تعیین مشترک مدت اجاره و سیاست تعمیر و نگهداری پیشگیرانه برای تجهیزات استیجاری با ارزش اسقاطی

This paper investigates the influence of the length of the lease period on the maintenance policy for leased equipment with residual value. The length of the lease period increases, however, the lessor’s income increases, and the maintenance cost of the equipment rises as well. Therefore, the lease payment and maintenance service of the equipment are crucial items in the lease contract for the lessor’s profit. If the equipment breaks down within the lease period, minimal repairs will be performed on the equipment and the lessor may incur a penalty cost if the repair time exceeds a pre-specified tolerable time. The imperfect preventive maintenance (PM) actions are carried out when the age of the equipment reaches a controlled-limit during the lease period. Under this maintenance scheme, the mathematical model of profit is constructed and then the optimal maintenance policy and the length of the lease period are obtained such that the expected total profit is maximized. Finally, numerical examples are given to illustrate the effects of the optimal length of the lease period and the maintenance policy for profit model.

Facing highly competitive markets, most enterprises may need complex or multi-functional equipment to provide a variety of products and services to meet the divergent needs of customers. In addition, due to diversification of financing methods, the concept of tax saving is gradually valued by enterprises (lessees). Therefore, many enterprises begin to use finance leasing (that is, capital leasing) to reduce investment risk and working capital. Finance leasing means that enterprises pay rent to a leasing company (lessor) for the leased equipment, and then the lessor offers the equipment and the maintenance service. Hence, a finance leasing contract usually contains the specific length of the lease period, the rent and the penalty clauses. The penalty clauses state that the lessor would be penalized when the leased equipment could not carry out its intended performance according to some specified requests by the lessee. For example, a penalty incurs when the number of failures of the equipment during the lease period or the repair time of the equipment exceeds the specified tolerance limits. Therefore, a well-designed structure of the lease contract and the maintenance plan of the leased equipment are very important issues for the lessor to obtain high profit. In general, the rent usually depends on the length of the leased period and the specified maintenance service required by the lessees. A longer length of the leased period is expected to increase the revenue of lessors, and the maintenance cost of the equipment rises as well. For reducing the repair cost and the penalty cost, some lessors undertake preventive maintenance (PM) actions to reduce the number of the equipment failures within the leased period. In addition, because of various reasons such as environmental concerns, shortage of material, economic benefit, and legislative pressure, re-use has been receiving growing attention and the reclaiming channels are gradually increasing. Therefore, some lessors take the residual value of the equipment into account when they are considering the length of the leased period. For instance, car rental companies sell their used cars to the second-hand markets and most of these cars have been sold by the time they are 2 years old (Pongpech & Murthy, 2006). As mentioned above, this paper proposes a leasing model of the durable and repairable equipment for lessors. The motives of the leasing model are to provide a PM scheme to reduce the total cost within the lease period and to consider the income from the residual value of the equipment at the end of the lease period. Therefore, taking the factor of the residual value of the equipment into account, this paper aims simultaneously to determine the length of the lease period and the PM scheme in the lease contract for the lessor so that the expected profit is maximized. The remainder of this paper is as follows. Section 2 includes a literature review about leasing and maintenance policies. The proposed model of this paper is described in Section 3. In Section 4, the optimal PM policy and the length of the lease period are obtained and an algorithm is constructed to organize the solving processes. Some numerical examples are offered to illustrate the leasing decisions and the results are compared with different situations in Section 5. Finally, conclusions are drawn.

In this paper, the age-reduction method is adopted to describe the degree of preventive maintenance and a mathematical model of profit is constructed for the leased equipment within the lease period. From the model of profit, we show that there exists a unique optimal length of lease period and maintenance policy within the lease period such that the expected total profit is maximized. Within the lease period, the equipment should be restored to its original state after each preventive maintenance action. That is, preventive maintenance actions should be performed at time epochs L/(n + 1), 2L/(n + 1), 3L/(n + 1), … , nL/(n + 1) with the same maintenance degree L/(n + 1). When the preventive maintenance cost b or β increases, the number of preventive maintenance actions n increases but preventive maintenance degree, controlled-limit and maximum profit decrease. The preventive maintenance number and maximum profit under the considered residual value are higher than the non-considered residual value. Under the equipment with residual value, the expected total profit is maximized. Further, two-phase maintenance of equipment and the interest rate of the company within the lease period are investigated for various maintenance plans.