A comment on Gerchak and Gupta’s ‘On apportioning costs to customers in centralized continuous review inventory systems’

In their recent article, Gerchak and Gupta discuss four different schemes for allocating joint inventory control costs. They demonstrate the benefits of consolidating inventories and note that allocating costs in proportion to the customers’ stand-alone costs ensured that each customer was always better off as part of the group. Their basis of allocation does not always distribute the benefits of consolidation; some customers may be worse off when new customers join up. This note applies the theory of the core from game theory to find a region of ‘fair’ cost allocations in which no one is worse off after consolidation. The Shapley Value is computed as the center of this region.