Pricing and lot sizing for an EPQ inventory model with rework and multiple shipments

Abstract

This paper deals with an economic production quantity (EPQ) inventory model with reworkable defective items when a given multi-shipment policy is used. In this work, it is assumed that in each cycle, the rework process of all defective items starts when the regular production process finishes. After the rework process, a portion of reworked items fails. This portion becomes scrap and only the perfect finished items can be delivered to customers at the end of rework process. A profit function is derived to model the inventory problem and it is shown that the profit function is concave. Due to the complexity of the optimization problem, an algorithm is developed to determine the optimal values of manufacturing lot size and price such that the long-run average profit function is maximized. Furthermore, two special cases are identified and explained. Finally, a numerical example is given to illustrate the applicability of the proposed inventory model.