external failure costs. Prevention costs are those
<figure><img src="image_39.png" /></figure>

incurred trying to stop errors occurring. Appraisal costs are those associated with quality control in order to detect errors (for example, setting up SPC systems, input and output inspection, quality audits and customer surveys). Internal failure costs are those associated with addressing failures such as reworking, material waste, lost capacity, and work stress when dealing with errors. Finally, external failure costs are incurred when a defective product or service is experienced by the customer. Such costs may involve replacing products or re-delivering services, damage to organisational reputation, compensation and litigation. In traditional quality management, the assumption is that there exists an optimum level of quality effort that will minimise the total cost of quality. Beyond this optimum level, prevention and appraisal costs combined are greater than internal and external failure costs combined. In contrast, TQM proponents argue that prevention and appraisal costs are significantly lower, and the costs of internal and external failure are significantly higher, than implied by traditional quality management. Therefore, TQM refutes the concept of an optimum quality threshold and instead places significant emphasis on managing prevention and appraisal to ensure product and service failure are kept to an absolute minimum.

We are now witnessing the fourth industrial revolution with its significant emphasis on servitisation, mass customisation and digital offerings (Gremyr et al. 2022; Kohtamäki et al. 2021). Furthermore, the continued rise of sustainability agendas across a wide range of sectors has increased attention on the potential ways in which quality management can support environmental and social dimensions of performance improvement (Siva et al. 2016). Arguably, this has necessitated the shift of quality functions away from a policing role to a more proactive role that involves greater levels of collaboration with both internal functions and external stakeholders, such as customers, suppliers, competitors, and regulators. Furthermore, it requires an even greater understanding of the subjective views of customers to inform the actions taken within quality management, for example in evaluating personalised customer feedback and in collecting customer data on products and services in use (Fundin and Elg 2006).

Several bodies have been established to encourage the adoption of quality management practises. Arguably, the most well-known of these is The Deming Prize, established in 1951 in honour of W Edwards Deming for his key role in the regeneration of Japan after the Second World War and his broader contributions to the quality improvement movement (Anderson, Rungtusanatham, and Schroeder 1994). This prize is awarded to organisations who have demonstrated leadership in

‘company-wide quality control’. In 1987, The Malcolm Baldrige National Quality Award was established to encourage the adoption of quality improvement in American organisations. The award had the effect of raising awareness amongst senior executives concerning the value of quality management and of the key role that employees play in driving operations improvement (Stanley and Wisner 2001). The European Foundation for Quality Management (EFQM) Excellence Award (now known as the EFQM Global Award), was first awarded in 1992. The award was established to recognise European businesses who demonstrated excellence in operations improvement.

## 2.11. Production control¹²

Production control is a crucial subset of activities within the broader topic of operations management. It focuses on execution, monitoring and optimisation of resources to ensure process efficiency, product quality and timely delivery to fulfil customers’ demands (Slack, Chambers, and Johnston 2010). Production control requires inputs from many other functions such as scheduling (Section 2.15) and planning (Section 2.14), but also plays a role in supporting inventory management (Section 2.3), capacity management (Section 2.2), material handling (Section 2.5), quality management (Section 2.10), operations excellence, and assembly line balancing (Section 2.13), amongst others. Production planning and control are often considered together, but they differ in that planning is about allocating resource according to what is expected to happen, while control is about executing the plan, monitoring the operations, and adapting to the actual conditions and unexpected changes. However, production planning and control are intricately connected as feedback loops between the two are often necessary to ensure successful product delivery. The line between the two are increasingly blurred with the rise of automation and more integrated systems with the increased digital maturity of manufacturing companies (digitisation Section 3.2), often combining planning and control functionalities as a single activity.

Traditionally, production control focuses on internal information flows and can generally be categorised as push (e.g. make-to-stock, driven by demand forecast) or pull (e.g. make-to-order, triggered by customer demand; Lödding 2011; Thürer et al. 2025). With push control, the flow of materials is pushed through successive processes from suppliers to inventory and then queues, workstations, buffers, etc. until the product is complete and ready to be delivered to the customer. In pull systems, production is triggered by an order (customer
<figure><img src="image_40.png" /></figure>

demand) which pulls the materials through the processes with the aim to minimise inventory and overproduction. In modern production control systems, hybrid systems are often used to combine push and pull logic. Common hybrid approaches include drum-buffer-rope and constant work in progress (CONWIP; Spearman, Woodruff, and Hopp 1990). Alternative Material Flow Control (MFC) methods have been proposed, such as order generation, order release and production authorisation (Thürer et al. 2025). The dominant trend remains with pull approaches as Lean, Kanban and Just-In-Time (JIT) systems have become established best practices for cost and waste reduction. This is further reinforced with the increased integration of external information flows with the rise of customisation, penalisation and engineer-to-order models.

To facilitate production control, a structured data exchange network is needed where resources and materials are documented and linked to what will happen when and where in the production chain (Givehchi et al. 2017). This interoperable network can be structured in several ways often categorised as centralised, distributed or hierarchical (Kasper et al. 2024). Traditionally, a hierarchical network with a tree-like structure has been used and is still in use for most production facilities. The distributed network – also known as decentralised, holonic or heterarchical control systems which resemble a spider web with resources connected to each other directly without hierarchy – has been under development for a long time (Bongaerts et al. 2000; Cupek et al. 2016; Mcfarlane and Bussmann 2000). Industry 4.0 developments, such as RAMI 4.0 (Hankel and Rexroth 2015) and GAIA-X (Eggers et al. 2020), are examples of standardisation developments and facilitators for a distributed control system.

The ISA-95 standard defines different levels for enterprise-control system integration (International Society of Automation 2010). Production control requires management tools ranging from IT systems at level 3-4 with Product Lifecycle Management (PLM), Enterprise Resource Planning (ERP), Manufacturing execution systems (MES) and Material Requirements Planning (MRP), all the way to actual production control with operational technology (OT) systems at level 0-2 with supervisory control and data acquisition (SCADA) systems, distributed control system (DCS), programmable logic controllers (PLC), and physical systems with sensors and actuators. While the top-level structure is well-defined (Cupek et al. 2016), the lower levels of detailed control on PLC level are not standardised to give manufacturers the freedom to choose appropriate approaches meeting their specific needs and conditions.

