多店滑雪租赁问题
The Multi-shop Ski Rental Problem
摘要：
我们考虑{ \em多店滑雪租赁}问题。这个问题将经典的滑雪板租赁问题推广到多商店环境，其中每个商店对于租赁和购买滑雪板都有不同的价格，并且\emph{consumer}必须决定何时何地购买。我们感兴趣的是{ \em最优在线（竞争比最小化）混合策略}从消费者的角度。对于我们的问题的基本形式，我们得到令人兴奋的封闭形式的解决方案和线性时间算法计算它们。我们进一步证明了我们的方法的一般性，通过调查我们的基本问题的三个扩展，即考虑进入一家商店或切换到另一家商店所产生的成本。我们对这些问题的解决方案表明，消费者必须在任何购买时间在\emph{exactly one}商店中分配正概率。我们的研究结果适用于许多现实世界的应用程序，从\texttt{IaaS}云的成本管理到分布式计算的调度。
英文摘要：
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.
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