具有概率分布在线租赁问题策略研究

中国管理科学 ›› 2005, Vol. ›› Issue (5): 33-38.

具有概率分布在线租赁问题策略研究

徐维军¹, 徐寅峰^1,2

1. 西安交通大学管理学院, 陕西, 西安, 710049;
2. 机械制造系统工程国家重点实验室, 陕西, 西安, 710000

收稿日期:2004-05-19 修回日期:2005-08-31 出版日期:2005-10-28 发布日期:2012-03-07
基金资助:
国家自然科学基金资助项目(10371094);国家自然科学基金资助项目(70471035)

Strategy Research for Online Leasing Problem with Probability Distribution

XU Wei-jun¹, XU Yin-feng^1,2

1. School of Management, Xi’an Jiaotong University, Xi’an 710049, China;
2. The State Key Lab for Manufacturing Systems Engineering, Xi’an 710049, China

Received:2004-05-19 Revised:2005-08-31 Online:2005-10-28 Published:2012-03-07

摘要/Abstract

摘要： 在经济系统中,决策越来越呈现出在线性特征,传统优化方法在解决这类在线问题时,通常假设未来输入是一随机变量从而寻求概率意义上的最优决策。近年来,在优化领域兴起了一种新的研究方法——在线算法与竞争分析,为解决这类在线问题提供了新的视角,但传统的竞争分析方法有意规避概率分布假设。对于在线租赁决策问题,由于其输入结构简单且具有良好的统计性质,似乎忽略这些有用的信息而只运用标准的竞争比方法分析显然具有不足之处。在本文中,我们将其输入结构的概率分布引入纯竞争分析方法中,从而建立了具有概率情形的最优在线租赁模型,并得到了最优竞争策略及其竞争比。

关键词: 在线算法, 金融租赁, 竞争分析, 竞争比

Abstract: In economic system,the decision making is representing the online characteristics.Dealing with online decision problem,the traditional Bayesian analysis often depends on the probabilitic assumptions so that it gives out the optimal result in the probability sense.However,there is coming a focus in the algorithmic fields in the recent years,which is the online algorithms and competitive analysis.It gives a new angle of view to deal with online problem,but this method always intentionally avoids probabilistic distribution.For the online leasing problem,beacuse its input structure has a simple and good statistical property,it would be a waste to ignore this knowledge which is precisely what the traditional competitive ratio does.In this paper,we introduce the information distribution of future input into the competitive analysis so as to build online leasing model with probability distribution,and obtain their optimal competitive strategies and competitive ratios.

Key words: online algorithm, financial leasing, competitive analysis, competitive ratio

中图分类号:

F830

徐维军, 徐寅峰. 具有概率分布在线租赁问题策略研究[J]. 中国管理科学, 2005, (5): 33-38.

XU Wei-jun, XU Yin-feng. Strategy Research for Online Leasing Problem with Probability Distribution[J]. Chinese Journal of Management Science, 2005, (5): 33-38.

参考文献

[1] Schall L D. The lease-or-buy and asset acquisition decisions[J]. Journal of Finance, 1974,29:1203-1214.
[2] Moller M H, Upton C W.Leasing, buying and the cost of capital services [J]. Journal of Finance, 1976,31: 761-768.
[3] Lippman S A, McCall J J.The economics of uncertainty:Selected topics and probabilistic methods[C]. In K. J. Arrow and M. D. Intriligator, editors, Handbook of Mathematical Economics. North-Holland, 1981,1 (6): 211-284.
[4] Mirman L J. Uncertainty and optimal consumption decisions[J]. Econometrica, 1971,39:179-185.
[5] 张金隆,王林,陈涛,曾宇容.连续生产模式下的不常用备件联合采购优化分析[J].中国管理科学,2004,12(5):58-62.
[6] 黎子良,郑祖康.生存分析[M].杭州:浙江科学技术出版社,1993.
[7] Zheng Z G,Fang K T.Bayesian procedure in time sequential sample plan[R].北京大学技术报告,1995.
[8] Wei L L, Zhang W X.Bayesian procedure in classification problem with linear exponential hazard function [J]. Acta Mathematica Scientia, 2003,23 (4): 436-443.
[9] 张俐杰,杨景平.一类判别分析问题的Bayes解[J].兰州大学学报(自然科学版),2000,36(3):36-41.
[10] Karp R. Online algorithms vessus offline algorithms. How much if it worth to know the future[J]. Proc. IFIP 12th World computer Congress,992,1:416-429.
[11] Karlin A R, Manaees M S, Mc Geogh L, Owichi S. Competitive randomize algorithms for nonuniform problems[J]. Algorithmica, 1994,11 (1): 542-571 .'
[12] Yaniv R E, Kaniel R, Linial N. Competitive optimal online leasing[J]. Algorithmica, 1999,25:116-140.
[13] al-Binali S.A risk-reward framework for the competitive analysis of financial games[J]. Algorithmica, 1999,25:99-115.
[14] Fujiwara H, Iwama K. Average-case competitive analyses for ski-rental problems[J]. ISAAC,2002,476-488.
[15] Fiat A,Woeginger G J .Online algorithms:The state of art[M]. Springer, 1998: 368-370.
[16] Borodin A, Yaniv R E.Online computation and competitive analysis[M]. Cambridge University Press, 1998.
[17] 杨永福,朱桂龙.管理模式和方法创新分析及其启示[J].中国管理科学,1999,7(2):67-75.
[18] 高农昌,何平.决策过程及最优决策时刻分析[J].中国管理科学,1995,3(4):53-58.