With Industry 4.0 developments and implementations, increased digitisation and Industrial Internet of Things (IIoT) are becoming more prevalent (Kolberg and Zühlke 2015). However, the amount and richness of data can be overwhelming, especially for SMEs (Moeuf et al. 2018). Machine learning and predictive methods used in simulation and optimisation models are promising ways to use the data for decision making and to increase production efficiency, flexibility and resilience (Martins et al. 2020). For example, using a predictive control strategy to adapt to unpredictable changes in material inputs, such as in pharmaceutical manufacturing, can help maintain consistent product quality and yields (Eslami and Jungbauer 2024). Digital twins for real-time monitoring and closed-loop feedback systems can address the challenges of adapting to rapidly changing manufacturing environments. For example at a process level, machine learning has been used for in-situ monitoring of metal additive manufacturing to take evasive or corrective actions when detecting avoidable defects and anomalies (Gunasegaram et al. 2024). At the manufacturing systems level, the use of real-time control methods to adapt operations to variable renewable energy supply and to support more self-sufficient and resilient manufacturing systems (Beier, Thiede, and Herrmann 2017). The ISO 23247 standardisation effort on 'Automation systems and integration - Digital twin framework for manufacturing' are beneficial for structuring production planning and control systems (International Organisation for Standardization 2021; Shao, Frechette, and Srinivasan 2023), including, for example, Part 1: Overview and general principles, Part 2: Reference architecture, Part 3: Digital representation of manufacturing elements, and Part 4: Information exchange. Additional validation and more detailed specification work including validation with demonstrators are ongoing as of now. Blockchain-like technologies are also on the rise to facilitate multi-stakeholder interoperability across value chains to enable traceability and transparency in production processes and along these value chains.

Numerous metrics and key performance indicators (KPIs) can be used to evaluate production control performance; e.g. cost, reliability, flexibility, productivity, speed, lead time, throughput, quality, overall equipment effectiveness (OEE), etc. (Bueno, Godinho Filho, and Frank 2020; Wheelwright 1978). Improvement approaches, such as Lean Six Sigma and Total Quality Management (TQM) are also effective to monitor and improve processes and production controls (Bendell 2006; Moeuf et al. 2018). In this respect, it is important to measure the right aspects to achieve more holistic improvements accounting for increased product variety, demand variability, product and process
<figure><img src="image_41.png" /></figure>

complexity, and others (Rahmani et al. 2022). Therefore, additional performance dimensions need to be further explored and developed as they are often overlooked under the Industry 4.0 paradigm, including environmental impacts (Despeisse et al. 2012), knowledge discovery and generation, and human factors (Usuga Cadavid et al. 2020).

Focusing on sustainability dimensions, the environmental and social dimensions are less well-addressed than the economic one, largely related to productivity, cost and quality. Various methods have been developed to include aspect of environmental management in production control, for example energy efficiency and waste minimisation (Dai et al. 2013; de Ron 1998; Matsunaga et al. 2022). Looking at strategies for production controls accounting for external information flows, new methods have been developed to support circular economy through production planning and control of remanufacturing operations (Dev, Shankar, and Qaiser 2020; Guide 2000). While automation is increasing, it remains essential to keep the human in the loop (Cimini et al. 2020; Pinzone et al. 2020). Production managers and operators have key roles to play in decision making and problem solving related to production control. Challenges remain with skills and education, as well as resistance to change, teamwork and other non-technical issues. This is in line with the upcoming trends guiding future developments in production control models and technologies, promising to be more digitalised, resilient, sustainable and human-centric under the Industry 5.0 paradigm.

## 2.12. Facility layout¹³

Facility layout applies to spatial arrangement of spaces (e.g. office spaces) and objects (e.g. machine tools). It has seen a tremendous coverage in the literature on manufacturing and other applications (Reed 1961; Snow 1961). Any manufacturing and service organisation includes facilities, workspaces, equipment, and furniture which need to be organised to meet the business objectives. The high computational complexity of the facility layout problem might have contributed to the diversity of models and algorithms that date back to 1950s (Koopmans and Beckmann 1957). The facility layout problem (FLP) has seen many applications and models, some having distinct properties reflected in the objective functions and constraints and names such as:

* Facility layout problem: Facilities may change shapes are located at different sites usually in predefined area in two-dimensional (Irani and Huang 2000) or three-dimensional space (Kalita and Datta 2024).

* Machine layout problem (Zuo et al. 2019): Machine tools have a fixed footprint while facilities may change their shape.

* Cutting stock problem (Hadj Salem et al. 2023): Arranging patterns to be extracted usually from a sheet of material (e.g. metal, wood, plastic). The literature reports models in 1, 1.5, and 2 dimensions.

* Wind turbine siting problem (Kusiak and Song 2010): Locating wind turbines at different sites, where the turbines are optimally located subject to constraints resembling those encountered in manufacturing applications.

* Facility location problem (Zhang et al. 2023): Locating facilities (e.g. manufacturing plants, warehouses, stores, restaurants) at different sites. Though most often it is solved in two dimensions, other cases are possible.

## Modelling the facility layout problems

FLPs are frequently applied to positioning departments in a facility. A common objective is to minimise the overall cost associated with inter-departmental logistics within the facility. The cost is often related to the transportation of materials, parts, or products, and is directly proportional the distances travelled between departments (Anjos and Vieira 2017). In many settings, the facility and its departments are rectangular in shape. The dimension of the facility is given and fixed, while those of the departments may vary. Typical constraints in FLPs can be categorised as: (i) requirements related to department shapes (e.g. specified areas, dimensions, and aspect ratios) and (ii) requirements concerning the placement of departments (e.g. non-overlapping departments and pre-specified locations); see also Anjos and Vieira (2017).

A widely studied class of FLP is the single and double row layout problem (Heragu and Kusiak 1991). The single row FLP involves departments with the known length. The objective is to optimally position the departments along this row to minimise the weighted sum of flow distances. This single-row FLP was discussed in, e.g. Ravi Kumar, Hadjinicola, and Lin (1995) and Maier and Taferner (2023). The row arrangement concept can be expanded to include the double-row FLP (Chung and Tanchoco 2010; Heragu and Kusiak 1988). In the double-row FLP, two rows of facilities are placed on the opposite sides of an aisle, and the two departments are to be arranged using the same objective as in the single-row FLP. The problem can be further generalised to the multi-row FLP (Wan et al. 2022), which deals with layouts across multiple rows. Additionally, loop layouts (Cheng and Gen 1998) and open-field layouts (Yang, Peters, and Tu 2005) are specific facility configurations that have been explored in the literature.
<figure><img src="image_42.png" /></figure>

Another popular class of FLPs is the unequal-area FLPs (UAFLPs; Armour and Buffa 1963; Montreuil 1991; Tate and Smith 1995). Similar to the row FLP, the height and the width of the facility are given and fixed. The UAFLP is to determine the positions and dimensions of departments within a facility while ensuring adherence to the constraints on the ranges of department widths and heights (and/or aspect ratios). Additionally, the non-overlapping condition needs to be met.

