Inventory Management under Product Mis-identification/Shipment Errors

Abstract

“Wrong-product” delivery - the delivery of a product different from that desired - is a significant, but as yet unexplored problem in supply-chain management research. There are basically two reasons for wrong-product delivery: either the wrong product is mistakenly ordered or the right product is ordered but the wrong product is picked/shipped. This paper defines and analyzes the “wrong-product delivery” problem using a 2-product newsvendor model. Two non-substitutable products may be ordered at the beginning of each time period. However, whenever product i is ordered, then with known probability i, product j is delivered; i, j = 1, 2(i 6= j). First, we analyze the “no-recourse scenario”, where management correctly stores whatever was received, but takes no other action. We establish the form of the optimal policy and conduct sensitivity analysis. Although our modeling framework is simple, our results are unexpected and non-intuitive. For example, it is well known that in the single-product newsvendor model, increasing the uncertainty of demand or supply will yield an increase in the corresponding target basestocks and safety stocks. However, increasing the risk of a wrong-product error yields a decrease in the corresponding basestocks and safety stocks. Further, although target basestocks in the single-product newsvendor model are invariant to increases in on-hand inventory, we show that the target basestock for either product is non-decreasing as its inventory increases. We also demonstrate that the cost impact of wrong-product uncertainty is comparable, if not larger than, the cost impact of demand uncertainty. Next, we analyze the “recourse scenario” where management is able to correct errors but only by incurring a fixed cost of $K. We show that it is optimal to take recourse when the wrong-product uncertainty is sufficiently small, but not take recourse when the wrong-product uncertainty is high. In strategic terms, our analysis provides insight into the cost impact of wrong-product errors, and, hence, the importance of reducing them.Supply chain management, Inventory management, Shipment errors, Ordering errors, Yield management, Unreliable supply