Abstract
Purpose
This paper aims to develop a Petri net model for analyzing the quality conflict and its resolution of a complex product. The result aims to assist decision makers (DMs) to properly select their activities when a quality conflict has happened.
Design/methodology/approach
According to the features of Petri net and conflict analysis theory, a novel Petri net for conflict analysis (PNCA) is designed which contains transition and preference labels to describe DMs' decision activities and profit comparisons. Additionally, a generating approach is proposed, which can help DMs to construct a PNCA. Furthermore, based on players' bounded rationality, the equilibrium of PNCA is studied to provide scientific supports for DMs' decision‐making. A case study on an aircraft production system is conducted to demonstrate the feasibility and effectiveness of the new model, which furnishes a fresh perspective on the supply chain quality management of a complex product.
Findings
A new methodology is proposed for the domain of conflict analysis, which is easier to understand and improves the operation efficiency. What is more important, DMs can clearly be aware of their following choices according to the corresponding transition information.
Originality/value
The paper contributes to conflict analysis theory by designing a new model and develops a new graph model for managing the supply chain quality of a complex product.
Keywords
Citation
Liu, Y., Fang, S., Fang, Z. and Hipel, K.W. (2012), "Petri net model for supply‐chain quality conflict resolution of a complex product", Kybernetes, Vol. 41 No. 7/8, pp. 920-928. https://doi.org/10.1108/03684921211257766
Publisher
:Emerald Group Publishing Limited
Copyright © 2012, Emerald Group Publishing Limited
1 Introduction
According to Hobday' (1999) statement, a complex product (Cop) can be considered as an item containing various complicated and technical‐intensive parts, components and systems, which is intricate from both engineering and management perspective (Hobday and Rush, 1999). The Cop, such as an aircraft, warship or satellite, is a high integration system. Moreover, the Cop is finally assembled by a main manufacturer with components or subsystems from its suppliers and is often produced either as one‐off or in a small batch, which is different from mass produced products.
Because of intricate product structure, strict engineering requirements, complicated manufacturing processes, numerous tests and long producing period, the Cop usually is created by a cooperation of enterprises, which is organized as a “main manufacturer – suppliers” (M‐S) production model. As the core of M‐S structure, the main manufacturer is the “production organizer” and “system integrator”, which is responsible for system overall design and stipulating quality requirements to its suppliers. After accepting all the quality‐satisfying components, the main manufacturer will assemble the final product with the outsourcing items and subsequently sell it to a customer.
In the complicated producing processes of the Cop, suppliers' manufacturing statuses strongly influence the main manufacturer's assemblage and may occur unexpected problems. As there exist uncertain factors in changeable environment, quality conflict between the main manufacturer and its suppliers is hand to avoid, especially on the inconsistency of quality requirement and reward. For example, there was a quality‐reward negotiation once a contract was signed. However, a force majeure, such as earthquake, strike or war, was happened in the production period. The supplier's production cost increases and the reward from the main manufacturer is not enough to produce having high quality. The supplier expect to increase the production reward or decrease the quality stipulation, which the main manufacturer may not accept that. So that, there is a quality conflict about quality level and production reward. If the supplier cannot deliver the components on time, the main manufacturer's assemblage will be greatly delayed, even affects further production and market development. How to analyze the quality conflict and select a suitable resolution is an important problem worthy of studying, which can assist the main manufacturer transfer the quality conflict to further cooperation and achieve mutual benefits.
In recent years, many scholars have carried out a series of related research and made many contributions to this topic. As a research hotspot, there exists substantial literature which concentrates on the conflict analysis and its resolution. One effective method is graph model for conflict analysis first introduced by Professor Kilgour et al. (1987), which based on game theory and metagame theory. This approach utilizes nodes to describe different decision states and employs arcs to connect nodes, which can help decision makers (DMs) to find the existing equilibrium of a conflict. According to the equilibrium, DMs can select appropriate activities to achieve their satisfying benefits. In recent 20 years, the graph model for conflict analysis is widely used in various areas, such as environment dispute, business negotiation and war resolution. Additionally, the theory of this technology is developing fast. Li et al. (2005) proposed a status quo analysis method to graph model for conflict, which consisted various algorithms to generate status quo diagrams. Xu et al. (2009) developed an algebraic approach to employ the status quo analysis within the matrix framework. Furthermore, Hipel et al. (2011), Walker et al. (2010), Wang et al. (2011) and Yousefi et al. (2011) made many contributions to this domain.
