# Influence of Collaboration in Sustainable Manufacturing Networks

Paula Graça, Luis M. Camarinha-Matos

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Paula Graça, Luis M. Camarinha-Matos. Influence of Collaboration in Sustainable Manufacturing Networks. 23th Working Conference on Virtual Enterprises (PRO-VE), Sep 2022, Lisbon, Portugal. pp.3-17, 10.1007/978-3-031-14844-6_1 . hal-04642028

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# Influence of Collaboration in Sustainable Manufacturing Networks

Paula Graça<sup>a,b</sup>, Luis M. Camarinha-Matos<sup>a</sup>

<sup>a</sup> School of Science and Technology and Uninova-CTS,
NOVA University of Lisbon, Campus de Caparica, 2829-516 Caparica, Portugal

<sup>b</sup> Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa,
Rua Conselheiro Emídio Navarro 1, 1959-007 Lisbon, Portugal
paula.graca@isel.pt, cam@uninova.pt

**Abstract.** Recent trends towards Industry 5.0 focus on a sustainable and resilient industry, aiming to make technology and innovation more focused on humans and today's societal concerns. Consequently, this trend also leads to more sustainable and resilient manufacturing, for which collaborative networks play a main role due to the needed involvement of multiple players, being important to consider a perspective of co-responsibility. Establishing adequate performance indicators to assess how collaborative manufacturing ecosystems can support sustainability is thus relevant. Furthermore, this work also analyses how such performance indicators can be used as an influencing factor contributing to improving the players' behaviour, representing the idea of co-responsibility for a more sustainable manufacturing network. This article proposes a set of performance indicators and a related simulation model to set up several scenarios to analyse how collaboration can influence sustainability in horizontal manufacturing networks. Results from simulation scenarios are included and discussed.

**Keywords:** Collaborative Networks, Sustainable Manufacturing, Performance Indicators.

## 1 Introduction

Recent trends towards Industry 5.0 aiming at a more sustainable and resilient industry are pushing the manufacturing sector engaged in the digital transformation to focus more on human and societal concerns. As a result, the notion of sustainable manufacturing is becoming more relevant in recent years [1]. To this end, the discipline of Collaborative Networks (CNs) plays an essential role in the collaborative perspective of the multiple stakeholders involved, which need to share co-responsibility in the achievement of such sustainability and resilience [2]. This evidence is agreed by various authors arguing that to address the challenges of sustainability: (i) there must be new strategies for organisations to collaborate with suppliers, customers and other stakeholders to fulfil not only their economic, social and environmental responsibilities but also to gain competitive advantages [3]; (ii)
there is a need for the development of structures and processes for collaboration to
achieve individually and collectively business sustainability [4]; and (iii) broader
collaboration is needed, as the changes required to go beyond the capacity and
capability of individual actors [2].

Sustainability is defined at the intersection of financial, social, and environmental “health” [4], and thus sustainable manufacturing encompasses these three dimensions. For its effective implementation, CNs and, more specifically, business communities (or business ecosystems) can offer important insights due to the interactions, interdependencies and co-responsibility of the actors involved regarding the underlying challenges [1]. As such, we propose that the establishment of adequate performance indicators to assess how collaborative manufacturing ecosystems (CMEs) can support sustainability in horizontal manufacturing networks is a critical issue. Furthermore, a simulation model to analyse how such performance indicators can influence the ecosystem’s players in contributing to improving their behaviour is also proposed. This influence relates to the idea of co-responsibility for a more sustainable manufacturing network. Various simulation scenarios are then characterised, established, and discussed.

The remaining sections of this article are organised as follows: section two presents the research approach, identifying the research question and hypothesis; section three explains the structure of the simulation model to represent a CME, including the embedded performance assessment and the influence mechanism; section four, presents several simulation scenarios discussing the results; the last section concludes identifying limitations of the study, and ongoing and future work.

## 2 Research Approach

This research work focuses on assessing the players' collaboration in horizontal
manufacturing networks and influencing their behaviour, expecting to improve the
network's sustainability. We do this by means of an Information System (IS) design
artefact in the form of a simulation model, which positions our research in the design
science research (DSR) paradigm [5]. DSR tries to focus human creativity on
designing and building artefacts that have utility in application environments [6].

