# Modelling Interdependencies Within Production Planning and Control: An Application-Motivated Approach

Alexander Mütze, Simon Hillnhagen, Matthias Schmidt, Peter Nyhuis

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Alexander Mütze, Simon Hillnhagen, Matthias Schmidt, Peter Nyhuis. Modelling Interdependencies Within Production Planning and Control: An Application-Motivated Approach. IFIP International Conference on Advances in Production Management Systems (APMS), Sep 2022, Gyeongju, South Korea. pp.518-525, 10.1007/978-3-031-16407-1_61. hal-05386140

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# Modelling Interdependencies Within Production Planning and Control: An Application-Motivated Approach

Alexander Mütze<fnref n="1" />✉, Simon Hillnhagen<fnref n="2" />✉, Matthias Schmidt<fnref n="2" />✉, and Peter Nyhuis<fnref n="1" />✉

**Abstract.** In literature on the investigation of cause-effect relationships within production planning and control (PPC), many models and approaches can be found. These range from the didactic description of cause-effect relationships to generally applicable models for describing the effects and impacts of a procedure selection or parameterisation for a PPC task to be fulfilled, right up to explorative simulation studies. Thus, research in the field of production planning and control can be roughly divided into the research areas of conceptual, analytical, empirical and simulation-based investigations.

While each of these approaches makes valuable contributions to prevailing theory, the purpose of this paper is to discuss an application-motivated approach making the complex network of interrelations within PPC easier to penetrate. Because, in particular from the point of view of the practical user, it is of crucial importance to gain a holistic perspective on the relationships and interdependencies within PPC in order to be able to configure it - as well as the entire production system - in the best possible way and in line with the company's objectives. Thus this contribution can be assigned as a conceptual investigation.

**Keywords:** Production planning and control · Modelling · Production management · Production organisation · PPC

## 1 Introduction

Several studies show that in industrial practice, there is still a lack of understanding of the concrete impact of PPC tasks and procedures on the logistical

Funded by Deutsche Forschungsgemeinschaft (DFG) - 434659386.

<footnote n="1">¹ Institute of Production Systems and Logistics, Leibniz University Hannover,
Garbsen, Germany
{muetze,office}@ifa.uni-hannover.de</footnote>

<footnote n="2">² Institute of Product and Process Innovation, Leuphana University Lüneburg,
Lüneburg, Germany
{simon.hillnhagen,matthias.schmidt}@leuphana.de</footnote>
objectives [1, 4, 19]. At the same time, however, the acceptance of automated
PPC solutions, i.e. solutions that in principle relieve the user of the need to
understand the complex interdependencies within PPC, is relatively low [1].
Also, market analyses show that the majority of respondents are not satisfied
with the process and organisation of their production planning (system) and
indicate that the most common problem lies in maintaining a high degree of
schedule compliance [4]. The question that arises is thus how the organisation
and the process, or overall the configuration of the entire PPC, can be improved
to achieve the market goals and ensure the company's profitability.

To tackle this question, there are generalised two points of view on the over-
arching topic of PPC and production organisation. While one stream tries to
increase further the system understanding concerning processes and interactions
by building models to describe processes, principals and interrelationships based
on knowledge and (physical) relationships (also referred to as white-box mod-
elling), the other stream, more or less assumes that further research in the field
of system understanding is more of a dead-end and focus their research activities
on topics such as digital twins, AI algorithms, and others (also referred to as
black-box modelling) (cf. [5] and [7]).

At this point, this discussion will not be taken up in-depth, but from the
authors' point of view, it is crucial to understand which fundamental interactions
exist within PPC and how the PPC configuration embeds itself in the overall
configuration of production [12]. Thus white-box modelling and in-depth research
of fundamental effects are necessary prerequisites for more advanced approaches
on the one side, and on the other side, essential for the practical user to gain a
clear system understanding.

This contribution is therefore based on the following proposition:

**Proposition 1.** Insight must precede application (Max Planck) - A valid understanding of the processes and interactions in PPC is a fundamental prerequisite for both in-depth white-box modelling and the architecture of black-box-based PPC models, algorithms and systems.

