On the on-line rent-or-buy problem in probabilistic environments

Fujiwara and Iwama [In: The 13th Annual International Symposium on Algorithms andComputation, 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 13thAnnual International SymposiumonAlgorithms 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.