Modeling and Solving a Multi-product Economic Order Quantity Problem with Imperfect Items and Emergency Buy or Repair Options

Abstract

In this paper, it has been proposed a multi-product economic order quantity (EOQ) model, assuming the presence of some imperfect items. They are inspected 100 percent as they are delivered, and defective items are withdrawn. We do not access to supplier to replace the imperfect items with perfect one. So for meeting the demand, there are two options for imperfect items: buy or repair. In buy option, we sell the imperfect items in second market with lower price, and then buy the imperfect items from local supplier with higher price; but in repair option, we will send the imperfect items to repairing workshop, and after they are delivered from repair facility, they are sold as perfect items. There are also some limitations in available budget and warehouse space, and thus we should determine the economic order quantity for each item by considering these limitations. Additional in repairing option, we have some constraints for repairing rate. In the proposed model, the shortage is not allowed, and we have considered this issue in employing alternatives. This paper extends the supposed assumes by Jaber et al. (سال؟؟؟). The Proposed problem is a Mixed Integer Non-Linear problem (MINLP). This field of problems are NP-Hard, and they are solved by Meta heuristic algorithms, but they can be solved by exact methods in small scale. So, the proposed problem in this paper is solved by exact method. We also solved numerical examples, and applied the sensitivity analysis for important parameters.