Lease Contract Case Study

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II. MODEL FORMULATION In this section, we define a two dimensional lease contract and other concepts that will be used later, such as the failure model and the formulation of a PM policy and its effect on reliability. Fig. 1. Key elements of lease contract considered Notations: ΩΓ=[0,Γ0)× [0,∞) : Lease coverage region δy :Preventive maintenance level D :Total downtime in (0,t] :Revenue, lease contract time Y :Usage rate C0 :Preventive maintenance cost per unit of time Cv :Degree of preventive maintenance cost :Penalty cost per unit of time Pn,Pu :Lease contract cost for used equipment and lease contract cost for new one over the contract period k :Number of PM during maintenance contract :Annual cost over the contract period …show more content…

We study the lease contracts proposed from the view points of the lessor and the lessee. The decision problem for the lessor is to determine the optimal price structure (i.e. the price of each lease option) such that to maximize the expected profit whilst the lessee is concerned with the best option which maximizes its expected …show more content…

Modelling of Failure We now model equipment failures under the two-dimensional lease contract. There are three different approaches to model failures occurring in a two-dimensional lease region [14]. In this paper, the one dimensional approach as in [15] is used to modeling the failures. Let be a usage rate of the truck. We consider that varies from truck to truck but is constant for a given truck (or agiven equipment). For a given truck with , the lease contract ceases at for 0 < ∞. Let be the conditional hazard function for the time to first failure for a given dump truck. As it is a repairable item, then failures are appropriate to model using the conditional hazard function . It is considered as a non-decreasing function of the age t and the usage rate y. We assume that is given by which is allowed to incorporate the age and usage for modeling the degradation the truck. As in general the usage rate does more impact to the degradation of the equipment, where . In other words, the truck with high usage intensity degrades much faster than that of the truck with low usage intensity . Furthermore, for a given truck, if all failures under the lease contract are minimally repaired and repair times are very small relative to the mean time between failures, then failures follow a non-homogeneous Poisson process (NHPP) with intensity function

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