Online Strategy For The Asset Leasing Problems With Compound Interest Rate And Its Competitive Analysis

Facing with unpredictable fluctuations in the market and the growing pressures of company cash flows,there are a growing number of companies that tend to obtain the right to use equipment or assets through leasing.Due to the rapid changes of business environment and increasing competition in the market,the decision-makers must make a decision to lease or buy based on current limited information,which is an online leasing problem.To deal with this kind of problem,the traditional methods assumed that future demand obeys some random distribution then got the optimal strategy using Bayesian analysis.But the distribution of a random variable in the actual market is usually very hard to depict.Because the online algorithm and competitive analysis can make decisions based on existed information without any assumptions on the future demand,they are widely used in the field of leasing decision.Based on the present studies this paper considers the time value of money,and studies the online operational and financial leasing problems by the method of online algorithm and competitive analysis.The corresponding optimal online strategies are given,and more flexible risk-reward strategies are built by combing the risk preferences and forecasts of decision-makers.This paper enriches the theoretical study of online algorithm and competitive analysis on the field of leasing decision and provides the decision-makers more practical references.Specific innovations and research contents are as follows.(1)This paper builds the deterministic competitive strategy and risk-reward strategy based on the decision-makers' forecast for the additive two-option operational leasing problem with continuously compound interest rate.And the online competitive strategy for the additive three-option operational leasing problem is given as an extention.Some companies often need to change equipment assets because of technical progress,product upgrading and other reasons.If they choose the purchase option every time they execute the update,then it may result in the waste of resources and certain economic loss.So they always choose the operational lease.Besides,some companies have not enough money to purchase the equipment assets and they can only produce goods by leasing the equipment assets.Hence this paper considers the online decision problem with operational leasing options only.For the online leasing problem with two operational leasing options,the optimal online competitive strategy and risk-reward strategy with compound interest rate are given by competitive analysis,which enriches the current research framework of this problem.In addition,considering that the researches on the operational leasing problem with multi-options just presented the upper and lower bounds of the optimal competitive ratio,this paper studies this problem with three operational leasing options.The online strategy and analytic expression of its competitive ratio are given under the market interest rate.And the competitive performance is analyzed.(2)This paper builds the online leasing model for the non-additive two-option operational leasing problem with continuously compound interest rate,and gives the risk-reward model by introducing the risk preference and forecast.In the actual leasing activity,sometimes the switching cost from one operational leasing option to another is not equal to the difference of one-time cost in these two options.If there is a discount,the switching cost is smaller than the difference.On the contrary,if the decision-maker needs to pay for the resulting loss of the lessor,the switching cost is bigger than the difference.Then this is a non-additive online operational leasing problem.However,most of the related literatures studied the additive online operational leasing problem,and the researches on the non-additive online operational leasing problem just gave the upper and lower bounds of randomized competitive ratio.Furthermore,though the study on the simplest and non-trivial non-additive two-option operational leasing problem gave the optimal deterministic and randomized strategies,the time value of money and the information on the risk preference of decision-makers were not considered.For this reason,based on the existing researches this paper introduces continuously compound interest rate and risk tolerance and forecasts of decision-makers into this problem,and gives the optimal deterministic online strategy and the risk-reward strategies with certain forecast and probabilistic forecasts,respectively.Numerical examples show that the introductions of compound interest rate and the forecasts of decision-makers can improve the strategies' competitive performance effectively.(3)This paper builds the online competitive strategy and risk-reward strategy with discrete compound interest rate for the problem of inseparable assets financial leasing.Financial leasing as another form of leasing is very popular among the investors because of its characteristics of financing funds and assets.However,most of the related literatures studied the online operational leasing problem,and the researches on the online financial leasing problem just gave simple online competitive strategy using competitive analysis.Therefore,this paper studies the online financial leasing problem for the common inseparable assets further and introduces the market interest rate and risk forecast into this problem.And the optimal online strategy and risk-reward strategy are presented for the online financial leasing problem without down payment,respectively.For the case with down payment,the optimal competitive strategies under different conditions are obtained by classified discussion.Finally,the influence of the parameters on the competitive performance of the strategies is analyzed by numerical examples.The strategies can provide references for the decision-makers facing financial leasing problem.(4)This paper considers discrete compound interest rate and establishes the strategy of controlling risk for the online financial leasing of separable assets.For the case without compound interest rate the optimal competitive strategy is given.In fact,there exists the financial leasing of separable assets such as the plant.However,most of the existing literatures studied the online leasing of inseparable assets,and the study on the online leasing of separable assets just considered the operational leasing problem.So,this paper analyzes the online financial leasing problem for the separable assets under compound interest rate.First,the optimal offline strategy of this problem is analyzed.Second,referring to the related studies this paper designs the financial leasing strategy of controlling risk under compound interest rate and gives its competitive ratio.Third,the strategy of controlling risk for the problem without compound interest rate is obtained using previous conclusion and it is proved to be optimal online competitive strategy.At last,numerical examples show that the competitive ratio of the financial leasing problem for the separable assets is smaller than that for the inseparable assets.This demonstrates that the strategy of leasing assets in batches is better than leasing the assets as a whole,which matches the actual situation.