An integrated model of preventive maintenance and safety stock for a used production unit under leasing

In this paper, we propose an integrated model of preventive maintenance (PM) and safety stock for an unreliable production unit, subject to random failures, acquired by leasing. Maintenance activities, both preventive and corrective, are performed by the lessor under the lease contract, incurring maintenance costs to the lessor. The leased production unit is used by the lessee to produce parts for the subsequent production stage. To prevent the subsequent production stage from being interrupted during breakdowns and PM, the lessee must produce a certain amount of safety stock, incurring inventory costs to the lessee. Unlike other models in the literature that implicitly assume that the leased production unit is a new item, in this paper, we investigate the case where the leased production unit is one that has already been used. In this case, the lessor can perform reconditioning, prior to leasing, on the production unit being leased incurring a reconditioning cost to the lessor. A mathematical model is developed to determine the optimal PM cycle duration, reconditioning level, and safety stock size to minimise the total expected cost to the lessor and the lessee combined over the leasing horizon. The numerical results show that calculating the optimal values of all three decision variables by considering the lessor and the lessee simultaneously yields a more satisfactory result, in terms of the total expected cost over the leasing horizon, than when the parties are considered individually. Some managerial insights useful to both the lessor and the lessee are provided in the sensitivity analysis section.