On the $$\varvec{(Q,r)}$$(Q,r) policy for perishables with positive lead times and multiple outstanding orders

Abstract

We consider an inventory system for perishables with fixed lifetimes, positive replenishment lead times and lost sales in the presence of non-negligible fixed ordering costs. The system is studied under the lotsize reorder level (Q, r) policy. An exact analysis of this system based on the stationary distribution of the remaining lifetime process is provided by Berk and Gurler (Oper Res 56(5):1238–1246, 2008) under the restriction that there is at most one outstanding order at any time ($$r<Q$$). In this work, we generalize their results to allow for more than one outstanding orders $$(r\ge Q)$$. We provide the operating characteristics of the inventory system and construct the exact expected cost rate expression using a renewal theoretic approach. An illustrative numerical study indicates that allowing for multiple outstanding orders $$(r\ge Q)$$ may result in significant savings in the expected cost rate, compared to the case with $$r<Q$$. In particular, when the fixed lifetimes are short and the ordering costs are low, expected costs can be reduced by more than half.