The ski-rental problem with multiple discount options

Authors:
Guiqing Zhang;Chung Keung Poon;Yinfeng Xu
Affiliations:
Management School, Xian Jiaotong University, Xian 710049, China;City University of Hong Kong, Hong Kong, China;Management School, Xian Jiaotong University, Xian 710049, China and Ministry of Education Key Lab for Intelligent Networks and Network Security, Xian 710049, China
Venue:
Information Processing Letters
Year:
2011

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Abstract

We propose the ski-rental problem with multiple discount options in which there are n options to rent an equipment. Every option has a rental duration; the longer the duration, the more the discount. This generalizes the standard ski-rental problem where one can only rent or buy. We present a 4-competitive on-line algorithm for our problem and show that no deterministic algorithm can have a smaller competitive ratio when n is large enough. Comparing with the original ski-rental problem, the competitive ratio becomes larger when there are more options.