Row FLPs and UAFLPs focus on the layout within a single floor. However, when FLPs require the arrangement of departments across multiple floors, a new class of problems, multi-floor FLPs (MFFLPs; Johnson 1982; Meller and Bozer 1997), is introduced. In MFFLPs, the dimensions of the facility's floors and the areas of the departments are pre-defined. MFFLPs require additional factors to be considered, which includes the consideration of floor heights and/or the utilisation of an elevator, capturing vertical travel costs in the planning process.

## Solving the facility layout problems

FLPs are known to be *NP*-hard (Anjos and Vieira 2017). There have been significant research efforts to devise computationally efficient algorithms for solving these complex problems (Kusiak and Heragu 1987). In the literature and industrial applications, two primary approaches have been adopted to tackle FLPs, mathematical programming and heuristics.

## Mathematical programming

Most FLPs are formulated as mixed-integer linear programmes (MILPs) or semidefinite programmes (SDPs) involving rigorous mathematical representations of the problem. A crucial aspect that FLPs account for is the cost associated with the flows within the facility. To capture the distances and flows across the departments, one needs to figure out the relative position of each department in relation to the other units. For instance, for a single-row FLP, one may need to determine the placement of department *i* with respect to department *j*. Concepts such as permutation and betweenness need to be incorporated in the formulation (Anjos and Vieira 2017). In a MILP formulation, binary variables taking values of 0 and 1 can be utilised to indicate whether one department is positioned between two others, with the use of a set of linear constraints (Amaral 2009). One the other hand, an SDP may require binary variables with values of -1 and 1 to indicate if one department is positioned right or left to another department, complemented by a set of quadratic constraints (Anjos and Liers 2012). For more complex cases of FLPs such as the multi-row FLP and MFFLP, additional binary variables and constraints are introduced to indicate the placement of a department

in a specific row or floor, while ensuring that the constraints related to the shape and position of each department are respected. The reader is referred to Kusiak and Heragu (1987) and Anjos and Vieira (2017) for detailed discussions on the MILP and SDP formulations of FLPs.

When using exact solution techniques such as the branch-and-bound algorithm to solve FLPs, using valid inequality constraints can significantly reduce the computational time. For instance, in the context of the row FLP, researchers have derived valid inequalities to strengthen formulations or offer polyhedral results (Amaral 2008, 2009; Amaral and Letchford 2013). Similarly, for UAFLPs, studies have investigated the use of valid inequalities to enhance the computational performance (Konak et al. 2006; Meller, Narayanan, and Vance 1998; Sherali, Fraticelli, and Meller 2003).

## Heuristic algorithms

As FLPs are *NP*-hard, optimal algorithms face computational challenges when tackling large-scale instances. In such situations, heuristics are usually adopted to obtain near-optimal solutions. A variety of heuristics, such as ant colony optimisation (Kulturel-Konak and Konak 2011; Zouein and Kattan 2022), genetic algorithms (Kulturel-Konak and Konak 2013), GRASP (Wan et al. 2022), simulated annealing (Meller and Bozer 1996), Tabu search (Kulturel-Konak 2012), and variable neighbourhood search (Herrán, Manuel Colmenar, and Duarte 2021), have been utilised to derive high-quality solutions for FLPs within reasonable computational times. In recent years, due to the advances in computing and data science, applications of reinforcement learning have emerged as new approaches for solving FLPs (Heinbach, Burggräf, and Wagner 2023; Kaven et al. 2024; Yan et al. 2022; Zhang et al. 2023).

## 2.13. Machining, assembly and disassembly line balancing¹⁴

Line balancing is a well-known combinatorial optimization problem, proved to be *NP*-hard in general. Initially developed for manual assembly environments, the core problem has been adapted to accommodate robotic, machining, and disassembly settings (Battaïa and Dolgui 2013, 2022). Despite the diversity of industrial environments and line configurations, the mathematical models employed usually share similar types of decisions, constraints and objective functions.

Generally, the goal of line balancing is to determine how to manufacture a product within the production line, which consists of a set of workstations (Scholl 1999). This involves assigning tasks to these workstations to meet specific requirements and optimise one or more
<figure><img src="image_43.png" /></figure>

objectives. By the time the line balancing step is reached, the layout of the production line is typically already established from a previous decision. Each layout imposes specific constraints that must be adhered to when assigning tasks to the workstations.

One of the earliest formulations of this problem was proposed by Salveson (1955) for manual assembly lines. It involves assigning a set of tasks *I* to a sequence of linearly ordered workstations *M* in such a way that the sum of durations of the tasks assigned to the same workstation does not exceed a given takt time and the precedence constraints between the tasks are respected. The objective function for this first formulation was to minimise the number of required workstations for the assignment of all given tasks.

This problem, known as the Simple Assembly Line Balancing Problem (SALBP) following the definition by Baybars (1986), was shown to be *NP*-hard in general (Wee and Magazine 1982). Early studies were dedicated to the development of efficient solution techniques for this simplified problem (Arcus 1965; Baybars 1986; Gutjahr and Nemhauser 1964; Hoffmann 1990).

SALBP represents a basic version of industrial line balancing problems existing in various manufacturing environments, such as machining, assembly and disassembly. Over the decades, more precise problem formulations have been developed to address the specific needs of various industrial contexts:

*   **Machining**: the first formulation for machining environment was developed for Transfer lines and named Transfer Line Balancing Problem (Dolgui, Guschinsky, and Levin 1999). Typically, in this context, there are fewer precedence relationships between tasks compared to assembly or disassembly processes. However, numerous compatibility constraints may determine which tasks must be performed together at the same workstation due to tolerance requirements, or conversely, which operations cannot be performed together due to fixturing limitations. These lines are generally automated. For further details, see (Battaïa, Dolgui, and Guschinsky 2024; Guschinskaya and Dolgui 2009).

*   **Assembly**: the various configurations of assembly lines were addressed ranging from fully manual, with one or multiple workers assigned to each workstation, eventually collaborating with cobots, to fully automated systems (Boysen, Fliedner, and Scholl 2007; Boysen, Schulze, and Scholl 2022; Scholl and Becker 2006).

*   **Disassembly**: The development of the circular economy has intensified the need for dis-assembly. The first formulation of Disassembly Line balancing Problem

is due to Mcgovern and Gupta (2007). Similar to Salveson's formulation, this model has since been extended to address a range of industrial configurations, from fully manual to fully automated systems (He et al. 2024; Mcgovern and Gupta 2011; Özceylan et al. 2019).