Design science was conceptualised by Simon [7] as a research paradigm that pointed to the need to create artefacts to solve real-world problems as a means for the production of scientific knowledge from an epistemological point of view. Adapting this thinking as well as the design research of other fields to the unique context of IS design research [6], the authors [5] came out with a conceptual framework for understanding IS research and a set of guidelines for conducting and evaluating good DSR. DSR seeks to develop prescriptive design expertise by building and evaluating innovative information technologies (IT) artefacts aimed at solving a class of identified problems [5] or shown to have utility [8]. DSR thus deals with a wide range of "socio-technical" artefacts, such as decision support systems, modelling tools, governance strategies, and IS evaluation methods [6].

To conduct this research, we adopted the methods and guidelines of Hevner et al.
[5] that support researchers in bringing a rigorous scientific design research process
[6] in which the three DSR cycles (Fig. 1) must be present and clearly identifiable [9]. Based on the identified research gaps, we developed an artefact, the Performance Assessment and Adjustment Model (PAAM), to evaluate a CME through simulation, to understand how the assessment of collaboration using a set of adopted performance indicators (with a given associated importance, i.e., a weight that can vary), can influence the behaviour of the players, contributing to improving the sustainability of the ecosystem.

<figure><img src="image_3.png" /><figcaption>Fig. 1 – DSR cycles of the research approach. Adapted from Hevner and Chatterjee [9, 6].</figcaption></figure>

## 2.1 Relevance Cycle

DSR starts with the Relevance Cycle, i.e. “the opportunity/problem to be addressed in the application domain as input and the acceptance criteria for evaluating the research results” [9]. The application domain of this work is in the area of horizontal manufacturing networks, referred to in this article as CMEs, and the problem is identified and expressed by the following research question:

*“How can performance assessment methods based on economic and social values promote sustainability in a CME?”*

The following corresponding hypothesis guides the research:

*“Performance indicators are a helpful mechanism for assessing a CME if they can contribute as a factor of influence for the stakeholders to evolve by self-adjusting their behaviour, thereby improving the ecosystem's performance and sustainability.”*

The primary grounding theories that underlie this research are the benefits of collaboration, the methods and mechanisms to evaluate that collaboration and sustainability. Collaboration thrives on divergent thinking for innovation, solving problems, developing new understandings, designing new products [10], and reducing or eliminating conflicts [11].
## 2.2 Design Cycle

The Design Cycle is the core of a DSR project, consisting of an iteration between the construction of the designed artefacts to find practical solutions for the identified opportunity/problem and their evaluation [5]. As such, to address the research question, we propose a novel artefact in the form of a simulation model designated by PAAM. The PAAM includes a Performance Assessment element composed of a set of performance indicators and an Influence Mechanism hoping to assess and influence the collaboration behaviour of the stakeholders in a CME, leading to improved performance and sustainability. The artefact evaluation process includes establishing several simulation scenarios using hypothetical data to characterize the organisations' profile and human resources used to handle collaboration opportunities.

## 2.3 Rigor Cycle

The Rigor Cycle provides the grounding theories, i.e., the experiences and expertise that represents the state-of-art in the application domain, connecting DSR activities with the “knowledge base” of the scientific foundations [5]. Thus, according to the purpose of this work, the main areas of research considered are Sustainable Manufacturing, CNs (including studies of collaboration benefits and value systems), Supply Chain Collaboration (SCC), and Social Network Analysis (SNA).

"Sustainable manufacturing is no longer just nice-to-have, but a business imperative" [12]. As manufacturing faces challenges of global resource depletion, climate change and pollution [13], many organisations have started to move to green growth, ensuring economically and environmentally sustainable development [12]. To address these concerns, the "Organisation for Economic Co-operation and Development" (OECD), in the assumption that performance measurement "is a vital first step to improvement", initiated the project OECD Sustainable Manufacturing Toolkit to provide a set of indicators internationally applicable to measure the environmental performance of manufacturing facilities [12].