Looking over the existing literature in recent years, one can notice that there is no label used to describe decision activities, which fails to analyze the affection of decision sequence on resolution. Especially in the quality conflict of a Cop system, the supplier usually first select its activity and the main manufacturer subsequently choose its feedback behaviour. Keeping in mind the above considerations, this paper contributes to supply‐chain quality management by studying the quality conflict and its resolution. Section 2 introduced Petri net (PN) as graph model to investigate a conflict, which contains transition labels to express different decision activities. Section 3 proposed an algorithm to form a PN and find equilibrium. In Section 4, a commercial aircraft production system is selected as a case study to illustrate the above research, whose result can confirm the feasibility and effectiveness of the new model. In Section 5, brief conclusions are contained and future research prospects are suggested.
2 PN model for conflict analysis
2.1 Graph model for conflict analysis
Traditional graph model for conflict analysis can be viewed as a set containing four parts: [N,S,(Ai)i∈N, (≽i, ∼i)i∈N]. N refers to the set of DMs and |N|≥2. S means the set of states in the conflict, where |S|≥2. Suppose that the number of DMs' strategy choice is {c1,c2, … ,cN}, cj∈{0, 1}, j∈N. The number of possible states is 2N. For DM i∈N (S, Ai), constitutes DM i's graph, in which S is the set of vertices and Ai means the set of arcs connecting the vertices in the graph. Binary operators (≽i, ∼i) represents the preferences for DM i. Suppose that Ri(S) is DM i's benefit on state S. For s, t∈S, if s≽it, it means that DM i prefer state s to t, Ri(s)>Ri(t); if s∼it, it means that DM i believes both s and t is almost same, Ri(s)=Ri(t).
2.2 PN and it application in conflict analysis
PN is first introduced by Carl A. Petri Doctor in his doctor thesis in 1962, which is a symbolic, visual, structural and graphic analysis model used to describe the system processes. Because PN cannot only define possible states and events, but also establish equations of continuous‐variable dynamic systems, PN is considered as one of the most effective methods to illustrate, analyze and control a discrete event system.
Nowadays, traditional Petri model has been widely used into many areas. Nowadays, traditional Petri model has extended to severe types, such as timed Petri net (TPN), stochastic PN, colored Petri net (CPN), object PN (CPN), fuzzy PN (TPN).
In order to employ PN to analyze a conflict, a novel model, Petri net for conflict analysis (PNCA), can be defined as following.
Definition 1
PNCA has five parameters (P, T, I, O, Λ), in which P, T, I, O, Λ refer to node, transition, input matrix, output matrix and preference, respectively:
- 1.
Node has the same meaning as state, which can be expressed as ○. Hence, the number of the possible nodes is 2N. In some cases, some node can be omitted. For example, if DM i has ci kinds of choices but he can only choose one of them, there is only ci choices left and 2ci−ci vertices can be ignored.
- 2.
Transition can be considered as a happening of a decision activity, which can be written as ▪. If DM i can obtain more benefit by moving from state s to t, s≽it, the corresponding transition will be triggered. If DM i believe the profits of states s and t are indifferent, the corresponding transition may be triggered.
- 3.
Input matrix means the number of directed arcs from P to T and can be written as I:P×T→N, in which N={0,1,…}.
- 4.
Similarly, output matrix refers to the number of directed arcs from T to P and can be written as O:T×P→N.
- 5.
Preference denotes DM i's choice that whether he will move from state s to t, which can be expressed as Λ={≽i, ∼i, ◃i}. Preference Λ has a closed relationship with transition T. ≽i, ∼i and Λi means the corresponding transition can, may, cannot be triggered, respectively.
3 Algorithm for generating PN model and its equilibrium
3.1 Algorithm for forming PNCA
From Definition 1, one can notice that PNCA is employed to describe the unilateral improvement (UI) and unilateral move (UM) of DMs. For dynamic game, there exist a moving sequence, which means a DM will first move from a starting state, S0(S0∈S), to another state. Each node in the PNCA is a feasible state which a DM can move to. Every arc connecting nodes refers to a DM's feasible choice in which his profit cannot decrease. Suppose that the quo state is S0 and DM i first decide to move; the set of nodes and transitions of PNCA when there are h moves are Ph and Th, respectively; DM i's mth new transition is tim. The algorithm for generating PNCA can be concluded as following:
- •
Step 1. DM i decides his choice whether move to another state. If there exists state(s) α, α≠S0(α∈S), Ri(α)≥Ri(S0). DM i can move from S0 to α. P1={S0, α} and T1={ti1}. If not, stop operation and output the PNCA, in which P=T=Ø.
- •
Step 2. Since each DM cannot move consequently, it is time for DM j, j≠i(j∈N), decides to move. If there exists state(s) β, β≠α(β∈S), Ri(β)≥Ri(α). DM i can move from α to β. If not, stop operation. Let α=β and i=j, update Ph and Th.
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Step 3. Continue step 2. If Ph=Ph−1 and Th=Th−1, stop operation and output the PNCA.
