Equal Surplus Sharing in Grey Inventory Games

This study introduces a model where inventory costs are represented as grey numbers, rather than traditional crisp or stochastic values. Utilizing grey calculus, we reinterpret game-theoretic solutions to address interval uncertainty within cooperative grey inventory games. Building on the works of van den Brink and Funaki (2009) and Olgun et al. (2017). We establish grey equal distribution rules for fair cost allocation. We determine problem parameters to construct a grey inventory game, applying it to three shotgun companies in Turkey. The calculated grey inventory costs and different game-theoretic solutions are presented. This study extends solutions like the Banzhaf value, CIS-value, ENSC- value, and ED- solution by incorporating interval uncertainty. Future research may explore extensions such as grey purchasing costs, stock out allowances, defective goods, and quantity discounts, enhancing the application of grey calculus in cooperative game theory and inventory management.