Effective control policies for stochastic inventory systems with a minimum order quantity and linear costs

We consider a model of single-item periodic-review inventory system with stochastic demand, linear ordering cost, where in each time period, the system must order either none or at least as much as a minimum order quantity (MOQ). Optimal inventory policies for such a system are typically too complicated to implement in practice. In fact, the (s,S) type of policies are often utilized in the real world. We study the performance of a simple heuristic policy that is easily implementable because it is specified by only two parameters (s,t). We develop an algorithm to compute the optimal values for these parameters in the infinite time horizon under the average cost criterion. Through an extensive numerical study, we demonstrate that the best (s,t) heuristic policy has performance close to that of the optimal policies when the coefficient of variation of the demand distribution is not very small. Furthermore, the best (s,t) policy always outperforms the best feasible (s,S) policies and on average the percentage differences are significant. Finally, we study the impact of MOQ on system performance.