Competitive Analysis for the 3-Slope Ski-Rental Problem with the Discount Rate

Hiroshi FUJIWARA; Shunsuke SATOU; Toshihiro FUJITO

doi:10.1587/transfun.E99.A.1075

Competitive Analysis for the 3-Slope Ski-Rental Problem with the Discount Rate

Hiroshi FUJIWARA, Shunsuke SATOU, Toshihiro FUJITO

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In the 3-slope ski-rental problem, the player is asked to determine a strategy, that is, (i) whether to buy a ski wear and then a ski set separately, or to buy them at once for a discount price, and (ii) when to buy these goods. If the player has not got any thing, he/she can rent it for some price. The objective is to minimize the total cost, under the assumption that the player does not know how many times he/she goes skiing in the future. We reveal that even with a large discount for buying at once available, there is some price setting for which to buy the goods separately is a more reasonable choice. We also show that the performance of the optimal strategy may become arbitrarily worse, when a large discount is offered.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.6 pp.1075-1083

Publication Date: 2016/06/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E99.A.1075

Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)

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Authors

Hiroshi FUJIWARA
  Shinshu University
Shunsuke SATOU
  Toyohashi University of Technology
Toshihiro FUJITO
  Toyohashi University of Technology

Keyword

online algorithm, competitive analysis, online optimization, ski-rental problems

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Hiroshi FUJIWARA, Shunsuke SATOU, Toshihiro FUJITO, "Competitive Analysis for the 3-Slope Ski-Rental Problem with the Discount Rate" in IEICE TRANSACTIONS on Fundamentals, vol. E99-A, no. 6, pp. 1075-1083, June 2016, doi: 10.1587/transfun.E99.A.1075.
Abstract: In the 3-slope ski-rental problem, the player is asked to determine a strategy, that is, (i) whether to buy a ski wear and then a ski set separately, or to buy them at once for a discount price, and (ii) when to buy these goods. If the player has not got any thing, he/she can rent it for some price. The objective is to minimize the total cost, under the assumption that the player does not know how many times he/she goes skiing in the future. We reveal that even with a large discount for buying at once available, there is some price setting for which to buy the goods separately is a more reasonable choice. We also show that the performance of the optimal strategy may become arbitrarily worse, when a large discount is offered.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.1075/_p

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@ARTICLE{e99-a_6_1075,
author={Hiroshi FUJIWARA, Shunsuke SATOU, Toshihiro FUJITO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Competitive Analysis for the 3-Slope Ski-Rental Problem with the Discount Rate},
year={2016},
volume={E99-A},
number={6},
pages={1075-1083},
abstract={In the 3-slope ski-rental problem, the player is asked to determine a strategy, that is, (i) whether to buy a ski wear and then a ski set separately, or to buy them at once for a discount price, and (ii) when to buy these goods. If the player has not got any thing, he/she can rent it for some price. The objective is to minimize the total cost, under the assumption that the player does not know how many times he/she goes skiing in the future. We reveal that even with a large discount for buying at once available, there is some price setting for which to buy the goods separately is a more reasonable choice. We also show that the performance of the optimal strategy may become arbitrarily worse, when a large discount is offered.},
keywords={},
doi={10.1587/transfun.E99.A.1075},
ISSN={1745-1337},
month={June},}

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TY - JOUR
TI - Competitive Analysis for the 3-Slope Ski-Rental Problem with the Discount Rate
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1075
EP - 1083
AU - Hiroshi FUJIWARA
AU - Shunsuke SATOU
AU - Toshihiro FUJITO
PY - 2016
DO - 10.1587/transfun.E99.A.1075
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2016
AB - In the 3-slope ski-rental problem, the player is asked to determine a strategy, that is, (i) whether to buy a ski wear and then a ski set separately, or to buy them at once for a discount price, and (ii) when to buy these goods. If the player has not got any thing, he/she can rent it for some price. The objective is to minimize the total cost, under the assumption that the player does not know how many times he/she goes skiing in the future. We reveal that even with a large discount for buying at once available, there is some price setting for which to buy the goods separately is a more reasonable choice. We also show that the performance of the optimal strategy may become arbitrarily worse, when a large discount is offered.
ER -