Imperfect Production System under Reverse Logistics in Stock-Out Situation: EPQ Model

This paper derives a reverse logistic inventory model with imperfect production, stock-dependent demand, flexible manufacturing, and shortages over infinite planning horizon. The objective is to determine the joint policy for optimal production, amount of remanufacturing, collection of reusable items, and collection as well as disposal of defective items which minimizes the total cost of the inventory system under consideration. To make the model more realistic, both of the cases of linear and nonlinear holding costs have been discussed. The results are discussed with a numerical example to illustrate the theory. 1. Introduction The assumption of perfect production is not ideal for practical production system. Even the best production system may produce defective items. The governmental guidelines clearly state reduction of wastages, conservation of precious resources, protection of environment, and prevention of environmental degradation as a guiding principles for the business organizations. The manufacturing organizations may reuse the defective items after suitably repairing and removal of defects in order to avoid waste of resources. The defective items which are either irreparable or cannot be repaired easily and cost effectively are disposed off. They also prefer to reuse or recycle the items procured from the customers and reconvert through the appropriate process to appear as new and useful. 2. Literature Review The classical production inventory model assumes that all the items produced are of perfect quality. Such an assumption appears impractical in real system. Therefore researchers have attracted towards model formation in which some parts of the items produced are of imperfect quality and they can be reworked and repaired. Rosenblatt and Lee [1], Lee and Rosenblatt [2], Cheng [3], Das and Sarkar [4], and Chung and Hou [5] worked on the issue of imperfect quality items and proved that production inventory cost is affected by rework or repair. Cheng [3] developed an economic order quantity model with demand-dependent unit production cost and imperfect production processes. Hayek and Salameh [6] assumed that all of the defective items produced are repairable and derived an optimal operating policy for EPQ model under the effect of reworking of imperfect quality items. Chung and Hou [5] investigated the production inventory model with imperfect production processes and allowable shortages. Chiu et al. [7] derived an economic production quantity (EPQ) model with scrap, rework, and stochastic machine breakdowns and assumed some portion of the