Production Planning and Allocation of Re-Entrance Flows with Stochastic Quality

Circular production promotes economic growth while conserving resources and energy. In this study, one aspect of production systems, the repair loop of returned products, is considered. The production system is composed of multiple flexible workstations that can process returns with different quality levels. This system aims to complete order production and deliver it on time by optimizing the use of the given resource levels. A sequential decision-making approach is employed to obtain rolling production decisions over a finite planning horizon. At each decision period, the manufacturer needs to simultaneously determine the optimal repair allocation plans for first returns and their potential second returns that will be back after certain periods. For traceability and quality reasons, a product at each return is required to be repaired on the same workstation; otherwise, a penalty cost is imposed. A stochastic mixed-integer programming model is developed based on sample average approximation (SAA) method, where the quality level of the second return is stochastic. Numerical results demonstrate that the value of the stochastic solution is significant compared with the average performance of solutions obtained by the existing deterministic model. Useful guidelines related to stochastic solutions and optimal capacity allocation patterns are also provided for production practices.