Optimal randomized algorithm for a generalized ski-rental with interest rate

  • Authors:

  • Xingyu Yang;Weiguo Zhang;Yong Zhang;Weijun Xu

  • Affiliations:

  • School of Business Administration, South China University of Technology, Guangzhou, Guangdong 510640, PR China;School of Business Administration, South China University of Technology, Guangzhou, Guangdong 510640, PR China;School of Business Administration, South China University of Technology, Guangzhou, Guangdong 510640, PR China;School of Business Administration, South China University of Technology, Guangzhou, Guangdong 510640, PR China

  • Venue:
  • Information Processing Letters
  • Year:
  • 2012

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Abstract

We introduce the continuously compounded interest rate into a generalized ski-rental problem with two options: either pay some rental proportionally to the usage time (the rent option), or buy the equipment and then pay some reduced rental proportionally to the usage time (the generalized buy option). Under the framework of competitive analysis, a randomized algorithm for the modified model is constructed and then is proved optimal by Yao@?s Lemma, and thus the optimal competitive ratio is obtained. The result shows that the introduction of the interest rate puts off the optimal purchase date and diminishes the uncertainty involved in the decision making.