The Two-Phase Stochastic Lotsizing Problem with Optimal Timing of Additional Replenishment

Recent advances in Information Technology have provided an opportunity to significantly improve the effectiveness of inventory systems. In particular, for periodic review systems it has become possible to receive actual and accurate sales data more than once in a period. We are given a single sales period and a single possibility to review the inventory level after the start of sales and to issue an additional replenishment if necessary. It is desirable to find the optimal quantity to replenish before the start of sales, the optimal moment of additional review, and the optimal quantity to replenish at the moment of additional review. In this paper we use analytical tools and propose an exact algorithm for simultaneously determining these policy decisions.