On the on-line rent-or-buy problem in probabilistic environments |
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Authors: | Yinfeng Xu Weijun Xu Hongyi Li |
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Institution: | (1) The State Key Lab for Manufacturing Systems Engineering, School of Management, Xi’an Jiaotong University, Xi’an, 710049, China;(2) School of Business Administration, South China University of Technology, Guangzhou, 510641, China;(3) Business Administration Faculty, The Chinese University of Hong Kong, Shatin, N.T, Hong Kong |
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Abstract: | Fujiwara and Iwama In: The 13th Annual International Symposium on Algorithms and Computation, pp. 476–488 (2002)] first integrated
probability distribution into the classical competitive analysis to study the rental problem. They assumed that the future
inputs are drawn from an exponential distribution, and obtained the optimal competitive strategy and the competitive ratio
by the derivative method. In this paper, we introduce the interest rate and tax rate into the continuous model of Fujiwra
and Iwama In: The 13th Annual International Symposium on Algorithms and Computation, pp. 476–488 (2002)]. Moreover, we use
the forward difference method in different probabilistic environments to consider discrete leasing models both with and without
the interest rate. We not only give the optimal competitive strategies and their competitive ratios in theory, but also give
numerical results. We find that with the introduction of the interest rate and tax rate, the uncertainty involved in the process
of decision making will diminish and the optimal purchasing date will be put off. |
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Keywords: | On-line algorithm Rent-or-buy problem Probabilistic distribution Competitive analysis |
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