Lost Sales Inventory Models with Batch Ordering and Handling Costs

In this paper, we integrate inventory and handling into a single model for analysis and optimization of inventory replenishment decisions for a grocery retail store. We consider a retailer who periodically manages his inventory of a single item facing stochastic demand. The retailer may only order in multiples of a xed batch size, the lead time is less than the review period length and all unmet demand is lost, which is a realistic situation for a large part of the assortment of grocery retailers. The replenishment cost includes both xed and variable components, dependent on the number of batches and units in the order. This structure captures the shelf-stacking costs in retail stores. We investigate the optimal policy structure under the long-run average cost criterion. Our results show that it is worthwhile to explicitly take handling costs into account when making inventory decisions. We use parameter values typical for rocery retail environments. For an important subset of the retail assortment, we show that signicant cost reductions exist by explicitly considering handling in the inventory policy. Keywords: Retail inventory control, Handling, Lost sales, Periodic review, Fixed batch sizes