An imperfect multi-product production system with rework

This study develops an imperfect, multi-product production system with rework. Our objective is to minimize the joint total cost of the system, subject to service level and budget constraints. Since the objective function in the problem is convex, the existence of global optimality is assured. A solution procedure is proposed and numerical examples are provided to demonstrate the applicability of the model in real-world manufacturing problems. Finally, sensitivity analyses are provided to provide managerial insights, as well as to investigate the interdependency of the parameters.