Calculating can-order policies for the joint replenishment problem by the compensation approach

In this paper we consider the stochastic joint replenishment problem. We coordinate the replenishment of an inventory with several items, where the fixed cost of a replenishment consists of a major order cost for each order and a minor order cost for each item participating in the order. The literature has focused on two kinds of policies: can-order policies and periodic replenishment policies. Generally speaking the can-order policy performs better when the major ordering cost is relatively low, and the periodic replenishment policies better when the major ordering cost is relatively high. We present a new method for calculating can-order policies, which dominates existing methods on examples where the can-order policy performs better than the periodic replenishment policies. The method is based on a compensation approach, where an item placing an order receives a compensation from other items benefitting from the order opportunity.