Abstract
This chapter analyzes the process of forming a coalition within a corporate network. The objective of the partner companies is to create a multistage manufacturing system, which generates a chain of increased value from raw materials to end-user market. This process is studied by cooperative game theory, through the key problems of maximizing the total profit and distributing it among the members of the coalition. To construct a pay-off policy that is both stable and fair, the study proposes to represent the productive resources of the firms not only by their capacity, but also by the work in progress (WIP) generated by product flows. The proposed profit sharing rule is then constructed from the dual of the profit maximization problem. It is both efficient and rational, with more fairness than the Owen set policy of classical linear production games.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Asmundsson JM, Rardin RL, Uzsoy R (2003) Tractable nonlinear capacity models for production planning. Research Report, Purdue University (USA)
Baker KR (1993) Requirements planning. In: Graves SC, Rinnooy Kan AHG, Zipkin PH (eds) Handbooks in operations research and management science Vol 4, pp 571–628. North-Holland, Amsterdam
Butera F (1991) La métamorphose de l’organisation: du château au réseau. Les Editions d’Organisation, Paris
Cachon GP, Netessine S (2004) Game theory in supply chain analysis. In: David Simchi-Levi S, Wu D, Shen ZJ (eds) Handbook of quantitative supply chain analysis: modeling in the eBusiness era. Kluwer Publisher, Boston
Fehr E, Schmidt KM (1999) A theory of fairness, competition, and cooperation. Q J Econ 114(3):817–868 (MIT Press)
Gerchak Y, Gupta D (1991) On apportioning costs to customers in centralized continuous review inventory systems. J Oper Manage 10(4):546–551
Granot D, Maschler M (1998) Spanning network games. Int J Game Theor 27:467–500
Hartman BC, Dror M, Shaked M (2000) Cores of inventory centralization games. Games Econ Behav 31:26–49
Hartman BC, Dror M (2003) Optimizing centralized inventory operations in a cooperative game theory setting. IIE Trans Oper Eng 35(3):243–257
Hartman BC, Dror M (2005) Allocations of gains from inventory centralization in newsvendor environments. IIE Trans Sched Logist 37(2):93–107
Hennet JC (2003) A bimodal scheme for multi-stage production and inventory control. Automatica 39(5):793–805
Hennet JC, Mahjoub S (2010) Toward the fair sharing of profit in a supply network formation. Int J Prod Econ 127(1):112–120
Hennet JC, Mahjoub S (2011) Coalitions of firms in manufacturing networks: stability and optimality issues. In: Bittanti S, Cenedese A, Zampieri S (eds) Preprints 18th World IFAC conference, Milano, Italy, pp 6419–6424
Karmarkar US (1993) Manufacturing lead times, order release and capacity loading. In: Graves SC, Rinnooy Kan AHG, Zipkin PH (eds) Handbooks in operations research and management science, vol 4. North-Holland, Amsterdam, pp 287–329
Lamothe J, Hadj-Hamou K, Aldanondo M (2005) Product family and supply chain design. In: Dolgui A, Soldek J, Zaikin O (eds) Supply chain optimisation—product/process design, facility location and flow control. Springer, New York, pp 175–190
Little JDC (1961) A proof for the queueing formula: L = λW. Oper Res 9:383–387
Lindner MA, Marquez FG, Chapman C, Clayman S, Hendriksson D (2010) Cloud Supply Chain - A Comprehensive Framework, CloudComp 2010, 2nd International ICST Conference on Cloud Computing, 25-28, Barcelona, Spain
Meca A, Timmer J, Garcia-Jurado I, Borm P (2004) Inventory games. Eur J Oper Res 156(1):127–139
Muller A, Scarsini M, Shaked M (2002) The newsvendor game has a non-empty core. Games Econ Behav 38:118–126
Myerson RB (1977) Graphs and cooperation in games. Math Oper Res 2(3):225–229
Nagarajan M, Sošic G (2008) Game-theoretic analysis of cooperation among supply chain agents: review and extensions. Eur J Oper Res 187(3):719–745
Osborne MJ, Rubinstein A (1994) A course in game theory. MIT Press, Cambridge
Owen G (1975) On the core of linear production games. Math Program 9(1):358–370
Paché G, Bacus-Montfort I (2003) Le management logistique intégré. Problèmes économiques. 2.792
Powell WW, Grodal S (2005) Networks of innovators. In: Fagerberg J, Mowery D, Nelson R (eds) The Oxford handbook of innovation. Oxford University Press, Oxford
Shapley LS (1953) A value for n-person games. Contribution to the theory of games vol II, Kuhn HW, Tucker AW (eds) Annals of mathematics studies 28. Princeton University Press, Princeton
Shapley LS, Shubik M (1972) The assignment game 1: the core. Int J Game Theor 1(1):111–130
Slikker M, Fransoo J, Wouters M (2005) Cooperation between multiple news-vendors with transshipments. Eur J Oper Res 167(2):370–380
Vaszonyi A (1955) The use of mathematics in production and inventory control. Manage Sci 1(1):70–85
Van Gellekom JRG, Potters JAM, Reijnierse JH, Engel MC, Tijs SH (2000) Characterization of the Owen set of linear production processes. Games Econ Behav 32(1):139–156
Williamson O (1981) The modern corporation: origins, evolution, attributes. J. Econ Lit 19:1537–1568
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag London
About this chapter
Cite this chapter
Mahjoub, S., Hennet, J.C. (2014). A Piecewise Linear Supply Chain Game for Manufacturing Network Formation. In: Benyoucef, L., Hennet, JC., Tiwari, M. (eds) Applications of Multi-Criteria and Game Theory Approaches. Springer Series in Advanced Manufacturing. Springer, London. https://doi.org/10.1007/978-1-4471-5295-8_14
Download citation
DOI: https://doi.org/10.1007/978-1-4471-5295-8_14
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-5294-1
Online ISBN: 978-1-4471-5295-8
eBook Packages: EngineeringEngineering (R0)