Cooperative grey games and an application on economic order quantity model

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.