RETAIL INVENTORY CONTROL WITH LOST SALES, SERVICE CONSTRAINTS, AND FRACTIONAL LEAD TIMES

This paper describes a periodic review, fixed lead time, single-product, single-facility model with random demand, lost sales and service constraints that was developed for potential application at a Western Canadian retailer. The objective of this study was to determine optimal (s, S) policies for a large number of products and locations. To this end, we evaluate the long run average cost and service level for a fixed (s, S) policy and then used a search procedure to locate an optimal policy. The search procedure is based on an efficient updating scheme for the transition probability matrix of the underlying Markov chain, bounds on S and monotonicity assumptions on the cost and service level functions. A distinguishing feature of this model is that lead times are shorter than review periods so that the stationary analysis underlying computation of costs and service levels requires subtle analyses. We compared the computed policies to those currently in use on a test bed of 420 products and found that stores currently hold inventories that are 40% to 50% higher than those recommended by our model and estimate that implementing the proposed policies for the entire system would result in significant cost savings.