特殊在线优惠卡问题及其竞争分析  

Special on-line Bahncard problem and its competitive analysis

作　　者：杨兴雨[1] 张卫国[1] 徐维军[1] 

机构地区：[1]华南理工大学工商管理学院,广州510640

出　　处：《系统工程理论与实践》2012年第7期1421-1428,共8页Systems Engineering-Theory & Practice

基　　金：国家杰出青年基金(70825005);国家自然科学基金(70801027);中国博士后科学基金(20110490090);教育部人文社会科学基金(10YJA630062)

摘　　要：商家在策划优惠卡发行时需要严密论证发行价格和折扣率等因素对消费者消费行为的影响.利用在线算法和竞争分析理论,研究了消费者对同时发行的两种优惠卡的在线决策问题.一方面得到了最优确定性策略及其竞争比;另一方面构造了一个随机性策略,得到了最优随机性策略竞争比的一个上界,并利用Yao引理得到了随机性策略最优竞争比的一个下界.借助于数值算例,分析了各因素对在线策略及其竞争比的影响.研究结果可以为优惠卡发行价格和折扣率的决策提供依据.While designing the issue of the discount card, stores need to strictly analyze the effect of factors such as the issue price and discount rate on the consumer＇s behavior. Using the theory of on-line algorithms and competitive analysis, this paper studied the on-line problem how consumers make decisions between two discount cards which are issued at the same time. On the one hand, the optimal deterministic strategy and its competitive ratio were obtained; on the other hand, a randomized strategy was constructed and an upper bound for the optimal randomized competitive ratio was obtained, and moreover, a lower bound for the optimal randomized competitive ratio was proved by Yao＇s Lemma. Thanks to numerical examples, the effect of the factors on the on-line strategies and their competitive ratios was analyzed. The results may instruct the stores in determining the issue price and discount rate of the discount card.

关 键 词：在线优惠卡问题 确定性策略 随机性策略 竞争比 

分 类 号：F069[经济管理—政治经济学]