## 2 Evolution Within the Research Field PPC

Production planning and control has been researched for many decades and
has been continuously refined [10,13]. Significant milestones have been the
more technical models of Material Requirements Planning (I+II) according to
ORLICKY [14] respective WIGHT [20], as well as Hierarchical Production Plan-
ning (HPP) and Advanced Planning Systems (APS) [9], but also conceptual or
descriptive frameworks such as the Aachen PPC model [18], the manufacturing
control model according to LÖDDING [6] and the Hanoverian Supply Chain Model
(HaSupMo) [17]. The latter is the basis for this contribution due to the integra-
tion of the PPC tasks along the internal supply chain with impact modelling
along a company's internal supply chain, i.e. generally speaking, a combination
of the modelling approach of the Aachen PPC model with the modelling logic
according to LÖDDING.
Through this previous work, a large body of knowledge exists covering, among other things, the question of the tasks to be carried out, the interfaces between PPC and core processes as well as system-theoretical questions about the appropriate degree of integration and the planning hierarchy when carrying out the individual tasks. Among others, a profound overview can be found in [12].

Looking further into the current research landscape, several trends can be identified. Thus scheduling in the context of integration of planning tasks appears as one of them [3]. Furthermore, the trends toward a smarter and more reactive PPC and the exploration of the use of machine learning and artificial intelligence (e.g. reinforcement learning [15]) can be identified, which, presumably, will end in an automated PPC (cf. [8]). The influence of the “simplexity” megatrend can thus be seen, which refers to the straightforward, intuitive operability and thus user-friendliness of simultaneously (e.g., technically) complex systems [2].

## 3 Research Question and Modelling Principles

Although digitisation significantly impacts PPC, the basis for decision-making is always a valid understanding of interrelationships and interactions. This is particularly important for smaller companies, which cannot rely on highly developed digital solutions for PPC because they lack sufficient data basis regarding quality and/or quantity. Therefore, a broad knowledge base remains essential for mastering and improving the production system.

Thus, this paper follows the **central research question**, how a modelling approach can look like, allowing in practical application to get a comprehensive overview of the interactions within PPC and reducing at the same time the high complexity in order to be easily applicable.

In order to be able to describe the interactions within the PPC in the following and to illustrate the approach, a basic description framework has first to be defined, showing which influencing factors and which output factors exist. Particularly in the range of the PPC, in which a multiplicity of complex interactions exist, it is therefore important to use uniform semantics.

For this purpose, the following definition is applied in this article:

**Definition 1.** *Logistical objectives are determined by control variables, each resulting from the derivation of so-called actuating variables. Actuating variables, in turn, are determined by the PPC tasks, whereby the PPC procedure selected in each case determines the exact influencing effect on the actuating variable. (based loosely on Lödding [6])*

Thus, it can basically be said that the modelling logic starts with a PPC task and moves from the organisational level to the process level via the selected procedure and the influenced actuating variables, control variables and objectives.

To tackle the research question, the following two main modelling views are introduced, followed by the presentation of the developed application-oriented, integrated approach iteratively combining both views.
# 4 Modelling Views on the Interdependencies Within PPC

Within PPC, a wide variety of interactions exists, both at individual levels (horizontal) and across levels (vertical), making the overall PPC system a complex network of effects and posing an immense challenge to practitioners. Thus, central aspects in modelling are which targets a company pursues, which tasks affect these targets and, if possible, how exactly individual procedures of a task have an effect. Figure 1 illustrates these levels of consideration through a hierarchisation using the production control task sequencing as an example.

<figure><img src="image_3.png" /><figcaption>Fig. 1. Levels of consideration towards interactions within PPC (based on [11]).</figcaption></figure>

From a practical point of view, there are generally two central questions or perspectives in the context of PPC modelling and configuration. On the one hand, the question arises how, starting from an unsatisfactory logistical performance, possible levers (PPC procedures and their parametrisation) can be found to counteract this. This viewpoint is referred to in the following as objective-centred (see Fig. 2 left). On the other hand, however, the question can be asked as to what potential the use of a particular PPC procedure has for the logistical achievement of objectives. This viewpoint is referred to as task- and procedure-centred (see Fig. 2 right). Both views are briefly explained in the following.

