Reduction of makespan through flexible production and remanufacturing to maintain the multi-stage automated complex production system

Multi-stage production systems have been increasingly popular with a smart production system that has automated and flexible production rates. However, due to the complex structure of such a production system, most studies approach this as a single-stage production system or multi-stage by only incorporating a minimum number of real features. Thus motivated, this study presents the importance of automation and flexibility to reduce the makespan for multi-stage work-in-process inventory under a complex production system. This is a pioneer study in reducing the makespan for flexible multi-stage production systems since each stage of production produces defective items and the former stage's production is required to finish before running the latter stage. We consider the automated multi-stage production system and aim to reduce makespan duration by optimally controlling the amount of production lot, production, and backorder rate. In this system, finished products are obtained in the last stage, and in each stage, there are defective items. To mitigate defective items, the production system has a remanufacturing process in each stage, in parallel with production, such that the makespan does not increase and defective products of that stage are transferred to perfect items. This study characterizes the optimal lot size, production rate, and backorder rate at each stage along with the optimal selling price to maximize the total profit of the system. In analyzing the production model, we use a classical optimization method. We also conducted numerical experiments to validate the model and performed a sensitivity analysis of key parameters to derive several managerial insights on the impacts of optimized backorder rate and lot sizing on the profit. The results show that a significant reduction of defective items as waste reduction can be achieved by the reduction of makespan that utilizes a flexible production rate and remanufacturing rate. Our results also show that the benefit of flexible production instead of traditional production is 11.48% and the benefits of variable backorder for multi-stage instead of fixed and no-backorder are 93.62% and 99.55%, respectively.