A company considers centralizing a single item inventory ordering for a number of stores whose demand fluctuates randomly. First, there must be savings passed on to the stores from this centralization arrangement. Then, the savings must be divided among the participating stores in a way that no store (or a subset) will have an incentive to order separately. We model this problem as a cooperative game whose players are the stores. When holding and penalty shortage costs are identical for all subsets of stores, a game based on optimal expected costs (or the corresponding benefits) is subadditive (there are savings from centralization), and for normally distributed demands, whatever their correlations the core is never empty When the stores' holding and penalty costs differ, the corresponding game may have an empty core, and in fact, centralization may not be beneficial. We give conditions on the holding and penalty costs that ensure subadditivity. Given inventory centralization and a cost allocation game based on demand realizations, even in the case of identical holding and penalty costs the cost game in each period might have an empty core. We give sufficient conditions for such an allocation to be justifiable and subsidy-free (nonempty core) and examine properties of a number of ex ante—ex post cost allocation procedures.
Mathematics Department, School of Science, and School of Economics and Business Administration, Saint Mary's College, 94575, Moraga, CA, USA 2:
Management Information Systems, College of Business and Public Administration, University of Arizona, 85721, Tucson, AZ, USA