All existing formulations for diverse line balancing problems can be classified according to common features such as variety of products treated in the line, layout of the line to be balanced, number of lines to be balanced, task characteristics (attributes), workstation characteristics (attributes), constraints to be observed, and objective function to be optimised (Battaïa and Dolgui 2013).

**Variety of products treated in the line.** Based on this criterion, the following types of production lines are commonly identified in the literature (Scholl 1999):

*   **Single-model lines**: A single homogeneous product is manufactured on the line (Otto, Otto, and Scholl 2013). During each cycle time, every workstation performs the same set of tasks assigned to it. Consequently, the line-balancing problem deals with the decision how to distribute the whole set of tasks required for the product completion among the workstations.

*   **Mixed-model lines**: Multiple models of products from a basic product family are produced simultaneously (Zeltzer, Aghezzaf, and Limère 2017). These models share similar core processes, differing only in certain attributes or optional features. As a result, the full set of tasks must be divided among the workstations, with each workstation assigned a subset of tasks for each model. The number of subsets associated with each workstation corresponds to the number of models being produced.

*   **Multi-model lines**: Several distinct products are produced in separate batches (Pereira 2018). In this scenario, the line can be rebalanced for each batch, allowing for setup times between them and an additional problem of sequencing of lots should be also solved if there are setup times.

**Line layout.** According to this criterion, the following types of production lines are commonly distinguished in the literature:

*   **Basic straight lines**: In this layout, each workpiece moves through a series of workstations in the order they are set up (Scholl 1999). A specific set of tasks is assigned to each workstation, and these tasks are performed sequentially within each station.
<figure><img src="image_44.png" /></figure>

*   **Straight lines with multiple workplaces:** Workstations are arranged in a straight line but each workstation includes several parallel (Lovato et al. 2023), sequential (Battaïa and Dolgui 2012), or mixed-activation workplaces (Dolgui and Ihnatsenka 2009). These workplaces enable workers or equipment to operate on each workpiece simultaneously, sequentially, or in a series-parallel manner.

*   **U-shaped lines:** These lines feature both the entry and exit points at the same location, and they are usually manual. Workers positioned between the two legs of the line can move between them allowing them to work on two or more workpieces during the same takt time (Fattahi and Turkay 2015).

*   **Lines with circular transfer:** Workstations are arranged around a rotating table which facilitates the loading, unloading, and transfer of parts between stations (Battaïa, Dolgui, and Guschinsky 2023). The process can be multi-turn (Battini et al. 2007).

*   **Asymmetric lines** are designed to delay product differentiation, maintaining a common line configuration for as long as possible (AlGeddawy and ElMaraghy 2010; Ko and Jack Hu 2008).

**Number of lines to be balanced.** Based on this criterion, the following types of production situations are commonly identified in the literature:

*   **Independent lines:** These lines can be identical or different and may produce the same product or different ones (Aguilar, García-Villoria, and Pastor 2020).

*   **Lines with multiline workstations:** In this configuration, workstations or workers per-form tasks across more than one line (Özcan et al. 2010). While this setup can reduce the total number of required workstations, a breakdown at a multiline workstation can impact production on multiple lines.

*   **Parallel lines with crossover workstations:** These lines have crossovers that allow workpieces to be transferred from one line to another in case of a failure (Spicer et al. 2002).

**Tasks attributes.** Task attributes such as task time, cost, may have constant/uncertain/dynamic values or be functions of partial assignment solutions.

**Workstations and their attributes.** Workstation can have scalar (e.g. the number of identical parallel workstations/machines/workers associated with a workstation) or vectorial attributes which indicate the repartition of the tasks assigned to the same workstation to its resources (equipment, operators, etc).

**Problem constraints.** Constraints are used to distinguish feasible assignments of tasks to workstations.

They can have technological, economical or logical origins. The most frequently modelled constraints include: assignment constraints, precedence constraints, inclusion/conjunctive/positive zoning constraints, exclusion/disjunctive/negative zoning constraints, distance and positional constraints, correspondence constraints (matching of task and workstation attributes) and constraints on performance measures calculated for workstations (takt time constraint, workstation space utilisation, ergonomic constraints, energy consumption constraints, workstation reliability, etc).

**Objective functions.** An objective function is used to evaluate the quality of feasible solutions and choose the best one, the most common objective functions are: the number of workstations, line takt time, line efficiency, system utilisation, line smoothness, line cost or profit, line reliability, energy consumption. Frequently, multiple objective functions are used (Laili et al. 2020).

**Hybridisation with other optimisation problems.** Making several decisions simultaneously along with line balancing leads to better final line performance and effectiveness, the most popular hybridisations in the literature are with task sequencing at each workstation (Özcan 2019), with process planning (Battaïa, Dolgui, and Guschinsky 2017; Bentaha et al. 2023), and with line design (Battaïa, Dolgui, and Guschinsky 2024).

**Solution methods.** From the perspective of the quality of the results, solution methods are of-ten divided into exact and approximate. More details on existing solution methods can be found in Sewell and Jacobson (2012), Morrison, Sewell, and Jacobson (2014), Pape (2015), Bukchin and Raviv (2018), and Boysen, Schulze, and Scholl (2022). To assess more precisely the performances of the line, simulation can be used to evaluate its dynamic behaviour (Cortés, Onieva, and Guadix 2010).

## 2.14. Planning¹⁵

Planning is the process of developing and implementing strategic and tactical measures to reach specific goals. It entails defining objectives, constraints, and using algorithms to optimise the coordination of material requirements, demand, production, and distribution. Effective planning aligns resources with strategic objectives, thereby optimising operational efficiency and enhancing customer satisfaction while minimising associated risks. Comprehensive planning requires the integration of suppliers, the enterprise, and customers. However, achieving true optimisation and integrated planning is often impractical due to the complexities introduced by numerous concurrent planning tasks (Fleischmann and Meyr 2003). This section provides an overview
<figure><img src="image_45.png" /></figure>

<figure><img src="image_46.png" /><figcaption>**Figure 4.** Hierarchical planning concept.</figcaption></figure>

of planning problems that occur in operations management, exploring hierarchical planning and advanced planning systems (APSs) together with their corresponding planning modules. We also address collaboration and information sharing as well as planning enabled by digital technologies.

