Effective inventory control policies with a minimum order quantity and batch ordering

In this paper, we consider a single-item periodic-review stochastic inventory system with both minimum order quantity (MOQ) and batch ordering requirements. In each time period, the firm can order either none or at least as much as the MOQ. At the same time, if an order is placed, the order quantity is required to be an integral multiple of a given specific batch size. We first adopt a heuristic policy which is specified by two parameters (s, t). Applying a discrete time Markov chain approach, we compute the system cost and optimize this (s, t) policy under the long-run average cost criterion. We also consider a simpler one-parameter policy, the so-called S policy, which is a special case of the (s, t) policy. In an intensive numerical study, we find that (1) both policies perform well in comparison with other policies and (2) the S policy also performs well and is compatible with the (s, t) policy; only in a few cases where demand variation is small, the latter outperforms the former significantly. We also evaluate the effects of some important parameters on system performance.