Production control problem integrating overhaul and subcontracting strategies for a quality deteriorating manufacturing system

We study an unreliable deteriorating manufacturing system that produces conforming and non-conforming parts to satisfy a constant demand product rate. The manufacturing system is comprised of a failure-prone machine. Due to the combined effect of random availability variations and deterioration, the system is not able to fulfill long-term product demand. In particular, when finished goods inventory is positive, clients demand are fulfilled on-time and without delay. When backlog exists, subcontracting options are available at a higher cost to supplement the limited production capacity of the manufacturing system. The effect of deterioration is observed mainly in the quality of the parts produced, since the rate of defectives increases as the machines deteriorate. Overhaul activities can be conducted to mitigate the effect of deterioration. We propose a joint feedback control policy based on a stochastic dynamic programming formulation which aims simultaneously to determine the production and overhaul rates, and the rate at which subcontractors are requested. The proposed joint control policy minimizes the total cost, including the inventory, backlog, repair, overhaul, defectives, production and subcontracting costs, over an infinite planning horizon. To determine the optimal control parameters, we adopt a numerical scheme to solve the optimality equations and a numerical example is presented as an illustration of the approach. The structure of the joint control policy is validated through an extensive sensitivity analysis.