Stochastic Production Control of a Closed-Loop Hybrid Manufacturing–Remanufacturing System Considering Greenhouse Gas Emissions

This paper addresses the stochastic optimal control of a closed-loop hybrid manufacturing–remanufacturing system (HMRS) operating under random machine failures and greenhouse gas (GHG) emission constraints in the context of sustainable industrial operations. The system consists of two dedicated machines for manufacturing and remanufacturing that jointly produce a single product in a dynamic production environment. The objective is to minimize the long-run expected total cost, including inventory holding and shortage costs, manufacturing and remanufacturing costs, and penalties associated with emissions exceeding a prescribed limit. The structure of the optimal production control policy is determined using a stochastic optimal control framework based on Hamilton–Jacobi–Bellman equations, whose optimality conditions are solved numerically. A sensitivity analysis is then conducted to examine the behavior of the resulting control policy under variations in key system parameters. The results show how coordinated manufacturing and remanufacturing decisions can be regulated through emission- and inventory-dependent thresholds in failure-prone hybrid production systems. This work contributes to the literature on sustainable manufacturing by providing a rigorous modeling and control framework for environmentally regulated hybrid manufacturing–remanufacturing systems.