On the other hand, the potential benefits of collaboration have extensive evidence in the literature, notably in the research area of CNs [14], in which the work on benefits analysis for CNs, value systems to promote sustainability in CNs, and a proposal of performance indicators for CNs [15, 16, 17] are examples, and whose concepts, methods and tools can strengthen the relationships of the multiple stakeholders who are the influential players in sustainability efforts [2].

The area of Inter-organisational Networks, a sub-area of collaborative networks, studies networks of organisations (linked to facilitate the achievement of a common objective) at the network level, emphasizing the whole network [18]. Moreover, collaboration through an inter-organisational network corresponds to an approach increasingly used to improve competitiveness and disaster preparedness, among other benefits [18].

The area of SCC, in which several works highlight collaboration as a means to improve performance in traditional supply chains [19, 20], provides a rich set of performance measures and metrics [21, 22, 23] and suggests that the success of collaboration leads to long-term future collaboration contributing for sustainable businesses [24].
Inspired by the motivations for sustainable manufacturing [12], combining the views of the above research areas with the social capital metaphor of a network structure [25] and concepts and measures of SNA [26, 27], complemented by the concepts of social and economic networks [28], we gathered the needed foundations to design the PAAM.

## 3 Performance Assessment and Adjustment Model

Networked structures arise in several contexts, such as the example of collaborative networks in the social context. Their topological structures show great heterogeneity in the connections' intensity, which can be represented in a graph by a weight proportional to such intensity [29]. Moreover, the analysis of the weights and the correlation between weights and the network topology gives complementary insights to understanding the architecture of real weighted networks [29]. Following this rationale, a CME can be modelled as a network of organisations or players (the nodes) connected by relationships (the links) that mean the market opportunities in which they participate, called collaboration opportunities (*CoOps*). The links are weighted by the number of collaboration opportunities (*#CoOps*) they participated in during a period. Fig. 2 shows the conceptual view of the CME simulation model designated for PAAM.

<figure><img src="image_4.png" /><figcaption>Fig. 2 – Conceptual view of the PAAM.</figcaption></figure>

A zoom-in of the agent shown in Fig. 2 shows the conceptual behaviour of an agent: when a new opportunity arises in the CME, the receiver can decide to invite a partner to collaborate. When the receiving partner receives the invitation, he may decide to accept it if he has available resources, creating a new relationship called *CoOp*.
## 3.1 Profile of the Organisations

Organisations have different profiles corresponding to a diversity of levels of collaboration willingness, which characterise their collaborative behaviour to be involved in relationships with the other players. As implicit in Virtual organisations Breeding Environments, the notion of business ecosystem facilitates the organisations' preparedness for being involved in collaboration in potential VOs and induces a perception of co-responsibility of all actors involved [2] regarding the sustainability challenges [1].

In the CME model, each profile consists of a set of attributes, e.g. *contact rate*, *accept rate*, and *sustainability index*, whose values (decimals between 0 and 1) represent a collaboration intensity factor, i.e., the “propensity to collaborate” by inviting other partners within the CME, the tendency to accept the invitations, and an intensity of sustainability according to the main facets: environmental, economic, and social [12]. Fig. 3 illustrates four different hypothetical profiles displayed in the form of radar charts.

<figure><img src="image_5.png" /><figcaption>Fig. 3 – Example profiles of the organisations involved in the CME, which are classified into four classes of “collaboration willingness” (A, B, C and D), displayed using radar charts showing the *contact rate* (Cr), *accept rate* (Ar), and *sustainability index* (Si).</figcaption></figure>

## 3.2 Performance Assessment

Establishing metrics that combine weighted and topological structures enables characterising the statistical properties of the links and nodes of the network [29]. Social and economic network analysis provides important insights based on network structure [26, 27, 28] and has been applied in many research areas such as CNs [30, 17, 15, 16, 31] and, more specifically, on Inter-organisational Networks [32, 18, 25, 33, 34]. In particular, measures of centrality and density allow the comparison of nodes providing information about how a given node relates to the whole network and describing the general characteristics of a network [26, 27, 28]. Several authors defined prestige and power of the nodes in a social network based on centrality measures [28].

