Rent or buy problems with a fixed time horizon

Leah Epstein, Hanan Zebedat-Haider

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We study several variants of a fixed length ski rental problem and related scheduling problems with rejection. A ski season consists of m days, and an equipment of cost 1 is to be used during these days. The equipment can be bought on any day, in which case it can be used without any additional cost starting that day and until the vacation ends. On each day, the algorithm is informed with the current non-negative cost of renting the equipment. As long as the algorithm did not buy the equipment, it must rent it every day of the vacation, paying the rental cost of each day of rental. We consider the case of arbitrary, non-increasing, and non-decreasing rental costs. We consider the case where the season cannot end before the mth day, and the case that it can end without prior notice. We propose optimal online algorithms for all values of m for all variants. The optimal competitive ratios are either defined by solutions of equations (closed formulas or finite recurrences) or sets of mathematical programs, and tend to 2 as m grows.

Original languageAmerican English
Title of host publicationMathematical Foundations of Computer Science 2013 - 38th International Symposium, MFCS 2013, Proceedings
Number of pages12
StatePublished - 2013
Event38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013 - Klosterneuburg, Austria
Duration: 26 Aug 201330 Aug 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8087 LNCS


Conference38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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