Abstract: The competition is becoming increasingly fierce among the financial leasing industries, so the lessee may provide some preferential policies in order to attract customers. This paper presents an online leasing issue based on the preferential contract that provided a discount for the lessee of continuous rental. First of all, we introduce the theory model of competitive ratio to obtain the optimal off-line strategy. Secondly, the deterministic strategy is designed by using the online algorithm and the theory of competitive analysis in the cases of the lessee giving up the preferential contract and signing the preferential contract, in order to achieve the optimal on-line strategy and its competitive ratio. Finally, as demonstrated by numerical examples, we prove that a car preferential contract is a better strategy, and further, deduces the best time to sign the preferential contract and the best time to purchase the equipment.

Key words: on-line rental problem, preferential contract, on-line algorithm, competitive ratio

摘要： 近年来租赁行业竞争日益激烈,租赁企业为了吸引客户有时会开展一些优惠活动。针对这一现状,本文讨论了存在优惠合同时承租方的在线租赁决策问题,其中假设该优惠合同 给予承租方一次以比较优惠的价格连续租赁设备多期的机会。首先,分析了存在优惠合同时的最优离线策略。其次,利用在线算法和竞争比理论分别设计了承租方放弃优惠合同和签订优惠 合同两种情形下的最优在线策略及最优竞争比。最后,通过汽车租赁优惠的数值算例说明选择签订优惠合同是更好的策略,进一步给出了签订优惠合同和购买设备的最佳时间。

关键词: 在线租赁问题, 优惠合同, 在线算法, 竞争比