Exact and heuristic linear-inflation policies for an inventory model with random yield and arbitrary lead times

We investigate a periodic inventory system for a single item with stochastic demand and random yield. Since the optimal policy for such a system is complicated we study the class of stationary linear-inflation policies where orders are only placed if the inventory position is below a critical stock level, and where the order quantity is controlled by a yield inflation factor. We consider two different models for the uncertain supply: binomial and stochastically proportional yield and we allow positive and constant lead times as well as asymmetric demand and yield distributions. In this paper we propose two novel approaches to derive optimal and near-optimal numerical values for the critical stock level, minimizing the average holding and backorder cost for a given inflation factor. First, we present a Markov chain approach, which is exact in case of negligible lead time. Second, we provide a steady state analysis to derive approximate closed-form expressions for the optimal critical stock level. We conduct an extensive numerical study to test the performance of our approaches. The numerical experiments reveal an excellent performance of both approaches. Since our derived formulas are easily implementable and highly accurate they are very valuable for practical application.