A multiproduct single machine economic production quantity model for an imperfect production system under warehouse construction cost

This paper develops an economic production quantity (EPQ) inventory model for a multiproduct single-machine lot-sizing problem with nonconforming items including scrap and rework, where reworks are classified into several groups based on failure severity. In this inventory model, shortage is allowed and is backordered. The aim is to determine the optimal period length, the lot size, and the allowable shortage of each product so as the total cost, including setup, production, warehouse construction, holding, shortage, reworking, and disposal is minimized. Besides, the available total budget is scarce and that there is a lower bound on the service level of each product. While the convexity is proved, an exact method is proposed to solve the nonlinear programming problem. A numerical example is provided at the end to demonstrate the applicability of the proposed solution procedure as well as to perform a sensitivity analysis.