A Mathematical Approach to Derive the Optimal Ordering Policy with Backorders and Inspection

Abstract

In this paper, a mathematical approach is proposed to derive optimal ordering with backorders with two scenarios for imperfect items. We assume a shipment contains a fraction of imperfect quality items which are screened out by 100% inspection. The first scenario assumes the imperfect items are repaired while the second one assumes that they are sold at a discounted price and are substituted with an emergency order. Time intervals are used as decision variables to derive the closed-form optimal solution. Two lemmas are provided to extract decision rule regarding the selection of optimal scenario. The managerial insights are discussed by a numerical example. The sensitivity analysis shows that the average total cost of second scenario increases with increase in cost of an emergency ordered item. Also, the results reveal that an increase in the imperfect rate of production system leads to lower optimal production quantity and lower backordering level, while the optimal average total cost increases along with imperfect rate.