购买价格递减的在线租赁问题策略设计
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摘要
运用在线问题与竞争分析的方法研究了购买价格递减的在线租赁问题。通过揭示相关费用函数的性质,先后给出了最优离线策略以及在线策略。通过竞争比分析,证明了我们给出的在线策略是该问题唯一最优策略,而且该策略的竞争比随购买价格的优惠率的增加呈严格递减趋势。竞争分析结果表明考虑购买价格递减因素能够改进在线策略的竞争比从而提高决策效率。
In this paper,we use the method of competitive analysis for online problem to study an online leasing problem with decreasing price for purchasing. By analyzing the properties of cost functions concerned,the optimal offline strategy and an online strategy are given. By way of the analysis of competitive rate,we prove online strategy to be the unique optimal strategy for this problem,and competitive rate of this strategy is strictly decreasing with the preferential rate of purchasing price. The result shows that taking the factors of the decreasing of purchasing price will improve the competitive rate of online strategy and thereby increase the decision-making efficiency.
In this paper,we use the method of competitive analysis for online problem to study an online leasing problem with decreasing price for purchasing. By analyzing the properties of cost functions concerned,the optimal offline strategy and an online strategy are given. By way of the analysis of competitive rate,we prove online strategy to be the unique optimal strategy for this problem,and competitive rate of this strategy is strictly decreasing with the preferential rate of purchasing price. The result shows that taking the factors of the decreasing of purchasing price will improve the competitive rate of online strategy and thereby increase the decision-making efficiency.
引文
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[2]Karlin A R,Manaees M S,Mc Geogh L,Owichi S.Competitive randomize algorithms for non-uniform problems[J].Algorithmica,1994,11(6):542-571.
[3]El-Yaniv R,Karp R.Nearly optimal competitive online replacement olicies[J].Mathematics of Operations Research,1997,22(4):814-839.
[4]El-Yaniv R,Kaniel R,Linial N.Competitive optimal oline leasing[J].Algorithmica,1999,25:116-140.
[5]Irani S,Ramanathan D.The problem of renting versus buying[Z].Personal communication,1998.
[6]Azar Y,et al.On capital investment[J].Algorithmica,1999,25:22-36.
[7]Fujiwara H,Iwama K.Average-case competitive analysis for ski-rental problems[J].Algorithmica,2005,42(1):95-107.
[8]Xu Y F,Xu W J,Li H Y.On the online rent or buy problem in probabilistic environments[J].Journal of Global Optimization,2007,38(1):1-20.
[9]王扬,徐维军,徐寅峰.一类占线融资租赁问题的最优竞争策略与风险补偿模型[J].管理学报,2011,8(12):1866-1871.
[10]董玉成,徐寅峰,徐维军.可退货在线租赁竞争分析及其风险回报模型[J].中国管理科学,2007,15(4):28-33.
[11]胡茂林.可分资产的在线租赁策略及其竞争分析[J].系统工程理论与实践,2011,31(1):144-150.
[12]徐维军,张卫国,胡茂林.购买价格和租金费用均连续可变的在线竞争策略分析[J].中国管理科学,2006,14(2):96-101.
[13]堵丁柱.k-车服务问题与竞争算法[J].数学的实践与认识,1991,(4):36-40.
[14]马卫民,王刊良.局内管理决策问题及其竞争策略[J].管理科学学报,2003,6(2):29-34.