A number of stores can save costs by forming a centralized inventory system. The number and location of centralized warehouses can be determined in minimizing total costs and then these cost reductions should be allocated fairly to each store. If no group of stores feel that they are paying to subsidize to the complementary set of stores, then that cost allocation is in core. That is, all stores become better off by forming a group. This study shows that there does not exist the core in some examples. Hence, we suggest a framework for the cost allocation both of the case in which the core exists and the core does not exist.