Joint Optimization of Production Rate and Spare Part Ordering with Maintenance Decisions for a Deteriorating System

Production systems are widely deployed across manufacturing industries to generate economic value. Ensuring their reliability is crucial to avoid costly failures and unplanned downtime. Condition-based maintenance has proven effective in managing degradation risks, yet most existing studies treat production rate control and spare part ordering as separate decisions, overlooking their coupled impact on system performance. This paper investigates a joint optimization framework for a deteriorating production system, where the degradation rate is directly controlled by the production rate. At each inspection epoch, the decisionmaker chooses between continuing production with an adjustable rate, or ordering a spare part that arrives after a fixed lead time followed by preventive maintenance. If failure occurs during normal operation, corrective maintenance is triggered at a high cost; if failure occurs while waiting for the spare part, only downtime losses are incurred. The problem is formulated as a discrete-time dynamic programming model and solved via value iteration. Numerical results reveal that the optimal policy exhibits a state-dependent threshold structure: order a spare part when the degradation level exceeds a threshold, otherwise continue production. Sensitivity analysis shows that the threshold increases with production revenue and preventive maintenance cost, and decreases with downtime cost, degradation rate, and lead time. Interestingly, the corrective maintenance cost has negligible impact on the threshold over a wide range of values. Comparative evaluations demonstrate that the proposed joint optimization approach outperforms heuristic strategies in balancing production revenue and maintenance-related losses.