Cost Allocation for Joint Replenishment Models

We consider the one-warehouse multiple retailer inventory model with a sub modular joint setup cost function. The objective of this model is to determine an inventoryreplenishment policy that minimizes the long-run average system cost over an infinitetime horizon. Although the optimal policy for this problem is still unknown, a class ofeasy-to-implement power-of-two policies are 98% effective. This paper focuses on howthe cost, under an optimal power-of-two policy, should be allocated to the retailers.This question generates an interesting cooperative game. We prove that this cooperative game has a non-empty core. The key to our result is a strong duality theorem for the one-warehouse multiple retailer problem under power-of-two policies