Joint optimization of preventive maintenance and inventory policies for multi-unit systems subject to deteriorating spare part inventory

•Joint models of maintenance and inventory management for multi-unit systems are proposed.•Deteriorating spare part inventory is also considered into the joint models.•Two different deteriorating inventory models are proposed due to the availability of data.•The preventive maintenance interval and maximum inventory level are jointly optimized.•The existence and uniqueness of the optimal maximum inventory level are strictly proved.

The interconnection of maintenance and spare part inventory management often puzzles managers and researchers. The deterioration of the inventory affects decision-making and increases losses. Block replacement and periodic review inventory policies were here used to evaluate a joint optimization problem for multi-unit systems in the presence of inventory deterioration. The deterministic deteriorating inventory (DDI) model was used to describe deteriorating inventory when deteriorating inventory data were available and the stochastic deteriorating inventory (SDI) model was used when they were not. Analytical joint optimization models were established, and the preventive replacement interval and the maximum inventory level served as decision variables to minimize the expected system total cost rate. This work proved the existence of the optimal maximum inventory level and gave the uniqueness condition under the DDI model. Numerical experiments based on the electric locomotives in Slovenian Railways were performed to confirm the effectiveness of the proposed models. Results showed the total cost rate to be sensitive to the maximum inventory level, which indicates that the research of this work is necessary. Further, the optimal preventive replacement interval was reduced and the optimal maximum inventory level was increased to balance the influence of deteriorating inventory. Monte Carlo experiments were used to show that the proposed policy is better than policies that do not take deteriorating inventory into account.