Cost minimising order schedules for a capacitated inventory system

In this paper, we study an inventory system with multiple retailers under periodic review and stochastic demand. The demand is modelled as a discrete random variable. Linear holding and backorder costs as well as fixed order costs are assumed. Orders to replenish inventories can be placed at a manufacturer with a limited capacity according to a cyclic order schedule. A fixed portion of the total available capacity in a period is allocated to each retailer, who follows a modified base‐stock policy to determine the order quantities. Thus, the order policy consists of four policy parameters for each retailer: the length of the review period, the first order point within a planning horizon, the individual capacity limit, and the modified base‐stock level. We present an algorithm to compute the exact optimal policy parameters and two heuristics. In a numerical study, we compare the results of these approaches and derive insights into the performance of the heuristics. In addition, we introduce three different schedule types and identify the situations, in which they perform best.