Here, we derive the optimal EMR policy and its corresponding cost by first finding the optimal MR policy as in [2]. Then, investigating cases where the inventory level is Li and . In these cases, violating the MR policy and allocating items to class icustomer may imply a backlog cost of future high priority arrivals, but saves holding and backlog costs. We derive the difference between the expected cost and saving implied by violating the MR policy. The set contains all the integers where this difference is negative.
We present here the method for the case n=2 and explain the generalization for n>2later. We refer to class 1 as the high priority class and to class 2 as the low priority class. For simplicity of the exposition, and to avoid trivialities, we assume that the system’s parameters are such that L20.