Two Dimensional Lease Limits

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Abstract -This study proposed a two-dimensional lease contract – age and usage limits – for new and used equipment. Under the lease contract, the lessee agrees that an additional cost will be charged when the usage rate exceeds a threshold value. The lessor performs both preventive and corrective maintenance actions. The decision problem for the lessor is to find the optimal price of each lease option offered, and for the lessee is to select the best lease option. We modeled using a cooperative game theory formulation, and the optimal decisions for the lessor and the lessee are coordinated in order to reach a win-win solution.
Keywords -cooperative game theory, coordination, expected profit, imperfect preventive maintenance, new and used equipment, …show more content…

The one dimensional lease contract is characterized by time/age limit whereas the two dimensional lease contract is characterized by age and usage limits. For the one-dimensional lease contract, a lot of works have been done but we are not aware for the two dimensional lease contract. For the new lease item, [3], [4], [5] developed the optimal PM policy, the optimal length of the lease period and derived the optimal number and degree of PM. Furthermore, [6], PM actions are done when the failure rate reaches a prespecified threshold and failures between PM are minimally repaired. The optimal threshold of failure rate is obtained by minimizing the total maintenance costs. The authors in [7] extends the model of [6] to the case where the length of the lease period is not fixed. For the used equipment, [8], [9], [10], and [11] investigated the optimal upgrade level before leasing, the optimal PM, the optimal length of the lease period, and the multi-phase periodic PM policy within the lease period. Finally, for the remanufactured item, [12] considered lease options which include a remanufactured …show more content…

1 year (called a one dimensional lease contract). For the case where equipment is used intensively, the usage will significantly influence the degradation of the equipment and this in turn will increase the number of failures during the lease period and hence a bigger total repair cost. This indicates the need to include usage in modeling the failure and defining the lease contract. In this paper, we propose a lease contract which involves two parameters – i.e. age and usage limits (called a two dimensional lease contract). In addition, due to fierce competition, the lessor tends to offer a longer period of a lease contract e.g. 2 to 5 years. A longer leased period gives more revenue to the lessor, but this increases the maintenance cost for servicing the equipment. An effective PM will reduce the number of equipment failures (and hence lower the repair cost) and avoid the penalty cost. In the lease contracts studied for a new item or a used item, the study is done for each item separately. In this paper, we consider the situation where the new and used item lease contracts are competing with each other, and examine them in the case of a two dimensional lease contract (See Fig. 1). Since the study from the lessor and lessee perspectives, we will use a game theory formulation to model the decision

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