Optimal imperfect preventive maintenance policy for equipment leased during successive periods

Abstract

In this paper, we consider randomly failing equipment leased several times during their life cycle with a given warranty period. A mathematical model is developed to determine the optimal efficiency levels of preventive maintenance (PM) to be performed on the equipment between successive lease periods, maximising the expected total profit of the lessor over the equipment life cycle. The model considers the expected leasing revenue as well as the equipment acquisition cost and the average PM and repair costs. PM actions allow reducing the age of the equipment to a certain extent with a corresponding cost depending on the PM level adopted. The efficiency of the PM is determinant of the expected revenue during the next lease period. Given a set of K possible PM levels and the number of lease periods n over the equipment life cycle, K^{n−1 PM} strategies are possible. A genetic algorithm is proposed in order to obtain nearly optimal policies in situations where the number of possibilities Kⁿ⁻¹ is very high. Obtained numerical results are discussed. Small- and big-size instances of the problem are considered in the case of a service company in the oil and gas industry specialised in leasing specific equipment such as separators, to oil companies for production activities with a limited duration of several months like well testing or short production tests.

Keywords:

• leasing
• imperfect preventive maintenance
• virtual age
• warranty
• genetic algorithms