Hierarchical planning offers a practical solution by segmenting the overall planning task into manageable subtasks (Hax and Meal 1973), organising planning tasks into three tiers: long-term, mid-term, and short-term planning (Anthony 1965). Long-term planning, also known as strategic planning or business planning, focuses on a multi-year horizon and shapes the company's strategic direction, influencing decisions related to supplier selection, production capacity, and distribution structure (Stadtler 2005). Mid-term planning comprises demand planning and master planning. It spans several months to a year and addresses aggregate-level issues such as production quantities, inventory levels, workforce requirements, and distribution channels (Pereira, Oliveira, and Carravilla 2020). Short-term planning, which includes scheduling and distribution planning, is conducted on a weekly or daily basis. It involves decisions regarding purchase quantities, production lot sizes, transportation modes, and vehicle routes (Bitran and Tirupati 1993, see also Section 2.15). These planning tasks are intricately linked, with a continuous flow of information across different levels, necessitating coordination to ensure alignment and integration of planning efforts across the hierarchical spectrum (Fleischmann and Meyr 2003; Ozdamar and Yazgac 1999). The hierarchical planning concept is illustrated in Figure 4 based on Meyr, Wagner, and Rohde (2002) and Rohde and Wagner (2005).

While various algorithms exist to manage planning tasks, addressing the entire task at once is often not possible. APSs provide a robust framework that integrates different modules and algorithms to tackle real-world planning challenges (Meyr, Wagner, and Rohde 2002). As decision support systems, APSs extract data from enterprise resource planning (ERP) systems, generate

high-quality solutions, and relay decisions back to the ERP for execution (Zoryk-Schalla, Fransoo, and de Kok 2004). Numerous vendors offer APS solutions, including Oracle, SAP, i2, and AspenTech (Jonsson, Kjellsdotter, and Rudberg 2007). An APS typically comprises several of the modules illustrated in Figure 4 (Meyr, Wagner, and Rohde 2002). These modules operate based on both constructional and organisational hierarchies, effectively addressing complex planning problems by decomposing them into simpler sub-problems and coordinating across distinct functional areas (Fleischmann and Meyr 2003).

Strategic planning sets the foundation for tactical and operational planning, occurring over a long-term horizon. Once established, strategies are generally costly to modify (Colotla, Shi, and Gregory 2003). The strategic planning module within APSs utilises problem-oriented heuristics for decision-making, providing rapid evaluations based on qualitative and quantitative criteria (Jonsson, Kjellsdotter, and Rudberg 2007).

Master (or tactical) planning addresses mid-term issues covering a planning horizon from a season to a year (Rohde and Wagner 2005). It serves as a conduit between strategic and short-term operational planning, utilising the infrastructure defined by strategic planning to optimise revenues and minimise costs while setting goals for operational activities. Typical decision variables in master planning include production, inventory, transport, sales, supply and backlog quantities, estimated hirings and lay-offs, as well as subcontracting and overtime, constrained by capacity limitations (Jonsson, Kjellsdotter, and Rudberg 2007). APSs employ linear programming or mixed-integer programming optimisers for solving master planning problems, although increasing model complexity may necessitate the use of heuristics or metaheuristics (Silver, Pyke, and Peterson 1998; Venkataraman and Smith 1996).

Demand planning considers both mid-term and short-term horizons. It comprises demand forecasting, what-if-analyses/simulation, and safety stock determination (Wagner 2002). Forecasting may employ top-down, bottom-up, or middle-out approaches to ensure consistency across various dimensions, such as product and time (year, month, week). Single-level forecasting can use time series models, explanatory models, Bayesian models or the Delphi-method (Box and Jenkins 1976; Fleischmann and Meyr 2003; Silver, Pyke, and Peterson 1998, see also Section 4.6). What-if-analyses/simulation help strategise the introduction of new products or promotions. Safety stocks are finally calculated to buffer against forecasting errors, lead time variability, or other uncertainties (Graves and Willems 2000).
<figure><img src="image_47.png" /></figure>

Turning to short-term planning, production planning and scheduling aims to optimally allocate resources within a single plant, featuring detailed daily minute-by-minute plans. It encompasses two levels: aggregate production planning (APP) and short-term scheduling. APP, similar to master planning, determines production quantities, overtime work, subcontract quantities, inventory levels, backlog quantities, external purchases, and aggregated lot-sizes over a finite time horizon (Nam and Logendran 1992). The result is then disaggregated into detailed lot-sizing (Glock, Grosse, and Ries 2014) and machine schedules (Nelson 1967), aiming to fully utilise available resources. Material requirements planning (MRP-I) and its extension, manufacturing resource planning (MRP-II), are widely used for APP. While MRP-I assumes infinite capacities, MRP-II incorporates capacity constraints and integrates functions such as aggregate planning, capacity checks, and short-term scheduling (Harhen 1988). MRP-II requires a step-by-step process to plan materials and capacities, and it is sometimes difficult to generate plans that consider volatility. APSs enhance these capabilities by providing adaptive plans that apply linear programming and mixed-integer programming and allow for the visualisation of planning results. This integration of adaptive planning through APSs bridges the gap between material and capacity planning and the operational execution of production, ensuring that production control processes are more responsive and aligned with real-time changes in demand and available resources (Section 2.11).

It is crucial to recognise that planning extends beyond a company-centric perspective to include an inter-organisational dimension. In this regard, distribution and transportation planning determine optimal prod-uct flows (Fahimnia, Davarzani, and Eshragh 2018). In a typical distribution network, products from different factories are transported to distribution centres, where they are bundled for long-distance transportation to regional warehouses or transshipment points. In pro-curement networks, materials from suppliers are col-lected at regional warehouses before being shipped to factories (Amiri 2006). APSs utilise information from demand planning and master planning to address the strategic distribution network configuration, mid-term plans (e.g. shipment frequencies), and short-term trans-portation plans (e.g. routes, shipment quantities, vehi-cle loading). The distribution planning module gener-ally focuses on longer-term planning issues, while the transportation module handles daily transport activities (Fleischmann and Meyr 2003).

Using advanced information and communication
technology enhances information sharing and processing,

enabling collaborative planning, forecasting, and replen-
ishment (CPFR). In the mid-1990s, practitioners intro-
duced the CPFR concept to facilitate the exchange
of strategic decisions, demand forecasts, and produc-
tion plans between retailers and manufacturers (Holl-
mann, Scavarda, and Thomé 2015). CPFR has since
found widespread application in industries such as food,
apparel, and manufacturing (Fliedner 2003). Through
collaborative business plan development, real-time data
sharing, and future demand forecasting, stakehold-
ers along the supply chain can synchronise inventory
replenishment processes, thereby reducing inventory
costs while enhancing product availability (Barratt and
Oliveira 2001). It is important to note that the use of
advanced information and communication technology is
essential for facilitating CPFR.

