中文摘要：

签订合同租赁是获得设备临时使用权的一种重要方式。设备承租方往往在不知道设备未来需求的情况下就需要确定合同的预租天数，这是一个在线决策问题。基于绩效比分析和线性分数规划方法，依次研究了合同约束下的单阶段和多阶段在线租赁决策问题，分别得到了最优的在线预租策略及其绩效比。借助于数值算例，进一步分析了日收益、租赁费、交易费和损失费等因素对最优预租策略及其绩效比的影响。研究结果可以为设备承租方确定预租天数提供一定的决策依据，也可以在确定租赁费、损失费等方面为设备出租方提供一定的理论指导。

英文摘要：

Signing leasing contracts is an important method to obtain the temporary using right of an equip- ment. The decision maker has to decide the number of the leasing days without knowing the number of theactual days he needs the equipment, and it is an online decision problem. Based on the performance ratio a nalysis and the linear fractional programming method, the single-period and multi-period online leasing problems are successively studied under contract constraint, and optimal leasing strategies and their per formance ratios, are obtained respectively in this paper. Thanks to numerical examples, the effects of the dail are y d return, the leasing fee and the loss fee on the optimal leasing strategies and their performance ratios iscussed. The results may instruct the online decision makers in determining the number of the leasing days, and the lessors in determining the leasing fee, the loss fee and so on.