Cooperative cellular manufacturing system: A cooperative game theory approach

Document Type : Article

Authors

1 Industrial Engineering College, South Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Management, Saveh Branch, Islamic Azad University, Saveh, Iran

Abstract

In the cellular industry, the components of products are increasingly being manufactured by multiple companies, which are distributed across different regions resulting in increased production costs. Here, a cooperative cellular manufacturing system is introduced to decrease these costs. A mathematical programming model has been proposed, which evaluates the production cost when companies work independently and the model is then extended to consider coalitional conditions in which the companies cooperate as an integrated cell formation system. A key question that arises in this scenario is how to arrange the cells and machines of multiple companies when their cell formation systems are designed cooperatively. Through a realistic case study of three high-tech suppliers of the Mega Motor Company, we show that these companies can reduce the costs through a cooperative cellular manufacturing system. We then compute the cost saving of each coalition of companies obtained from cooperation to get a fair allocation of the cost savings among the cooperating firms. Four cooperative game theory methods including Shapley value, τ -value, core-center, and least core are proposed to examine fair sharing of cost saving. A comprehensive analysis of the case study reveals important managerial insights.

Keywords


References

[1] Aalaei, A., & Davoudpour, H. (2016). A robust optimization model for cellular manufacturing system into supply chain management. International Journal of Production Economics.
[2] Sayadi, M.K., Hafezalkotob A., Naini, S.G.J. (2013), Fired-inspired algorithm for discrete optimization problems: an application to manufacturing cell formation. Journal of Manufacturing System, 32(1), 78-84.
[3] Dimopoulos C, Zalzala AM. Recent developments in evolutionary computation for manufacturing optimization: problems, solutions, and comparisons. IEEE Transactions on Evolutionary Computation. 2000 Jul;4(2):93-113.
[4] Akturk MS, Turkcan A. Cellular manufacturing system design using a holonistic approach. International Journal of Production Research. 2000 Jul 1;38(10):2327-47.
[5] Tavakkoli-Moghaddam R, Javadian N, Javadi B, Safaei N. Design of a facility layout problem in cellular manufacturing systems with stochastic demands. Applied Mathematics and Computation. 2007 Jan 15;184(2):721-8.
 [6] Wang TY, Wu KB, Liu YW. A simulated annealing algorithm for facility layout problems under variable demand in cellular manufacturing systems. Computers in industry. 2001 Sep 30;46(2):181-8.
 [7] Wang S, Sarker BR. Locating cells with bottleneck machines in cellular manufacturing systems. International Journal of Production Research. 2002 Jan 1;40(2):403-24
 [8] Mahdavi I, Mahadevan B. CLASS: An algorithm for cellular manufacturing system and layout design using sequence data. Robotics and Computer-Integrated Manufacturing. 2008 Jun 30;24(3):488-97.
[9]  Bagheri M, Bashiri M. A new mathematical model towards the integration of cell formation with operator assignment and inter-cell layout problems in a dynamic environment. Applied Mathematical Modelling. 2014 Feb 15;38(4):1237-54.
 [10] Chen M, Cao D. Coordinating production planning in cellular manufacturing environment using Tabu search. Computers & Industrial Engineering. 2004 Jun 30;46(3):571-88.
 [11] Defersha FM, Chen M. A comprehensive mathematical model for the design of cellular manufacturing systems. International Journal of Production Economics. 2006 Oct 31;103(2):767-83.
 [12] Safaei N, Saidi-Mehrabad M, Jabal-Ameli MS. A hybrid simulated annealing for solving an extended model of dynamic cellular manufacturing system. European Journal of Operational Research. 2008 Mar 1;185(2):563-92.
 [13] Mahdavi I, Aalaei A, Paydar MM, Solimanpur M. Designing a mathematical model for dynamic cellular manufacturing systems considering production planning and worker assignment. Computers & Mathematics with Applications. 2010 Aug 31;60(4):1014-25.
[14] Ahkioon S, Bulgak AA, Bektas T. Cellular manufacturing systems design with routing flexibility, machine procurement, production planning and dynamic system reconfiguration. International Journal of Production Research. 2009 Mar 15;47(6):1573-600.
[15] Safaei N, Tavakkoli-Moghaddam R. Integrated multi-period cell formation and subcontracting production planning in dynamic cellular manufacturing systems. International Journal of Production Economics. 2009 Aug 31;120(2):301-14.