The increasing computing power and advancement in digital technologies such as the Internet of Things (IoT), big data, cloud computing, and artificial intelligence (AI) are further revolutionising planning capabilities. For example, big data and machine learning can uncover complex patterns from vast datasets, enhancing demand forecasting accuracy (Carbonneau, Laframboise, and Vahidov 2008; Seyedan and Mafakheri 2020). Incorporating IoT and machine learning into planning processes allows for real-time data collection and facilitates better informed decisions in production, inventory control, and vehicle routing (Bai et al. 2023; Rolf et al. 2023). The application of machine learning is particularly promising for addressing problems with uncertainty or nonlinear properties (Esteso et al. 2023). As AI technology continues to evolve, it is expected to provide more visible, transparent, and intelligent planning solutions (Jackson et al. 2024; Rolf et al. 2023).

Planning problems are often complex due to the interplay of multiple objectives, constraints, time horizons, and decision layers. To address these challenges, numerous mathematical modelling approaches have been developed, ranging from mixed-integer (linear) programming (e.g. Bilgen and Ozkarahan 2007; Dogan and Goetschalckx 1999) to fuzzy programming (e.g. Peidro, Mula, and Jiménez 2010), or stochastic programming (e.g. Sabri and Beamon 2000), aiming to obtain optimal or near-optimal solutions. The richness of this modelling landscape reflects the diversity of planning environments, each requiring tailored formulations to capture domain-specific characteristics. Reviews by Fleckenstein, Klein, and Steinhardt (2023), Gelders and Van Wassenhove (1981), and Mula et al. (2010) provide valuable overviews of optimisation-based models that support planning.
<figure><img src="image_48.png" /></figure>

## 2.15. Scheduling¹⁶

Scheduling is the allocation of resources to tasks over time. The result is a schedule, which gives information on the start time and the completion time of each task as well as the times when resources are processing (which) tasks throughout the planning horizon. Synonyms for tasks in the literature are jobs or activities. Scheduling is one of the major and classical planning problems in operations management, see, e.g. Sections 2.4, 2.11, 2.16, and 2.18. Recently, scheduling is also addressed in supply chain management, see Amaro and Barbosa-Póvoa (2008), Chen and Hall (2022), Kreipl and Pinedo (2004), and Sawik (2011). In most cases, scheduling is a short- to mid-term planning problem, where the planning horizon stretches from a few hours to several months. Scheduling is done in manufacturing and services, see, e.g. Pinedo (2009). In manufacturing, tasks relate to physical products, which have to be processed in production facilities. In services, the main fields for scheduling problems are in transportation (e.g. trucks, which have to be (un)loaded at terminal gates, see Boysen and Fliedner, 2010, ships which have to be (un)loaded at berths, see Bierwirth and Meisel, 2010, and Bierwirth and Meisel, 2015, containers, which have to be moved by cranes, see Boysen, Briskorn, and Meisel, 2017, aircrafts, which have to use runways for starting and landing, see Ikli et al., 2021), healthcare (e.g. patients, which have to be treated by doctors, see Hall, 2012, and Youn, Geismar, and Pinedo, 2022), sports (see Kendall et al. 2010; Ribeiro 2013), and workforce scheduling (see Van den Bergh et al. 2013). See also Pinedo (2009) and Pinedo, Zacharias, and Zhu (2015) for a survey of scheduling in services.

For a general overview over scheduling as a field we refer to Błażewicz et al. (2019), Brucker (2006), Brucker and Knust (2012), Leung (2004), Pinedo (2009, 2022), and Schwindt and Zimmermann (2015a, 2015b).

### Tasks

While being processed a task occupies resources. In the most simple case the resource is occupied completely and cannot handle any other tasks in parallel. However, tasks also might seize a fraction of a resource's capacity and, if it is sufficiently small, the resource might handle other tasks in parallel. A task's processing time specifies how long it occupies the resource. In most cases, the processing time is a given parameter. In more involved settings the decision maker might have the opportunity to decide on the processing time (Gawiejnowicz 2020; Shabtay and Steiner 2007; Weglarz et al. 2011). Once the processing of a task has started it may or may not be preempted. However, processing a task is only allowed within a time

interval between its release date and its deadline. In (quite common) special cases, release dates and deadlines may not impose any relevant restrictions and we can think of them as non-existent.

### Precedence constraints

The times when tasks are processed are interdependent through the joint need for scarce resources. Hence, processing one task might restrict the freedom when to process another tasks. Another form of interdependency is precedence constraint between task pairs. The most common precedence constraint is a minimal time lag of 0 between the completion time of the predecessor task and the start time of the successor task. In its most general from, precedence constraints impose minimal or maximal time lags on the start and/or completion times of two tasks (Neumann, Schwindt, and Zimmermann 2003). General precedence constraints are powerful modelling tools, allowing to depict many settings such as two tasks, which must not be processed in parallel or are partially processed in parallel, or completion of two tasks within a given time frame, just to name a couple (Hartmann and Briskorn 2022).

### Resources

There are two predominant generic concepts in the literature: machine scheduling and project scheduling. In machine scheduling resources are typically fully occupied while processing one task. Since in this case one machine does process no more than one task at a time, we often simply seek a sequence of tasks (potentially with idle time in between consecutive tasks) on each machine. Different settings with multiple machines differ in the relation of machines. In settings with parallel machines we consider alternative resources where each task requires to be processed by one machine only. These alternative resources might differ in their processing capabilities, e. g., in their speeds, or not (Pinedo 2022). In shop settings, each task needs to be processed by each machine. The order in which machines are visited is given and identical for all tasks in a flow shop setting (Rossit, Tohmé, and Frutos 2018) given and individual in a job shop and flexible job shop setting (Dauzère-Pérès et al. 2024; Xiong et al. 2022), and to be determined for each task as part of the decision process in an open shop setting (Ahmadian et al. 2021). In project scheduling resources are capable of processing multiple tasks at a time (Hartmann and Briskorn 2010, 2022; Kolisch and Padman 2001). Processing a task induces a certain load of capacity for each resource. As far as capacities are concerned, a set of tasks can be handled in parallel if the total load does not exceed the capacity of any resource. With respect to the capacity of resources there are different concepts, which
<figure><img src="image_49.png" /></figure>

can be combined. The most frequent one are *renewable resources*, where the capacity of a resource is available in each period anew. The capacities of non-renewable resources are available only once for all periods of the planning horizon (Weglarz et al. 2011) while the capacities of partially renewable resources are only available for subsets of the periods of the planning horizon (Alvarez-Valdes, Tamarit, and Villa 2015). In most settings capacities of resources are given and might by dynamic over time or not (Hartmann 2015). However, there are problems where the capacity of resources has to be determined as part of the decision problem, e.g. the *resource investment problem* and the *resource levelling problems*, see Rieck, Zimmermann, and Gather (2012) and Part V of Schwindt and Zimmermann (2015a).

