TY - GEN

T1 - Rent or buy problems with a fixed time horizon

AU - Epstein, Leah

AU - Zebedat-Haider, Hanan

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84885206250&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-40313-2_33

DO - 10.1007/978-3-642-40313-2_33

M3 - Conference contribution

AN - SCOPUS:84885206250

SN - 9783642403125

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 361

EP - 372

BT - Mathematical Foundations of Computer Science 2013 - 38th International Symposium, MFCS 2013, Proceedings

T2 - 38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013

Y2 - 26 August 2013 through 30 August 2013

ER -