On the other hand, some authors have interpreted network structures as social capital: identifying structural holes (absence of connections between groups, measured as a structural hole centrality [35]) as a competitive advantage for those who fill the holes by offering connections between separated or sparsely interconnected groups [25], network closure (related to dense networks) as a mean to
facilitate access to information to improve communication [25], denser organisational networks likely to have more frequent innovations [33]. The strength of the ties (strength of social relationships) is seen as a measure of the frequency of the interactions during a period of time [36], also calculated by the frequency of the interactions among organisations [33].

Finally, doing business by adopting good environmental practices is increasingly critical in the eyes of all ecosystem players, bringing reputation, attracting investment, stimulating innovation, and securing loyal customers [12]. Well established indicators contribute to measuring, tracking, and improving performance [12]. Table 1 shows an example adapted from [12] of quantitative metrics to measure environmental performance in the three stages of manufacturing: raw materials, operations and products. Organisations can adopt the most relevant metrics according to the environmental and business impact and normalise the values using other peers' same normalisation factors (NFs). The CME manager can provide standard factors.

<table><caption>**Table 1** – Example of environmental sustainability metrics for sustainable manufacturing (adapted from [12]).</caption><thead><tr><th colspan="5">Environmental sustainability metrics</th></tr><tr><th></th><th>Raw materials</th><th colspan="2">Operations</th><th>Products</th></tr></thead><tbody><tr><td>R<sub>1</sub></td><td>Non-renewable materials intensity</td><td>O<sub>1</sub></td><td>Water intensity</td><td>P<sub>1</sub> Recycled/reused content</td></tr><tr><td>R<sub>2</sub></td><td>Restricted substance intensity</td><td>O<sub>2</sub></td><td>Energy intensity</td><td>P<sub>2</sub> Recyclability of products</td></tr><tr><td rowspan="3">R<sub>3</sub></td><td rowspan="3">Recycled/reused materials</td><td>O<sub>3</sub></td><td>Residuals intensity</td><td>P<sub>3</sub> Renewable materials content</td></tr><tr><td>O<sub>4</sub></td><td>Air releases intensity</td><td>P<sub>4</sub> Greenhouse gas emission intensity</td></tr><tr><td>O<sub>5</sub></td><td>Water releases intensity</td><td></td></tr></tbody></table>

The metrics to evaluate the organisations, i.e., the players in a CME, as described in Table 2, were defined assuming the above assumptions, thus relying mainly on measures of density, centrality, and links' strength. Based on the metrics defined in Table 2, we propose a set of performance indicators that allow the individual evaluation of CME's organisations (players) in terms of collaboration and the CME globally.

