Online Leasing Problem with Nonlinear Exponential Buy-back Contract
Yinfeng Xu · Systems Engineering · 2012
Considering that the life of the equipment generally presents a non-linear decay,we establish online leasing model with non-linear buy-back contracts,i.e.,exponential price function,and then give its optimal competitive strategy.First,we characterize the mathematical model of this non-linear buy-back contract and discuss some properties.Second,we study optimal offline leasing problem with existence of the second-hand market,and propose online leasing strategy.Finally,we use competitive analysis to prove perfectly the optimality of this strategy,and find its competitive ratio is smaller than that of Karp's model.Also,the optimal competitive performance of the strategy is discussed and illustrated by numerical analysis.In addition,our proposed online leasing model with the constraint of the above buy-back contract has expanded the previous studies that only allow for new products in the market.Our model considers old products into the lease market,which is a useful supplement to the existing literature of online leasing models.