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Cooperative grey games and an application on economic order quantity model

Mehmet Onur Olgun (Department of Industrial Engineering, Süleyman Demirel University, Isparta, Turkey)
Sırma Zeynep Alparslan Gök (Department of Mathematics, Süleyman Demirel University, Isparta, Turkey)
Gültekin Özdemir (Department of Industrial Engineering, Süleyman Demirel University, Isparta, Turkey)


ISSN: 0368-492X

Article publication date: 3 May 2016




The purpose of this paper is to extend the results of Meca et al. (2004) depending on the grey information revealed by the individual firms.


The authors introduce cooperative grey games and focus on sharing ordering cost rule (SOC-rule) to distribute the joint cost.


In this study, the authors introduce a model, where inventory costs are assumed as grey numbers instead of crisp or stochastic ones studied in literature. At first, grey numbers and classical cooperative inventory games are recalled. Then, cooperative grey games are introduced and related results are given. Finally, an application is performed for three shotgun companies in Turkey.


It is an effective approach for theoretical analysis of systems with imprecise information and incomplete samples. Therefore, grey system theory, rather than the traditional probability theory and fuzzy set theory, is better suited to model the inventory problems by using cooperative game theory. To the best of the knowledge no study exists modeling inventory situations by using cooperative grey games. From this point of view this study is a pioneering work on a promising topic.



Part of the work reported in this paper was performed within a project founded both by TUBITAK (The Scientific and Technological Research Council of Turkey) through its 2214-A Doctorate degree thesis incentive scholarship program and by Suleyman Demirel University Scientific Research Projects Unit (SDU-BAP) with Grand No. 3664-D1-13. The financial supports are gratefully acknowledged. The authors would like to thank both institutions.


Olgun, M.O., Alparslan Gök, S.Z. and Özdemir, G. (2016), "Cooperative grey games and an application on economic order quantity model", Kybernetes, Vol. 45 No. 5, pp. 828-838.



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