[16] Kia R, Khaksar-Haghani F, Javadian N, Tavakkoli-Moghaddam R. Solving a multi-floor layout design model of a dynamic cellular manufacturing system by an efficient genetic algorithm. Journal of Manufacturing Systems. 2014 Jan 31;33(1):218-32.
[17] Kia R, Baboli A, Javadian N, Tavakkoli-Moghaddam R, Kazemi M, Khorrami J. Solving a group layout design model of a dynamic cellular manufacturing system with alternative process routings, lot splitting and flexible reconfiguration by simulated annealing. Computers & Operations Research. 2012 Nov 30;39(11):2642-58.
[18] Chatain O. Cooperative and non-cooperative game theory. Mie Augier, David J. Teece, Macmillan Publishers,2014.
[19] Chalkiadakis, G, Elkind, E,  Wooldridge, M.Cooperative game theory  Basic concepts and computational challenges. IEEE Intelligent Systems.2012 (3): 86-90
[20] Battista DG, Giovanna P. Coopetition strategy: Towards a new kind of interfirm dynamics for value creation. InEURAM 2nd annual conference, Stockholm School of Entrepreneurship, Sweden 2002 May (pp. 8-10).
[21] Krajewska MA, Kopfer H, Laporte G, Ropke S, Zaccour G. Horizontal cooperation among freight carriers: request allocation and profit sharing. Journal of the Operational Research Society. 2008 Nov 1;59(11):1483-91.
[22] Frisk M, Göthe-Lundgren M, Jörnsten K, Rönnqvist M. Cost allocation in collaborative forest transportation. European Journal of Operational Research. 2010 Sep 1;205(2):448-58.
[23] Özener OÖ, Ergun Ö. Allocating costs in a collaborative transportation procurement network. Transportation Science. 2008 May;42(2):146-65.
[24] Sherali HD, Lunday BJ. Equitable apportionment of railcars within a pooling agreement for shipping automobiles. Transportation Research Part E: Logistics and Transportation Review. 2011 Mar 31;47(2):263-83.
[25] Audy JF, D’Amours S, Rousseau LM. Cost allocation in the establishment of a collaborative transportation agreement—an application in the furniture industry. Journal of the Operational Research Society. 2011 Jun 1;62(6):960-70.
[26] Lozano S, Moreno P, Adenso-Díaz B, Algaba E. Cooperative game theory approach to allocating benefits of horizontal cooperation. European Journal of Operational Research. 2013 Sep 1;229(2):444-52.
[27] Hafezalkotob A, Makui A. Cooperative maximum-flow problem under uncertainty in logistic networks. Applied Mathematics and Computation. 2015 Jan 1;250:593-604.
[28] Guajardo M, Rönnqvist M. Operations research models for coalition structure in collaborative logistics. European Journal of Operational Research. 2015 Jan 1;240(1):147-59.
[29] Mohebbi S, Li X. Coalitional game theory approach to modeling suppliers' collaboration in supply networks. International Journal of Production Economics. 2015 Nov 30;169:333-42.
[30] Hezarkhani B, Slikker M, Van Woensel T. A competitive solution for cooperative truckload delivery. OR Spectrum. 2016 Jan 1;38(1):51-80.
[31] Zibaei, S., Hafezalkotob, A., Ghashami S.S. (2016). Cooperative vehicle routing problem: an opportunity for cost saving. Journal of Industrial Engineering International, 1-16.
[32] Sakawa M, Nishizaki I, Uemura Y. Fuzzy programming and profit and cost allocation for a production and transportation problem. European Journal of Operational Research. 2001 May 16;131(1):1-5.
[33] Curiel I, Potters J, Prasad R, Tijs S, Veltman B. Cooperation in one machine scheduling. Zeitschrift für Operations Research. 1993 Jun 1;38(2):113-29.
[34] Mohammaditabar D, Ghodsypour SH, Hafezalkotob A. (2015). A game theoretical analysis in capacity-constrained supplier-selection and cooperation by considering the total supply chain inventory costs, International Journal of Production Economics, in press.
[35] Barron, E. N. (2013). Game theory: an introduction (Vol. 2). John Wiley & Sons.
[36] Drechsel, J., & Kimms, A. (2010). Computing core allocations in cooperative games with an application to cooperative procurement. International Journal of Production Economics, 128(1), 310-321.
[37] Tijs SH, Driessen TS. Game theory and cost allocation problems. Management Science. 1986 Aug;32(8):1015-28.
[38] Mirás Calvo MA, Sánchez Rodríguez, E, 2006, TUGlab: A Cooperative Game Theory Toolbox <http //websuvigoes/mmiras/TUGlab/TUGl abICM06pdf> (accessed 080113)
[39] Shapley LS, A value for n-person games, Ann. Math. Stud. 28 (1953) 307–317.
[40] Shapley LS, Cores of convex games. International journal of game theory. 1971 Dec 1;1(1):11-26.
Volume 28, Issue 5
Transactions on Industrial Engineering (E)
September and October 2021
Pages 2769-2788
  • Receive Date: 21 January 2018
  • Revise Date: 30 October 2019
  • Accept Date: 18 January 2020