Stochastic Models For Leasing And Sharing Products

In this paper,two stochastic models are proposed for repairable leasing equipment.The first model is a hybrid imperfect preventive maintenance model based on the traditional leasing model.During the lease period,the lessor provides the maintenance service of the leased equipment,including preventive maintenance and minimum maintenance.Preventive maintenance is imperfect,and the time interval of imperfect preventive maintenance decreases in the form of equal ratio,the lessor carries out the minimal maintenance following failures.When the number of failures exceeds the given threshold,penalty fees will be incurred for the lessor.The hybrid imperfect preventive maintenance can reduce the age of equipment and increase the failure rate of equipment at the same time.By determining the time interval of the first preventive maintenance,the time interval of the n preventive maintenances and the number of failures can be obtained,then we can get the expected cost during the lease period.By using the gradient descent to get the optimal time interval of the first preventive maintenance,which minimizes the expected cost of the lessor.The second model is under the background of shared economy.Taking shared bicycle as an example,a profit model of shared bicycle is established.Based on the randomness of time-sharing lease,this model quantitatively describes the arrival process of deposit,the withdrawal process of deposit and the shared bicycle were used process with three independent non-homogeneous Poisson processes.It is assumed that the failure rate of bicycle is only related to the riding time.For each failure,only the minimal maintenance is carried out,and the maintenance time is negligible.Through the integration of deposit profit,use profit and maintenance cost,the expected profit of the manufacturer in the operating time is obtained.In addition,the paper also discusses the situation when three non-homogeneous Poisson processes are homogeneous Poisson processes,and obtains the expected profit of the manufacturer in the operating time.The stochastic models are illustrated by numerical examples,which verify the applicability and rationality of the conclusions.