Table 3 describes the indicators and respective calculation formulas of the individual organisations (players), and Table 4 shows the same information but considering the CME as a whole. In short, the indicators here used are the Contribution Indicator (CI), to account for the organisations that create the most opportunities for collaboration in the CME; the Prestige Indicator (PI), to account for the organisations that stand out as being involved in “collaboration opportunities” in the CME; and the Sustainability Indicator (SI), to measure the sustainability commitment and practices in the CME. The values of these indicators are normalised in the scale [0..1].
<table><caption>**Table 2** – Metrics to evaluate the organisations (players) in a CME, individually and as a whole.</caption><thead><tr><th colspan="2">Metrics of the organisations (players) in a CME</th></tr><tr><th>Metric</th><th>Description</th></tr></thead><tbody><tr><td>O<sub>1</sub>..O<sub>n</sub></td><td>Organisations in the CME</td></tr><tr><td>#CoOp<sub>i</sub> in</td><td>Number of collaboration opportunities O<sub>i</sub> caught from the CME</td></tr><tr><td>#CoOp<sub>i</sub> out</td><td>Number of collaboration opportunities O<sub>i</sub> brought to the CME</td></tr><tr><td>#CoOp<sub>i</sub></td><td>Number of collaboration opportunities in which O<sub>i</sub> had relationships in the CME</td></tr><tr><td>#CoOp<sub>kj</sub></td><td>No. of collaboration opportunities between O<sub>k</sub> and O<sub>j</sub> in the CME</td></tr><tr><td>C<sub>D</sub>(O<sub>i</sub>) in/out</td><td>Weighted indegree/outdegree centrality (C<sub>D</sub>) of O<sub>i</sub> in the CME, meaning the sum of direct connections in/out of O<sub>i</sub> to the others O<sub>j</sub>, with weight #CoOp<sub>ij</sub></td></tr><tr><td>C<sub>B</sub>(O<sub>i</sub>) in/out</td><td>Weighted betweenness centrality (C<sub>B</sub>) of O<sub>i</sub> in the CME, meaning the sum of overall partial betweenness of O<sub>i</sub> relative to all pairs O<sub>kj</sub>, assuming that connections between O<sub>k</sub> and O<sub>j</sub> weight #CoOp<sub>kj</sub></td></tr><tr><td>Rsl<sub>i</sub> = &sum;rk R<sub>rk</sub>/NF</td><td>Raw materials sustainability level of O<sub>i</sub> (rk = nr. of raw materials adopted metrics)</td></tr><tr><td>Osl<sub>i</sub> = &sum;ok O<sub>ok</sub>/NF</td><td>Operations sustainability level of O<sub>i</sub> (ok = nr. of adopted operations metrics)</td></tr><tr><td>Psl<sub>i</sub> = &sum;pk P<sub>pk</sub>/NF</td><td>Products sustainability level of O<sub>i</sub> (pk = nr. of adopted products metrics)</td></tr></tbody><thead><tr><th colspan="2">Metrics related to all organisations (players) in a CME</th></tr><tr><th>Metric</th><th>Description</th></tr></thead><tbody><tr><td>#O</td><td>Total number of organisations in the CME</td></tr><tr><td>&sum;i #CoOp<sub>i</sub></td><td>Total number of collaboration opportunities generated in the CME</td></tr><tr><td>C<sub>D</sub>(O<sup>*</sup>) in/out</td><td>Maximum indegree/outdegree centrality of all O<sub>1</sub>..O<sub>n</sub></td></tr><tr><td>C<sub>B</sub>(O<sup>*</sup>)</td><td>Maximum betweenness centrality of all O<sub>1</sub>..O<sub>n</sub></td></tr><tr><td>&sum;i Rsl<sub>i</sub></td><td>Raw materials sustainability level of all O<sub>1</sub>..O<sub>n</sub></td></tr><tr><td>&sum;i Osl<sub>i</sub></td><td>Operations sustainability level of all O<sub>1</sub>..O<sub>n</sub></td></tr><tr><td>&sum;i Psl<sub>i</sub></td><td>Products sustainability level of all O<sub>1</sub>..O<sub>n</sub></td></tr></tbody></table>

<table><caption>**Table 3** – Individual performance Indicators of the organisations (players) in a CME.</caption><thead><tr><th colspan="2">Performance Indicators of the organisations (players) in a CME</th></tr><tr><th>Performance Indicator</th><th>Description</th></tr></thead><tbody><tr><td>CI<sub>i</sub>in = C<sub>D</sub>(O<sub>i</sub>)in / C<sub>D</sub>(O<sup>*</sup>)in = (Σ<sub>j</sub> O<sub>ij</sub> #CoOp<sub>ij</sub>in) / (maxΣ<sub>j</sub> O<sub>ij</sub> #CoOp<sub>ij</sub>in)</td><td>Evaluates the contribution of O<sub>i</sub> related to the number of accepted CoOps (#CoOp<sub>in</sub>)</td></tr><tr><td>CI<sub>i</sub>out = C<sub>D</sub>(O<sub>i</sub>)out / C<sub>D</sub>(O<sup>*</sup>)out = (Σ<sub>j</sub> O<sub>ij</sub> #CoOp<sub>ij</sub>out) / (maxΣ<sub>j</sub> O<sub>ij</sub> #CoOp<sub>ij</sub>out)</td><td>Evaluates the contribution of O<sub>i</sub> related to the number of created CoOps (#CoOp<sub>out</sub>)</td></tr><tr><td>PI<sub>i</sub> = C<sub>B</sub>(O<sub>i</sub>) / C<sub>B</sub>(O<sup>*</sup>) = (Σ<sub>k</sub> Σ<sub>j</sub> O<sub>kj</sub>(O<sub>i</sub>)) / (maxΣ<sub>k</sub> Σ<sub>j</sub> O<sub>kj</sub>(O<sub>i</sub>))</td><td>Evaluates the prominence/ influence of O<sub>i</sub> related to the number of CoOps (#CoOp)</td></tr><tr><td>SI<sub>i</sub> = (w<sub>r</sub> Σ<sup>rk</sup><sub>k=1</sub> Rsl<sub>k</sub> + w<sub>o</sub> Σ<sup>ok</sup><sub>k=1</sub> Osl<sub>k</sub> + w<sub>p</sub> Σ<sup>pk</sup><sub>k=1</sub> Psl<sub>k</sub>) / (w<sub>r</sub> + w<sub>o</sub> + w<sub>p</sub>)</td><td>Evaluates the sustainability of O<sub>i</sub> considering different weights</td></tr></tbody></table>
$(w_r, w_o$ and $w_p)$ of the raw material, operations and products

