The Multi-shop Ski Rental Problem
Abstract
We consider the {\em multi-shop ski rental} problem. This problem generalizes the classic ski rental problem to a multi-shop setting, in which each shop has different prices for renting and purchasing a pair of skis, and a \emph{consumer} has to make decisions on when and where to buy. We are interested in the {\em optimal online (competitive-ratio minimizing) mixed strategy} from the consumer's perspective. For our problem in its basic form, we obtain exciting closed-form solutions and a linear time algorithm for computing them. We further demonstrate the generality of our approach by investigating three extensions of our basic problem, namely ones that consider costs incurred by entering a shop or switching to another shop. Our solutions to these problems suggest that the consumer must assign positive probability in \emph{exactly one} shop at any buying time. Our results apply to many real-world applications, ranging from cost management in \texttt{IaaS} cloud to scheduling in distributed computing.
Keywords
Cite
@article{arxiv.1404.2671,
title = {The Multi-shop Ski Rental Problem},
author = {Lingqing Ai and Xian Wu and Lingxiao Huang and Longbo Huang and Pingzhong Tang and Jian Li},
journal= {arXiv preprint arXiv:1404.2671},
year = {2014}
}