## Objectives

Naturally, finding an arbitrary feasible schedule is often not sufficient (although this might prove challenging enough) but a good or even optimal one with respect to a given objective is to be determined. While we can find a huge variety of objectives in the literature, we restrict ourselves to classic objectives in scheduling. We, first, address *time objectives* and consider *cost objectives* afterwards. The classical and most prominent scheduling objective is to minimise the so-called *makespan*, which is the last completion time among all tasks. Instead of focussing on the bottleneck task which completes last, we also might be interested in minimising the *sum of completion times* of all tasks which is equivalent to minimising the average completion time among tasks. Several objectives involve a due date associated with each task. As opposed to deadlines implied by time windows, due dates may be violated which is, however, penalised in terms of the objective. The *lateness* of a task is defined as the difference between the task's completion time and its due date. A positive lateness is termed as * tardiness* and the absolute value of negative lateness as *earliness*. The most common objective concerning lateness is to minimise the *maximum lateness* among tasks. Further objectives related to lateness are to minimise the *sum of tardiness* of tasks or the *number of tardy tasks*. For sum of completion times, sum of tardiness, and number of tardy jobs, also weighted versions are prominent where each task has a *weight*, reflecting its impact on the objective value. Minimising the weighted sum of earliness and tardiness of tasks is an important objective for just-in-time manufacturing (e.g. Józefowska 2007). In project scheduling, cost objectives are addressed in particular when the availability of capacities is to be decided. In the resource investment problem, the total *cost for buying capacity* is to be minimised while in the resource renting problem, the *renting cost*, potentially reflecting setup costs and linear costs,

are to be minimised. Furthermore, the *net present value* objective seeks to maximise the sum of discounted task costs, where tasks costs are incurred at the start or completion time of tasks (Gu et al. 2015). Of course it might be interesting to consider not only a single objective but to account for multiple objectives (T'Kindt and Billaut 2006).

## Solution methods

Scheduling problems are combinatorial in nature and the vast majority is NP-hard. Hence, classical methods for solving scheduling problems exactly are mixed-integer linear programmes (MIPs), branch-and-bound, and dynamic programming (Agnetis et al. 2025). Constraint programming (CP; Baptiste and Nuijten 2012) is a solution approach, which is particularly suited to scheduling problems. Recent results show that for certain scheduling problems, CP is superior to MIPs (Naderi, Ruiz, and Roshanaei 2023). Additionally, combining MIP and CP is a promising solution strategy (Pohl, Artigues, and Kolisch 2022). Heuristics such as priority rules and metaheuristics are used to solve large problem instances (Agnetis et al. 2025; Ruiz 2018). Furthermore, matheuristics and CP heuristics successfully combine heuristic techniques with MIP- and CP-approaches (Agnetis et al. 2025). Recent research investigates machine learning methods, most prominently reinforcement learning and deep reinforcement learning (Kayhan and Yildiz 2023; Khadivi et al. 2025). For the latter, graph neural networks are of particular interest, since the precedence constraints between tasks are naturally represented by graphs (Smit et al. 2025).

## Beyond deterministic offline scheduling

While almost all scheduling problems revolve around the components introduced above, we can distinguish different problem classes according to the nature of the information available for decision making. While in *deterministic scheduling problems* the parameters involved are not subject to any kind of stochasticity but specific numerical values are known, in *stochastic scheduling problems* one or more parameters are stochastic (Cai, Wu, and Zhou 2014). When we encounter stochastic parameters, *robustness* of schedules becomes an interesting feature (Kouvelis and Yu 1997). Robustness can be addressed with respect to feasibility of the schedule and/or the achieved objective value. In *offline problems* all parameters (stochastic or not) are revealed beforehand while in *online problems* some or maybe even all tasks or their parameters are revealed over time (Albers 2009; Robert and Vivien 2009). In stochastic settings or in online settings the goal often is not to determine a full schedule
<figure><img src="image_50.png" /></figure>

immediately. Instead, a policy is determined which constructs a schedule over time when tasks or their parameters are revealed.

## 2.16. Project management¹⁷

The work done by individuals, teams, and organisations falls along a spectrum, from repetition of identical tasks to the invention of new ones (Browning 2017; Hayes and Wheelwright 1984). While operations management (OM; Section 2) pertains to the management of all such work, project management (PM) is a subset dealing with the latter end of the spectrum – where a ‘temporary’ set of tasks must be ‘undertaken to create a unique product, service, or result’ (PMI 2021, 245). That is, PM is a discipline that involves planning, organising, securing, managing, leading, and controlling resources to achieve specific goals within a defined timeline (Browning 2017; Davies and Hobday 2005). It is a structured approach to guide a project across its lifecycle from its inception through to its completion (Meredith, Shafer, and Mantel 2021). Because PM involves so many aspects of management, PM techniques naturally draw upon numerous areas of general management theory and other management areas (e.g. innovation; Davies, Manning, and Söderlund 2018), yet key aspects of PM theory tend to emerge from the temporary and unique characteristics of project work.

The importance of PM to public, private, and not-for-profit organisations as well as whole industries and governments cannot be overstated, given its significant economic and social value creation (Roehrich et al. 2024). Economically, effective PM – characterised by ensuring that resources are utilised efficiently, objectives are met within budget and on schedule, and the quality of the deliverables is maintained – strongly contributes to higher productivity, reduced costs, and enhanced profitability. From a societal and social value perspective, PM may lead to improved infrastructure, better services (Section 2.21), and overall societal advancement by, for example, developing skillsets through apprenticeships or upskilling small- and medium-sized enterprises (SMEs; Section 5.8) in deprived regions (Kalra and Roehrich 2019).

Conversely, poor PM may have severe consequences, including cost overruns, delayed timelines, and subpar quality, resulting in an organisation's or government's financial losses, wasted resources, and reputational damages (Bendoly and Swink 2007; Maylor et al. 2018). High-profile project failures such as the Denver International Airport's baggage handling system serve as reminders of the implications of poor PM. These project failures are often caused by poor planning, miscommunication or

lack of collaboration between (key) stakeholders, and/or scope changes, highlighting the vital need for robust and continuous (across the project lifecycle) PM practices by all project stakeholders – individuals, groups, and/or organisations that have an interest in or are affected by the outcome of a project (Donaldson and Preston 1995).