<table><caption>**Table 4** – Performance Indicators to evaluate the collaboration in a CME as a whole.</caption><thead><tr><th colspan="2">Performance Indicators related to all organisations (players) in the CME</th></tr><tr><th>Performance Indicator</th><th>Description</th></tr></thead><tbody><tr><td>$CI_{CBE}in = \frac{\sum_i [C_D(O^*)in - C_D(O_i)in]}{C_D(O^*)in * (#O - 1)}$</td><td>Evaluates the degree to which the most popular organisation [$C_D(O^*)in$] exceeds the contribution of the others</td></tr><tr><td>$CI_{CBE}out = \frac{\sum_i [C_D(O^*)out - C_D(O_i)out]}{C_D(O^*)out * (#O - 1)}$</td><td>Evaluates the degree to which the most active organisation [$C_D(O^*)out$] exceeds the contribution of the others</td></tr><tr><td>$CI_{CBE}t = \frac{\sum_i \#CoOp_i}{\#O}$</td><td>Ratio of the $\#CoOp$ created/ accepted in the CME by $\#O$</td></tr><tr><td>$PI_{CBE} = \frac{\sum_i [C_B(O^*) - C_B(O_i)]}{C_B(O^*) * (#O - 1)}$</td><td>Evaluates the degree to which the most prominent/influent organisation [$C_B(O^*)$] exceeds the contribution of the others</td></tr><tr><td>$SI_{CBE} = \frac{\sum_i SI_i}{\#O}$</td><td>Ratio of the total value of sustainability of all $O_1...O_n$ by $\#O$</td></tr></tbody></table>

### 3.3 Influence Mechanism

Considering the organisations (players) of a CME featured by a profile as described in Fig. 3, the CME Manager can use the Performance Assessment to assign a certain weight to each adopted performance indicator ($wCI$, $wPI$, $wSI$) and vary these weights, hoping to influence the players so that they change their behaviour towards improved performance and sustainability of the CME. This process of influencing, assuming a reaction of the CME players similar to that of individuals when they are evaluated, consists of the proposed **Influence Mechanism**. The inferred influence on the organisations is calculated by adding a percentage of a given factor of influence ($0<FI<1$) to their collaborative profile, as described in Table 5. The CI weight ($wCI$) influences the *contact rate*, the PI weight ($wPI$) influences the *accept rate*, and the SI weight ($wSI$) influences the *sustainability index*.

<table><caption>**Table 5** – Calculation method of the Influence Mechanism used in the PAAM</caption><thead><tr><th>P. Indicator (weight)</th><th>Influence</th><th>Influence FI</th></tr></thead><tbody><tr><td>CI (wCI)</td><td>Contact rate</td><td>contact<sub>rate</sub> += FI<sub>wCI</sub></td></tr><tr><td>PI (wPI)</td><td>Accept rate</td><td>accept<sub>rate</sub> += FI<sub>wPI</sub></td></tr><tr><td>SI (wSI)</td><td>Sustainability index</td><td>sustainab<sub>index</sub> += FI<sub>wSI</sub></td></tr></tbody></table>

The formulas to calculate the respective factors of influence are listed in (1), (2) and (3). An additional factor ($\pm F_e$) is also considered to allow introducing a random positive or negative influence due to exogenous causes. This factor can be used in the
simulation model, for example, to induce collaboration in a player that did not ever accept or invite others, or it can be used to decrease collaboration in cases where it deteriorates and fails.

