Purpose: This paper deals with a particular type of leasing contracts according to which an equipment is leased for free with the condition for the lessee to purchase a predetermined minimum quantity of consumables during each leasing period. Maintenance actions are performed by the lessor and borne by him. Imperfect preventive maintenance is carried out every t time units throughout the leasing period. Minimal repairs are performed following equipment failures. At the end of the leasing period, an overhaul which restores the equipment to “as good as new” state is performed. The equipment is leased many times during its life cycle. The purpose of this paper is to determine the values of the decision variables for the lessor, which are the preventive maintenance (PM) period and the minimum quantity of consumables to be sold to ensure profit.Design/methodology/approach: A mathematical model is developed to express the expected maintenance cost per time unit incurred by the lessor as well as his expected profit over the equipment life cycle. The optimal PM period minimizing the maintenance cost is determined first. Then, given the corresponding minimum maintenance cost, the minimum quantity of consumables (the lessor's break-even point) to be purchased by the lessee is computed. A numerical example and a sensitivity study are presented, and the obtained results are discussed.Findings: The outcome of this work is supposed to help the lessors determining two key values to be included in each leasing contract, namely: (1) the periodicity according to which they will commit to perform preventive maintenance actions such that their average total cost of maintenance is minimized, (2) the minimum quantity of consumables that the lessee must commit to purchasing during the leasing period. This quantity must be between the break-even point and the maximum quantity associated with the capacity of the equipment.Practical implications: Practically, the objective of this work is first to determine the optimal strategy to be adopted by the lessor in terms of effort relating to PM and second to determine the minimum quantity of consumables that the lessee must purchase during the leasing period such as profit is insured for the lessor.Originality/value: This type of leasing (for free) has not been addressed in the literature particularly when considering maintenance strategies.

Leasing has proven to be a business model that is perfectly suited to the circular economy. It significantly contributes to sustainable development by enabling the reuse of machinery and equipment after each lease period and by including preventive maintenance and overhauls within and between lease terms. This helps to extend the life cycle of equipment, promote value recovery, and reduce waste. This paper examines an imperfect preventive maintenance (PM) strategy applied to equipment rented under the terms of “free leasing”. In free leasing, the lessor makes the equipment available to the customer for a specified period of time without charging rent. In return, the customer is required to purchase the equipment’s consumables exclusively from the lessor. The lessor is also responsible for the maintenance of the equipment at the customer’s premises. The greater the quantity of consumables used by the customer, the more the equipment will deteriorate. Consequently, the lessor must be able to determine the most effective approach to preventive maintenance, ensuring that it aligns with the customer’s planned usage rate while maximizing profit. This work proposes a PM strategy to be adopted by the lessor during the free lease period. This strategy involves the performance of imperfect PM actions just before the start of the lease period and then periodically. Different packages of preventive actions can be applied each time, with each package having a different cost depending on the level of effectiveness in terms of rejuvenating the equipment. Minimal repairs are performed in the event of equipment failure. The decision variables are the PM period to be adopted and the maintenance efficiency level to be chosen for each preventive intervention. The objective is to determine, for a given customer with an estimated consumption rate profile of consumables, the optimal values of these decision variables so that the lessor maximizes their profit. A mathematical model is developed to express the lessor’s average profit over each lease period. A solution procedure is developed for small instances of the problem, and an Artificial Bee Colony algorithm is implemented for larger instances. A numerical example and a sensitivity analysis are presented.