LOT SIZING IN A SUPPLY CHAIN SCHEDULING IN A TWO-ITEMS PRODUCTION SYSTEM WITH REWORK

In classical models of inventory and production control, it is assumed that all kinds of production machineries in various stages produce items with no defect and the quality of output of production stages are equal. However in practice, due to several reasons like the error of machinery and operators of productions, the performance quality of the production processes uctuates after a time and producing the low-quality and defective items is inevitable. On the other hand, producing defective items, which may be reworked or deposed, has a direct and signicant eect on optimal lot sizing and relatedcosts. Hence, inproblemsraisedinpracticalsupply chain systems including dierent levels like supplier, manufacturer and customer, the defective production of items has been considered increasingly in recent years. In these systems, generally it is assumed that the lowquality products are returned to the prior level in production process and they come back in manufacturing system again after passing a rework cycle. In this situation, modeling the problem and determining the optimal polices in inventory and production planning, such as optimal lot sizing, are of the great concern for production managers. In this paper, an extended version of economic production quantity problem (EPQ) in which a nal product consisting of two parts is considered. In this problem, there is a dual echelon supply chain which includes the parts suppliers in rst level and the nal product producer in the second one. In both echelons, it is assumed that the production process is accomplished with a positive defective rate, which may be dierent for parts and nal product. In this study, production rate and rework rate are limited, demand is continuous, and shortage is not allowed. We model the problem with average cost approach and determine the optimal lot. The model is validated while illustrating a numerical example. Finally, we analyze sensitivity of cost depending on inventory and economic lot sizing according to the change in defective production, rework rate, and production rate.