The history of traditional PM tools and frameworks such as the Gantt chart and Work Breakdown Structure (Gantt 1919; Miller 2008) traces back to the early 20th century, with the advent of complex industrial and engineering projects necessitating more systematic approaches. However, it could be argued that early roots can be seen in the construction of the Egyptian pyramids and the Great Wall of China, where rudimentary PM principles (rather than tools) were employed (Cleland 2004). Modern PM began to take shape during the 1950s with the development of methodologies like the Critical Path Method (CPM; Meredith, Shafer, and Mantel 2021) and Program Evaluation and Review Technique (PERT; Malcolm et al. 1959). These methodologies formalised the way the ‘triple constraint’ of projects – time, cost, and quality – was planned and managed.

Over the last decades, PM principles have expanded beyond engineering and construction to other sectors such as healthcare and information technology, often spanning public and private organisations (Chakkol, Selviaridis, and Finne 2018; Roehrich and Kivleniece 2022). Prior PM scholars have drawn attention to the fact that we are experiencing an ongoing ‘projectification’ of work (Midler 1995), where economic activities are increasingly delivered via projects. The establishment of professional bodies, such as the Project Management Institute (PMI) and the Association for Project Management (APM), and the emergence of PM degrees, modules, courses, and programmes at (higher) educational institutions further normalised the discipline, offering standardised guidelines, certifications, and a shared body of knowledge. PMI’s Project Management Body of Knowledge (PMBOK) Guide has provided a framework that has since been continuously updated since the 1980s (PMI 2021). This development was also further supported by an increasing number of academic scholars researching various aspects of PM (e.g. Davies and Hobday 2005; Morris 1994; Söderlund 2011).

Technically, PM encompasses various models, frameworks, and tools designed to optimise project execution. Most such tools assume that project activities and their relationships can be specified in advance and thus modelled as an activity network, from which schedules, resource-loading profiles, and other decision-support views may be derived and optimised (Browning 2010).
<figure><img src="image_51.png" /></figure>

However, scholars and practitioners have recently ques-
tioned the underlying assumptions of project predictabil-
ity that enables detailed planning and optimisation. Some
aspects of unpredictability can be anticipated, such as
the typical failure modes causing rework (e.g. Eppinger
and Browning 2012) and other project risks (e.g. Hill-
son and Simon 2020), whereas others, called ‘unknown
unknowns’, can render some detailed planning moot
(e.g. Ramasesh and Browning 2014). On the other hand,
Agile PM methodology, which emerged in the soft-
ware industry, promotes iterative development, flexibil-
ity, and customer collaboration (e.g. Highsmith 2009).
Agile methods, such as Scrum, focus on delivering incre-
mental value and adapting to changing requirements.
Agile’s iterative cycles, known as sprints, allow teams to
review progress and replan between sprints in response
to evolving customer needs.

Apart from the more technical considerations of PM,
behavioural, sociocultural, and sociopolitical aspects of
PM are equally crucial. Here, effective interpersonal and
interorganisational relationships are the bedrock of suc-
cessful project execution, including integrated project
teams (Roehrich et al. 2019) and relational coordina-
tion and cooperation (Roehrich et al. 2023; Taubeneder
et al. 2024). Stakeholder management (Section 3.7) is
vital to ensure that all parties involved are aligned with
the project's goals, and their expectations are man-
aged appropriately from project front-end (Lewis 2023)
to transition to the operations phase (Zerjav, Edkins,
and Davies 2018). Dynamics between members of the
project team also play a critical role in project success.
Project managers and leaders must possess strong inter-
personal skills, including communication, negotiation,
and empathy, to effectively lead diverse teams to fos-
ter a collaborative environment, manage conflicts con-
structively, use nudges to drive performance, and ensure
learning across projects (e.g. Brady and Davies 2004;
Bukoye et al. 2022; Mishra, Chandrasekaran, and Mac-
Cormack 2015). Power dynamics (between team mem-
bers, and/or organisations), as well as (organisational)
politics and culture can influence project outcomes sig-
nificantly (e.g. Clegg and Courpasson 2004). Project
managers and teams must navigate these complexities,
balancing the interests of different stakeholders while
maintaining focus on the project goals and objectives.

Emerging themes in current PM research highlight
the growing complexity and scale of projects (Harri-
son et al. 2024). Large interorganisational (or mega-
) projects (LIPs; Denicol, Davies, and Krystallis 2020;
Flyvbjerg 2014; Roehrich et al. 2024) are deployed for
infrastructure developments and major technological
implementations, and bring significant economic and
social value, but also pose substantial challenges such as

managing cooperation between large, often competing,
firms (Taubeneder et al. 2024) or public and private
organisations with different objectives (e.g. Roehrich and
Kivleniece 2022). These projects require sophisticated
management techniques to address their scale, complex-
ity, uncertainty, resource constraints, risks, and impact
(Browning 2019; Geraldi, Maylor, and Williams 2011;
Pich, Loch, and Meyer 2002; Ramasesh and Brown-
ing 2014).

The role of emerging technologies (Section 4.8.2), digitisation (Section 3.2), and data in PM are other critical areas of research and practice. Advances in data analytics, artificial intelligence (AI), and digital tools are transforming PM practices (Müller et al. 2024; Whyte 2019). Data analytics enables project managers to derive insights from project data, facilitating better decision-making and risk management. AI-powered tools can automate routine tasks, such as scheduling and progress tracking, allowing project managers to focus on strategic activities. Similarly, Building Information Modelling (BIM) is revolutionising PM in the construction industry by providing detailed 3D models that integrate design, construction, and operational information (Volk, Stengel, and Schultmann 2014).

In conclusion, PM is a vital discipline that encom-
passes technical, sociocultural, and emerging aspects to
ensure the successful completion of projects. From its
historical roots to its modern methodologies and tools,
PM continues to evolve, addressing the growing com-
plexities of contemporary projects. Effective PM drives
economic and social value, mitigates risks, and ensures
that resources are utilised optimally to achieve the desired
outcomes. Through continuous innovation and adapta-
tion, PM will remain a critical enabler of progress and
development for individuals, organisations, industries,
and governments. However, PM is fraught with many
interesting challenges and open questions, leaving plenty
of opportunities for exciting and impactful research at the
intersection of academia, practice, and policy.

2.17. Programme management¹⁸

Programme management is often positioned in the
project management literature, highlighting the man-
agement of projects, programmes and portfolios (Mor-
ris 2013; Morris, Pinto, and Soderlund 2011). Project
management is often concerned with the achievement
of traditional performance metrics (time, cost, quality),
whilst programme management incorporates connec-
tions with a more strategic level of organisations, exter-
nal stakeholders, and wider society (Artto et al. 2009;
Rijke et al. 2014). The programme management domain
is the integration of multiple temporary organisations