3.2 Equilibrium of PNCA for a quality conflict
Suppose that DM i's UI and UM from state k are Si+(k) and Si(k), respectively. Some definitions of stabilities are introduced as follows.
Definition 2 (Nash stability)
Let i∈N, a state k is Nash stable (or individual rational) (R) for DM i iff Si+(k)=Ø.
Under Nash stable, DM believes that the state he choose idea the last state and he will not move to other states because of benefit losing.
Definition 3 (general metarationality)
For i∈N, a state k is general metarational (GMR) for DM i iff for every k1∈Si+(k), there exists at least one k2∈Sj(k1) with Ri(k2)≤Ri(k).
Under GMR, DM considers that his opponents will strike back his decision and his profit will be decreased. The state, which can cause counterattack, is stable state.
Definition 4 (symmetric metarationality)
Let i∈N, a state k is symmetric metarational (SMR) for DM i iff for every k1∈Si+(k), there exists at least one k2∈Sj(k1), such that Ri(k2)≤Ri(k) and Ri(k3)≤Ri(k) for all k3∈Si(k2).
SMR is similar with GMR. The difference is that DM can decide once more to decrease his rival's benefit. The game will end after his second decision.
Definition 5 (sequential stability)
For i∈N, a state k is sequential stable (SEQ) for DM i iff for every k1∈Si+(k), there exists k2∈Sj+(k1) with Ri(k2)≤Ri(k).
Under SEQ, DM's opponent counterattacks only if his profit will be increased.
In the quality conflict of a Cop, the main manufacturer and the suppliers are rational players, who expect gaining additional profits when they move to another state. As a consequence, the equilibrium for PNCA can be concluded as follows.
Proposition 1
Suppose that there is a PNCA which composes several chains λi(i=1,2,…). The equilibrium of PNCA can be obtained at the following nodes:
- •
the ending node of each chain; and
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the nodes in which DM 's profits is not worse than that of the ending point of a chain.
Prove
(1) According to the algorithm designed in Section 3.1 suppose that DM i choose his activity at the ending point of a chain. As there is no downstream node, no state can be reached in which DM i's profit will be increased, which means he is not willing to move to other nodes. Nash equilibrium is obtained.
(2) Because DM i is aware of PNCA, if there are two nodes where his profits are same, he can choose move or stay. After other DMs' decisions, if he finds that his profit is increased, he will move for a better benefit, where the indifferent node is not equilibrium. If he notice that his profit is not increased, he will be not willing to move, which means the indifferent node is equilibrium.
4 Case study for analyzing a quality conflict of a Cop
4.1 Background
A commercial aircraft company (main manufacturer, M) made a deal with an aircraft body supplier (S) about wings with a high quality requirement. Unexpectedly, there was an earthquake happened and the supplier's equipments got a terrible damage, which cannot assure the production quality. Hence, the supplier wanted to decrease the quality requirement to the satisfying level so that it can maintain its normal profit, which was hard for the main manufacturer to accept. Additionally, their administrator, ministry of industry and information (A), expected that both of the parties can smoothly negotiate and received a good result. Specifically, there were three options for supplier: decrease production quality (c1), keep high quality (c2) and terminate the contract (c3). The main manufacturer had two alternative strategies: purchase the components (c4) and stop ordering (c5). The administrator decided whether promote further cooperation (c6).
4.2 Feasible states and DMs' preferences
Because there are three DMs and a total of six options, the number of states is 26=64. However, each DM can choose at most one strategy at a time. Additionally, if the supplier chooses “terminate the contract”, the negotiation is over. Hence, there are 11 the feasible states shown in Table I. Furthermore, the DMs' preferences of all the states can be determined as Table II.
4.3 Generation of PNCA
Suppose that pi(sj) refers to the ith node with state sj and tm(cn) means the mth transition having option cn. The generation of PNCA in this case can be illustrated as following:
- 1.
According to actual situation, the supplier first decides whether moves to another state and State 1 can be considered as the beginning state. There are two states it can move: States 2 and 3. Based on the supplier's preference, 2∼S1 and 1≽S3. Consequently, the supplier may move to State 2 and will not go to State 1 as illustrated in part a of Figure 2.
- 2.
At State 2, it is time for the main manufacturer or administrator to decide. If the administrator moves, it cannot go to State 4 where 2≽A4. If the main manufacturer moves, it can go to States 6 and 10. As 6≽M2 and 10∼M2, the main manufacturer may move to State 10 as shown in part b.
- 3.
Continuing the above operations until no new nodes and arcs can be addition, one can obtain the final PN as shown in Figure 3.
- 4.
