基于最小最大后悔值的应急救灾网络构建鲁棒优化模型与算法

中国管理科学 ›› 2014, Vol. 22 ›› Issue (7): 131-139.

基于最小最大后悔值的应急救灾网络构建鲁棒优化模型与算法

张玲¹, 陈涛², 黄钧²

1. 惠州学院经济管理系, 广东惠州 516007;
2. 中国科学院大学数学科学学院, 北京 100049

收稿日期:2013-02-04 修回日期:2013-09-01 出版日期:2014-07-20 发布日期:2014-07-24
作者简介:张玲（1980-），女（汉族），山东泰安人，惠州学院经济管理系，讲师，博士，研究方向：应急管理。
基金资助:
广东省优秀青年创新人才培养计划项目（LYM11119）；广东省自然基金项目（S2011040004017）；北京市哲学社会科学规划项目（13JGC089）

Emergency Network Model and Algorithm Based on Min-Max Regret Robust Optimization

ZHANG Ling¹, CHEN Tao², HUANG Jun²

1. Department of Economics and Management, Huizhou University, Guangdong 516007, China;
2. School of Mathematica Science, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2013-02-04 Revised:2013-09-01 Online:2014-07-20 Published:2014-07-24

摘要/Abstract

摘要： 应急救灾过程分为两个阶段：第一阶段启动应急救灾网络构建，在灾区附近设立临时应急配送中心，并由应急资源供应方向其紧急调配应急资源；第二阶段将应急资源从临时应急配送中心向灾区受灾点进行调度，以保证救灾过程顺利进行。本文研究第一阶段应急救灾网络的构建问题，考虑到突发灾害初期灾情相关参数概率分布情况难以获取，建立了基于情景的最小最大后悔值准则的应急救灾网络构建鲁棒优化模型。求解模型时，利用有限情景集表示第二阶段的不确定性数据，并将模型化为与其等价的混合整数规划模型，利用情景松弛的迭代算法进行求解。数值试验中给出相应的绝对鲁棒模型与本文偏差鲁棒模型作了比较，结果表明基于最小最大后悔值准则的应急救灾网络优化模型具有良好的鲁棒性，而且算法也是有效的。

关键词: 应急救灾网络, 不确定条件, 两阶段规划, 最小最大后悔准则, 鲁棒优化, 情景松弛

Abstract: After emergency, rescue process is represented by two stage. First stage is to start the emergency rescue network, including building temporary distribution centers, allocating reasonable emergency resource to assure rescue process working smoothly. The second stage is to dispatch emergency resource from temporary distribution centers to demand points. A min-max regret robust emergency network model is proposed for natural disasters under uncertainty, taking the second stage as auxiliary decision. Uncertain information is random and represented by finite scenarios. The proposed model is solved using scenario relaxation algorithm. Finally, a case study is proposed to highlight efficiency of the proposed model and solution algorithm.

Key words: emergency rescue network plan, uncertain information, two-stage programing, min-max regret criterion, robust optimization, scenairio relaxation

中图分类号:

O224

张玲, 陈涛, 黄钧. 基于最小最大后悔值的应急救灾网络构建鲁棒优化模型与算法[J]. 中国管理科学, 2014, 22(7): 131-139.

ZHANG Ling, CHEN Tao, HUANG Jun. Emergency Network Model and Algorithm Based on Min-Max Regret Robust Optimization[J]. Chinese Journal of Management Science, 2014, 22(7): 131-139.

参考文献

[1] Hakimi S L. Optimum locations of switching centers and the absolute centers and medians of a graph[J]. Operations Research, 1964, 12: 450-459.

[2] Fiedrich F, Gehbauer F, Rickers U. Optimized resource allocation for emergency response after earthquake disasters[J]. Safety Science, 2000, 35: 41-57.

[3] 刘春林, 何建敏, 施建军. 一类应急物资调度的优化模型研究[J]. 中国管理科学, 2001, 9(3): 29-36.

[4] Ozdamar L, Ekinci E, Kucukyzici B. Emergency logistics planning in natural disasters[J]. Annals of Operations Research, 2004, 129: 217-245.

[5] 曾敏刚, 崔增收, 余高辉. 基于应急物流的减灾系统LRP研究[J]. 中国管理科学, 2010, 2(18): 75-80.

[6] 李进, 张江华, 朱道立. 灾害链中多资源应急调度模型与算法[J]. 系统工程理论与实践, 2011, 3(11): 488-495.

[7] Tzeng G H, Cheng H J, Huang T D. Multi-objective optimal planning for designing relief delivery systems[J]. Transportation Research Part E, 2007, 43(6): 673-686.

[8] Ali B A, Jabalameli M S. Mirzapour S M. A multi-objective robust stochastic programming model for disaster relief logistics under uncertainty[J]. OR Spectrum, 2011, 8: 1-30.

[9] Chang M S, Tseng Y L, Chen J W. A scenario planning approach for the flood emergency logistics preparation problem under uncertainty[J]. Transportation Research Part E: Logistics and Transportation Review, 2007, 43(6): 737-754.

[10] Salmeron J, Apte A. Stochastic optimization for natural disaster asset pre-positioning [J]. Production and Operating Management, 2010, 19(5): 561-574.

[11] 张玲,黄钧,韩继业. 应对自然灾害的应急资源布局模型与算法[J]. 系统工程理论与实践, 2010, 9(30): 1615-1621.

[12] El-Ghaoui L, Lebret H, Oustry F. Robust solutions to uncertain semi-definite programs[J]. SIAM Journal of Optimization, 1998, 9(1):33-52.

[13] Ben-Tal A, Nemirovski A. Robust Convex Optimization[J]. Mathematics of Operations Research,1998, 23(4): 769-805.

[14] Ben-Tal A, Nemirovski A. Robust solutions of Linear Programming problems contaminated with uncertain data[J]. Mathematical Programming, 2000, 88(3): 411-424.

[15] Ben-Tal A, Nemirovski A. Robust optimization- methodology and applications[J]. Mathematical Programming, 2002, 92(3): 453-480.

[16] Bertsimas D, Sim M. Robust discrete optimization and network flows[J]. Mathematical Programming, 2003, 98(1): 49-71.

[17] Sim M. Robust Optimization[M]. Cambridge: Massachusetts Institute of Technology Sloan School of Management, 2004.

[18] 王英楠, 韩继业, 孙华. 一种不确定需求下库存定价模型的鲁棒优化方法[J]. 应用数学学报, 2008, 31(5): 910-921.

[19] Nalan G, Dessislava P, Ethem C. Robust strategies for facility location under uncertainty[J]. European Journal of Operational Research, 2013, 225(1): 21-35.

[20] Kouvelis P, Yu G. Robust discrete optimization and its applications[M]. Dordrecht, The Netherlands: Kluwer Academic Publishers, 1997.