$$ contact_{rate}(O_i) += contact_{rate}(O_i) * wCI * \frac{FI}{wCI + wPI + wSI} + F_e \quad (1) $$

$$ accept_{rate}(O_i) += accept_{rate}(O_i) * wPI * \frac{FI}{wCI + wPI + wSI} + F_e \quad (2) $$

$$ sustainability_{index}(O_i) += sustainability_{index}(O_i) * wSI * \frac{FI}{wCI + wPI + wSI} + F_e \quad (3) $$

## 4 Experimental Evaluation

The experimental evaluation uses hypothetical data (although inspired on real cases) to instantiate some simulation scenarios of the artefact PAAM. The PAAM was designed using the AnyLogic tool [37] and comprises agent-based modelling to simulate the autonomous organisations (players), and system dynamics to keep and manage human resources (expressed in person-day). The classes of willingness that characterise the collaboration behaviour of the agents use distribution functions; in this case, the Bernoulli distribution [37], parametrised by the contact rate, accept rate and sustainability index, meaning that the higher the parameter, the higher the probability of resulting in an answer “yes”.

Fig. 4 shows a snapshot of a simulation scenario using PAAM, instantiated with six organisations (players) from each profile as defined in Fig. 3. A Poisson distribution [37] is used to generate the incoming market opportunities. After running for a year (virtual time), the connections are established due to the collaboration, allowing the use of the adopted performance indicators to assess the organisations and the CME.

<figure><img src="image_6.png" /><figcaption>Fig. 4 – A snapshot of the PAAM artefact for a CME instantiated with 6 organisations (CME players) from each profile defined by the classes of willingness (A, B, C and D).</figcaption></figure>
For the performance assessment and use of the influence mechanism, the following scenarios were established:

(1) The CI, PI and were adopted considering the weights $wCI=2$, $wPI=2$ and $wSI=2$. No factor of influence was used;

(2) The CI, PI and were adopted considering the weights $wCI=2$, $wPI=2$ and $wSI=2$. A factor of influence $FI=20\%$ was used;

(3) The CI, PI and SI were adopted, increasing the weight $wSI=4$. The factor of influence was maintained.

After running PAAM for one year (virtual time) for each scenario, we have achieved the results of Table 6, a measure of density $CI_{CBET}$ - the ratio of the number of CoOp generated in the CME by the total number of organisations, a measure of centrality $PI_{CBE}$ - the degree to which the most prominent/influent organisation in the CME exceeds the contribution of the others, and a measure of sustainability $SI_{CBE}$ - the ratio of the value of sustainability of all the organisations in the CME by the total number of organisations.

Table 7 details the results of $PI_i$ of individual organisations for each simulation scenario, whose graphical view is shown in Fig. 5. The node sizes are related to the $PI_i$ value, i.e., the larger the nodes, the larger the measures; the links strength represents the number of shared CoOps. The strengths of connections are weighted by the number of exchanged CoOps.

<table><caption>Table 6 – CI, PI and SI measures of the CME globally.</caption><thead><tr><th>Perf. Indicators</th><th>CI<sub>CBE</sub>t</th><th>PI<sub>CBE</sub></th><th>SI<sub>CBE</sub></th></tr></thead><tbody><tr><td>Scenario (1)</td><td>21,417</td><td>0,750</td><td>0,325</td></tr><tr><td>Scenario (2)</td><td>23,917</td><td>0,782</td><td>0,325</td></tr><tr><td>Scenario (3)</td><td>24,250</td><td>0,808</td><td>0,325</td></tr></tbody></table>

