Production and replacement planning of a deteriorating remanufacturing system in a closed-loop configuration

This paper deals with the control of a hybrid manufacturing/remanufacturing system subject to random breakdowns and repairs. Given the heterogeneity of returned products, the remanufacturing machine deteriorates with time as a result of imperfect repairs, and needs to be replaced. The manufacturing machine receives homogeneous raw materials, and is not affected by this type of deterioration. The main objective of this paper is to find the production rates of both machines and the replacement rate of the remanufacturing machine that minimize the total cost, including production, inventory holding, backlog, repair and replacement costs, over an infinite planning horizon. A novel mathematical model is proposed for the underlying class of problems related to the history of breakdowns and repairs. This model is characterized by the extension of the state space, leading to a Markov decision model, allowing a derivation of the optimality conditions. Otherwise, such conditions are impossible to obtain. Optimality conditions in the form of Hamilton-Jacobi-Bellman (HJB) equations are thus developed. We show that despite the increased state space dimension, the problem remains tractable, and the solutions of HJB equations are obtained numerically. Finally, an illustrative example and a sensitivity analysis are provided to verify the robustness of the control policies obtained.