Optimal purchasing and production control for a circular production system

The paper investigates the optimal purchasing and production control policy within a circular production system that processes two returned material types through a shared manufacturing center. Materials are purchased or rejected upon arrival, with differences in procurement cost. At each decision epoch, the system must decide whether to purchase incoming materials and which type to prioritize for production. The problem is formulated as a Markov decision process, and a linear programming approach is developed to compute the optimal purchasing and production policy for the system under both non-preemption and preemption rules. Theoretically, the structure of the optimal policy is analytically characterized under the preemption rule in the case of equal production rates. Numerical experiments reveal that this policy remains optimal or near-optimal for the system under non-preemption and preemption rules with varying production rates. Additionally, comparisons of the optimal policies between non-preemption and preemption rules demonstrate that the system under the preemption rule yields higher average reward than that under the non-preemption rule, to varying degrees depending on system parameters, such as production rate, holding cost, and arrival rate.