Optimality of myopic inventory policy for a single-product, multi-period, stochastic inventory problem with batch ordering and capacity commitment

The single-product, multi-period, stochastic inventory problem with batch ordering has been studied for decades. However, most existing research focuses only on the case in which there is no capacity constraint on the ordered quantity. This article generalizes that research to the case in which the capacity is purchased at the beginning of a planning horizon and the total ordered quantity over the planning horizon is constrained by the capacity. The objective is to minimize the expected total cost (the cost of purchasing capacity plus the minimum expected sum of the ordering, storage, and shortage costs incurred over the planning horizon for the given capacity). The conditions that ensure that a myopic ordering policy is optimal for any given capacity commitment are obtained. The structure of the expected total cost is characterized under these conditions and an algorithm is presented that can be used to calculate the optimal capacity commitment. A simulation study is performed to better understand the impact of various parameters on the performance of the model.