Analytical Study of Multi-Item Joint Replenishment Problem

This study evaluates the performance of a multi-item joint replenishment inventory model. In this model, the retailer uses a continuous review QS inventory policy. We assume that the customers who can not be satisfied by the retailer immediately will be lost, which is the main difference between this study and the previous research, and also the main contribution of this article. Based on the lost sale assumption and other assumptions on the outstanding orders during retailer lead time, we analyze the order quantity distribution of each item in their joint order. After that, by decomposing the multi-item joint replenishment problem to multiple single item inventory models, we derive the expression of the retailer cost analytically. At last, we give some suggestions for future research.