Optimal length of lease period and maintenance policy for leased equipment with a control-limit on age

This paper investigates the optimal length of lease period and maintenance policy for leased equipment. In order to have steady revenue, the lessor (owner) of equipment may provide a discount to encourage the lessee (user) to sign a contract with a longer lease period. However, as the lease period increases, the maintenance cost also increases due to the deterioration or usage of the equipment. Therefore, there is a need to determine an appropriate length of lease period and a corresponding maintenance policy for the leased equipment from the viewpoint of the lessor such that the expected total profit is maximized. In this paper, the following maintenance scheme is considered. When the leased equipment fails, a minimal repair is conducted to bring the equipment back to an operating condition. Furthermore, when the age of the equipment reaches a specified level (called as a control-limit), an imperfect preventive maintenance (PM) is carried out to avoid possible failures. Under this maintenance scheme, the mathematical model of the expected total profit is developed and the optimal length of lease period and the corresponding optimal maintenance policy are derived. Finally, some numerical examples are given to illustrate the effects of the length of lease period and the maintenance policy on the expected total profit.