Lease Contracts with Servicing Strategy Model for Used Product Considering Crisp and Fuzzy Usage Rates

Abstract

Leasing activity is becoming popular in recent years for several reasons. One among the reasons is in regards to extremely high cost of purchasing for some products or equipment, e.g. heavy equipment used in a mining industry and other manufactures using sophisticated equipment. In these areas, due to the expensive production equipment, many operators adopt a leasing contract, rather than purchasing the equipment directly. In this paper, we study lease contracts for used product involving servicing strategy. The lessor (agent) will give servicing strategies which allows more than one imperfect repair to the lessee. A penalty cost incurred when the time required to perform a repair action exceeds a predetermined target. The servicing strategy proposed reduces equipment failures and hence decreases total maintenance cost during the lease contract. We develop a mathematical model to find the optimal maintenance strategy, such as the cost structure and the maintenance degree during the lease period. We find the optimal maintenance level and the threshold values for the servicing strategy such that to minimize the expected total maintenance cost. Numerical examples are presented to illustrate the optimal solution, firstly by considering crisp usage rates level and secondly by considering fuzzy usage rates level.