Optimal Replenishment and Lot Sizing Strategy for Inventory Mechanism with Step-Shaped Demand and Backordering

This paper discusses the inventory mechanism with backordering and with the infinite planning horizon consisting of two stages wherein the demand rate in the first stage is strictly greater than that in the second stage. To minimize the retailer’s inventory cost, we establish a lot sizing decision model. On the basis of the inventory cost analysis, we present a closed-form solution to the model and provide an optimal replenishment and stocking strategy to the retailer. The given numerical experiments show the validity of the model.