An integrated production-inventory model for deteriorating production with defective item rework and joint material replenishment policy

This paper considers an integrated production-inventory model which determines an optimal production cycle time and economic joint replenishment quantity of raw materials in a batch production system. The production process is assumed to be imperfect, and thus certain amount of item produced become defective. The defective items are assumed to be reworked immediately after the regular production ends and rework efforts are assumed to be performed under perfect condition. The objective is to minimize the expected total cost for the system over an infinite horizon. An algorithm to obtain an optimal or near optimal solution is presented. To demonstrate the model's fidelity, a numerical example is provided to illustrate the model. Sensitivity analysis is also performed and discussed. This deterministic model attempts to provide mangers with guidelines to evaluate the proper production cycle time and the purchase quantity of raw materials of an imperfect production process simultaneously under defective item rework and joint material replenishment policy.