## 4.1 The Objective-Centred Modelling View

In the objective-centred modelling view, the focus is clearly on the logistical objectives of the core processes along the company's internal supply chain. This means that the question is posed *via which actuators and which cause-effect relationships a positive or negative effect on the objectives can be achieved*. In industrial practice, the starting point for this is often a poor logistical performance, which is traced back to the variables to be changed, e.g. using a so-called root-cause analysis (cf. [16]), subsequently enabling the target-oriented selection of a PPC procedure.
<figure><img src="image_4.png" /><figcaption>Fig. 2. Views on modelling interdependencies within PPC from a practical perspective.</figcaption></figure>

## 4.2 The Task- and Procedure-Centred Modelling View

The task- and procedure-centred modelling view aims at understanding which effects a PPC task or a specific procedure of a PPC task, e.g. the setup-optimal sequencing at work systems, finally has on the logistical objectives. As illustrated in Fig. 2 right, it is therefore considered how the cause-effect relationships start from the configured PPC task via the actuating and control variables to the influenced objectives. The central question is, therefore: *How does a PPC task/procedure affect the logistical target achievement?*

## 5 Integrative Application-Oriented Approach

Considering the two approaches presented, these provide proper results for their respective underlying problem in their “pure form”; however, neither provides a sufficiently comprehensive perspective to support holistic and target-oriented PPC configuration decisions in practice. As indicated in Fig. 2 for the objective-centred view, the direction of investigation and focus exclude possibly important cause-effect relationships from consideration. Thus, the it lacks a loopback from the PPC procedure to be selected to other affected actuating and control variables and objectives. Similarly, for the task- and procedure-centred view, even though the (direct) effect of a PPC procedure on the objectives is examined, no backtracking to possibly similarly acting or indirectly attacked PPC tasks and procedures as well actuating and control variables is conducted.

In order to meet these challenges, different possibilities are conceivable. One option is to develop a comprehensive model that includes all possible interactions between PPC procedures, tasks, actuating and control variables and objectives. A first example of such a model was presented by [12]. Although this offers a comprehensive view, the practitioner has to deal with an extensive network of interactions with the high probability of being unable to handle this complexity.
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Integrative application-oriented approach using iterative loopbacks</figcaption></figure>

For this reason, an integrative approach of the two modelling views based on iterative loopbacks is proposed for practical application, as shown in Fig. 3. As the figure shows, the two modelling views are linked together with a loopback, resulting in two new modes of observation, the iterative object-centred modelling view and the iterative task and procedure-centred view. Through the respective loopback using the prior opposite perspective, a previously existing blind spot of interactions can be included in the observation, whereby the interactions can be considered not only along the ordinal viewing direction but also on the first level of the respective view, resulting in a more comprehensive view. In the iterative objective-centred view, the effect of a possible lever (PPC procedure) on other objectives can be included in the consideration. In the iterative task- and procedure-centred view, there is a loopback to consider possible PPC tasks and procedures that are also affected or have a similar effect on related objectives.

A second essential basis supporting this integrative approach is the knowledge of the hierarchical structure within PPC itself, shown by Fig. 4.

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Planning stages to visualize the hierarchical cause-effect relationships in PPC.</figcaption></figure>
As shown in the figure, the influence of PPC on the objectives can be seen as a kind of layer model, with the outermost layer (referred to as planning stage) setting the guard rails or the degree of freedom for the next layer (as can be seen highly generalised in terms of scheduling and capacity planning). By being aware of these comparatively simple hierarchical relationships and their ultimate effect on the logistical objectives, the PPC configuration can also be improved and a greater awareness of interactions and dependencies is encouraged.

# 6 Conclusion

The presented, application-oriented integrative approach for modeling interactions within PPC closes the gap of previous, complex models and provides a procedure for the practical user, which allows him to overview the consequences of decisions within the configuration of PPC. By this, it is expected that possible loopbacks, which, e.g. come along with the decision for or against a procedure, are better overlooked and foreseen. Furthermore, the presented approach fits seamlessly into the existing theory for modelling PPC and thus provides a complement to current (frame-) works. By combining the knowledge of the planning stages within PPC, it can also be assumed that better decisions can be made in practice in terms of a holistic and target-oriented PPC configuration.

The presented approach is a conceptual model which has been developed based on various experiences of the authors in industrial practice. A comprehensive evaluation of the approach in practice is currently pending and represents the central limitation of this contribution. However, the approach opens up several possibilities for future research activities: it can be integrated into existing frameworks; also, further research should be done on the simple, practice-oriented PPC configuration, especially to support structural decisions and improve the logistical target achievement of companies.

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