From Figure 3 one can easily find that there are three ending nodes of chains, which are p2,p8 and p10. Hence, one can obtain three equilibriums for the above quality conflict:
- •
Equilibrium 1 (Node p2). At Node p2, the supplier wants to decrease the quality requirement, which the main manufacturer does not accept. Since their administrator may take over the matter, the main manufacturer will wait for the administrator's next activity. If there is no time limit, the main manufacturer can wait for a long time.
- •
Equilibrium 2 (Node p10). If the administrator does not promote the cooperation, the main manufacturer will refuse the supplier's demands, which means if the supplier decrease the quality, the main manufacturer can say no to the components.
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Equilibrium 3 (Node p8). If the administrator negotiates the quality conflict, the main manufacturer could accept the quality‐satisfying components for the future cooperation or other profits.
- •
5 Conclusions and future work
According to the quality conflict of a Cop, PN is first utilized as a graph model to solve the quality negotiation. More specifically, a new model, PNCA is designed to describe the conflict processes and DMs' preferences. Additionally, the generating method of PNCA is proposed to assist DMs to establish a conflict analysis frame. Furthermore, the equilibriums of PNCA is studied as resolutions of a quality conflict, which can assist DMs to choose appropriate activities.
The research contributions in this paper naturally indicate worthwhile future research directions. For example, DMs may have uncertain preferences to different strategies. How to evaluate the uncertain or incomplete information is an important problem which should be addressed in future research.
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China with grant No. 70971064, funding of Jiangsu Province Innovation Program for Graduate Education (CX10B_044R), and funding for Outstanding Doctoral Dissertation at Nanjing University of Aeronautics Astronautics (BCXJ10‐14).
About the authors
Yuan Liu, a researcher, received BE and MS degrees in Industrial Engineering from Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China, in 2006 and 2009, respectively, where he is currently pursuing a PhD degree in Management Science and Engineering. He is currently a visiting scholar of Systems Design Engineering at the University of Waterloo. His major research interests are supply chain management, quality control and industrial engineering. He is the author of both journal and conference papers on these topics. He is a member of the Chinese Society of Optimization, Overall Planning and Economy Mathematics. Yuan Liu is the corresponding author and can be contacted at: [email protected]
Shili Fang, an economist, is currently a PhD student at the Nanjing University of Aeronautics and Astronautics and a Director of the Finance Department in China Academic of Launch Vehicle Technology. He received a bachelor degree from Peking University, a Master's degree from Renming University of China and an EMBA from Nankai University. He has published one book and several papers in China.
Dr Zhigeng Fang is University Professor at Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China, where he received his PhD degree in 2008. His major research interests are regional economy development, management science and grey system theory. He is the author or co‐author of more than seven books, about 70 journal papers, as well as many conference and encyclopedia articles. Additionally, he is the reviewer of several journals, which are famous in China.
Professor Keith W. Hipel is currently University Professor of Systems Design Engineering at the University of Waterloo where he is the Coordinator of the Conflict Analysis Group and is Chair of the Board of Governors of Renison University College. He is Senior Fellow with the Centre for International Governance Innovation. His major research interests are the development of conflict resolution, multiple objective decision making and time series analysis techniques from a systems design engineering perspective with application to water resources management, hydrology, environmental engineering and sustainable development. He is the author or co‐author of four books, 11 edited books, 236 journal papers, as well as many conference and encyclopedia articles.
References
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Further Reading
Acha, V., Davies, A., Hobday, A. and Salter, M. (2004), “Exploring the capital goods economy: complex product systems in the UK”, Industrial and Cooperate Change, Vol. 13 No. 3, pp. 505‐29.
Hipel, K.W. and Walker, S.B. (2011), “Conflict analysis in environmental management”, Environmetrics, Vol. 22 No. 3, pp. 279‐93.
Howard, N. (1971), Paradoxes of Rationality: Theory of Metagames and Political Behavior, MIT Press, Cambridge, MA.
Nemann, J.V. and Morgenstern, O. (1994), Theory of Games and Economics Behavior, Princeton Press, Princeton, NJ.
Obeidi, A., Hipel, K.W. and Kilgour, D.M. (2002), “Canadian bulk water exports: analyzing the sun belt conflict using the graph model for conflict resolution”, Knowledge, Technology, and Policy, Vol. 14 No. 4, pp. 145‐63.
Rahimnia, F., Moghadasian, M. and Mashreghi, E. (2011), “Application of grey theory approach to evaluation of organizational vision”, Grey Systems: Theory and Application, Vol. 1 No. 1, pp. 33‐46.
Yu, J.Q., Cha, J.Z., Lu, Y.P., Xu, W.S. and Sobolewski, M. (2010), “A CAE‐integrated distributed collaborative design system for finite element analysis of complex product based on SOOA”, Advances in Engineering Software, Vol. 41 No. 4, pp. 590‐603.