<table><caption>Table 7 – PI measures of individual organisations (CME players) resulting from each simulation scenario $PI_i$ (1), $PI_i$ (2) and $PI_i$ (3).</caption><thead><tr><th>Profile</th><th colspan="5">Class A</th><th colspan="5">Class B</th><th colspan="5">Class C</th><th colspan="5">Class D</th></tr><tr><th>O<sub>i</sub></th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th><th>16</th><th>17</th><th>18</th><th>19</th><th>20</th><th>21</th><th>22</th><th>23</th></tr></thead><tbody><tr><th>PI<sub>i</sub> (1)</th><td>0,00</td><td>0,00</td><td>0,02</td><td>0,00</td><td>0,00</td><td>0,00</td><td>0,76</td><td>0,57</td><td>0,34</td><td>0,11</td><td>0,25</td><td>0,19</td><td>0,02</td><td>0,00</td><td>0,00</td><td>0,05</td><td>0,03</td><td>0,00</td><td>1,00</td><td>0,84</td><td>0,39</td><td>0,59</td><td>0,26</td><td>0,55</td></tr><tr><th>PI<sub>i</sub> (2)</th><td>0,01</td><td>0,00</td><td>0,00</td><td>0,01</td><td>0,00</td><td>0,03</td><td>0,16</td><td>0,10</td><td>0,38</td><td>0,29</td><td>0,28</td><td>0,18</td><td>0,08</td><td>0,03</td><td>0,13</td><td>0,03</td><td>0,05</td><td>0,05</td><td>1,00</td><td>0,68</td><td>0,80</td><td>0,38</td><td>0,14</td><td>0,44</td></tr><tr><th>PI<sub>i</sub> (3)</th><td>0,00</td><td>0,00</td><td>0,00</td><td>0,00</td><td>0,00</td><td>0,00</td><td>0,30</td><td>0,07</td><td>0,60</td><td>0,18</td><td>0,08</td><td>0,13</td><td>0,01</td><td>0,06</td><td>0,04</td><td>0,08</td><td>0,02</td><td>0,11</td><td>1,00</td><td>0,38</td><td>0,64</td><td>0,32</td><td>0,12</td><td>0,47</td></tr></tbody></table>

<table><tr><td>Scenario (1)</td><td>Scenario (2)</td><td>Scenario (3)</td></tr></table>
<figure><img src="image_7.png" /><figcaption>Fig. 5 – Graphical view of the PI measures of individual organisations (CME players).</figcaption></figure>

After analysing the results related to $CI_{CBet}$ in Table 6 (collaboration activity in the CME) in the three simulation scenarios, we can note that after influencing the CME by introducing a FI=20%, considering $wCI=2$, $wPI=2$ and $wSI=2$ (scenario 2), the organisations in response, tried to be more active, creating more collaboration in the CME: $CI_{CBet}$ increased from 21,417 to 23,917. The influence also increased the value of $PI_{CBE}$ from 0,75 to 0,782, meaning a more prominence/influence of some organisations with higher collaboration rates.

The increment of the $wSI$ from 2 to 4 (scenario 3) resulted in even more collaboration: $CI_{CBet}$ increased to 24,250. The greater weight of sustainability induced in organisations with a high collaboration rate, an even greater collaboration with the partners with a higher index of sustainability. As a result, once again, the $PI_{CBE}$ increased to 0,808, meaning the reinforcement of organisations with more influence in the CME.

# 5 Conclusions

The contribution of this work is a design artefact, the PAAM, consisting of a simulation model that includes a “Performance Assessment and an Influence Mechanism” that allows the exploration by the CME Manager of simulation scenarios, considering diverse CME players with different profiles, seeking benefits due to collaboration [15] and more sustainability [10, 11, 12].

We can conclude that we have partially answered the research question. A set of performance indicators can be adopted to measure and influence the collaborative behaviour of organisations, varying the weights of the indicators to induce changes in the desired direction of more sustainability. However, this work has some limitations. Due to the difficulty of getting actual collaboration information, we used hypothetical data considering the same number of organisations of each profile, which can differ from a real context of a CME.

For future work, we aim to gather some actual data from manufacturing cases to deduce and analyse simulation scenarios more consistent with reality, add the social and economic facets to the SI metrics and use different combinations of the set of performance indicators adopted by the CME.
Furthermore, considering that the area of manufacturing is vast, including not only different manufacturing processes but also different collaborative manufacturing processes, future work should consider the specificities of the different sectors. A framework and methodology of collaborative performance management [38] can be established to guide how a set of performance indicators can be applied to different collaborative manufacturing processes.

## Acknowledgement

This work was supported in part by the Portuguese FCT program UIDB/00066/2020 (Center of Technology and Systems – CTS).

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