Exploration of finite production rate model with overtime and rework of nonconforming products

This study explores a finite production rate (FPR) model featuring overtime option and rework of nonconforming products. Classic FPR model assumed all items produced are of perfect quality. However, in real fabrication systems, owing to diverse uncontrollable conditions, production of nonconforming items is inevitable. To maintain high product quality and lower production cost allow present-day's manufacturing firms to gain competition advantage. Also, due to limited in-house capacity, to be able to smooth production schedule enables management to meet due dates and better allocate fabrication resources. Motivated by these practical issues, the present study investigates a FPR model considering overtime and rework of nonconforming items. An exact model is developed to specifically describe the problem. Mathematical analysis and differential calculus are employed to help obtain the expected system cost function and prove its convexity, and then derive the optimal lot size per replenishment cycle. Moreover, sensitivity analysis and diverse effects of key system factors on the problem are demonstrated via numerical illustrations to help managerial decision-making.