Competitive analysis of online leasing problem with discount quotation

This paper is concerned with online leasing problem with discount quotation in which some leasing firm sells certain discount cards that offer the decision-makers different levels of lease fee discounts. In addition to paying the full lease price or buying equipments, the decision-makers also have the option of buying these discount cards to reduce their lease costs. In this paper, we develop an online algorithm to identify the discount card that minimizes the competitive ratio and the optimal timing for applying it. We show that the proposed online algorithm yields the competitive ratio of 2, and this is the best possible result.