中文摘要：

在经典的Karp在线租雪橇模型的基础上,提出并研究了存在市场利率的连续松弛多重在线租赁问题.首先,给出该问题的最优离线策略并分析最优离线费用与市场利率的关系.其次,应用在线问题之竞争分析的方法考虑了该问题的最优在线策略：针对离线对手可随时停止使用资产或设备使得承租人陷于刚刚买入而又不再使用的高风险之中的在线特征,提出了风险均衡策略;根据在线算法竞争比分析和求解原理,给出了风险均衡策略的竞争比并证明了这一竞争比是该问题的最优竞争比.最后,对最优竞争比中相关变量的单调性进行了分析,结果表明：市场利率的引入和租赁对象的多单位化能够降低问题的竞争比,从而提高在线租赁决策的效率.

英文摘要：

Based on the study of Karp＇ s ski rental model for the classical online leasing problem,this paper considers the multiple online leasing model for continuous relaxation problem with market interest rate.Firstly,we investigate the optimal offline strategy and show the relationship between the optimal offline cost and market interest rate.Then,based on the online characteristics that offline adversary might stop using assets at anytime so that online players may encounter a high-risk situation like no longer using assets shortly after purchasing,we propose a balancing risk strategy and obtain its optimal competitive ratio by using online algorithm and competitive analysis.Meanwhile,we prove that the competitive ratio of the balancing risk strategy is the optimal ratio for this problem.At last,the monotonicity of relevant variables in the optimal competitive ratio is discussed,and the result shows that the competitive performance of online strategy improves significantly with the factor of market interest rate and multi-unit asset,thereby enhancing the online rental decision-making efliciency.