Lot-sizing problem for a defective processing system with categorized items, backordering and pricing policy

Abstract

The lot-sizing problem with a defective processing system is one of the most widely known inventory control models that can be regarded as the generalized form of the economic production quantity (EPQ). This paper proposes a model for lot sizing problem within a defective processing system. The study assumes that the processed items are from different categories: high-quality, low-quality, reworked, and rejected items. In addition, to identify items associated with each category, an online full screening inspection of the items would be implemented. We model the system considering immediate rework after regular processing cycle where reworked items are sold at the same price as high-quality items. The rejected items are also scrapped at the end of the production cycle. Motivation of this paper is proposing a model for the EPQ problem with faulty products, scrap, and rework. Moreover, to integrate decisions for increasing the system’s profitability, the model aims to provide a practical and general framework to integrate pricing decisions, optimal processing order quantities, and optimum level of shortage with respect to maximizing system’s profits. Then, a numerical example is presented to illustrate performance of the proposed model and solution algorithm. Finally, we perform a sensitivity analysis to evaluate the influence of the model parameters on optimal decisions.