不确定性物流网络设计的区间规划模型与算法研究
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摘要
物流网络设计是现代物流科学、合理、持续发展的基础性问题,随着国民经济的稳定发展,在国家宏观政策对物流产业振兴的大力支持下,物流行业的市场化不断深入,需求潜力巨大,物流系统的复杂性以及需求的不确定性越发突出。不确定性物流网络设计的理论与方法研究具有重要的理论价值与实践意义。
本文运用区间规划的思想与理论研究不确定性需求下的物流网络设计问题,通过分析物流网络结构的不确定性需求特征,以区间数的形式约束不确定性变量及参数,建立物流网络设计的区间规划模型,并设计区间优化求解算法,主要研究内容有：
(1)区间不确定物流网络设计的优越性论证
分析物流网络需求不确定性的影响因素,指出其不确定性的需求特征主要表现为物流设施选址(节点决策)的风险性；物流网络结构的不确定性以及配送线路优化的不确定性等三个方面。随机规划与模糊规划是当前解决不确定性物流网络设计的主要方法,区间规划相对应用较少,但其优势在于能够得到区间解,同时还具备情景决策的优越性,在实践中为最终决策提供更为广泛的可行决策空间。
(2)区间物流网络规划的提出及一般模型的构建
通过不确定性需求分析,指出区间物流网络规划是对已给定的物流网络,以区间变量或区间参数约束不确定性变量,构建适合物流网络结构特征的规划模型,以区间算法与优化算法相结合设计求解模式,辅以计算机程序设计,对问题求解。同时建立了区间物流网络规划的一般模型结构。
(3)区间连续型物流网络设计模型及算法
以重心法为基础,建立了多商品、多决策节点的连续型物流网络区间规划模型以及考虑区域障碍约束的区间规划模型,设计了区间迭代遗传算法的求解模式。算例测试表明,该模型及算法的求解结果具有区间坐标解的优越性,以一个“有限的区域”范围内的任何一个可行坐标满足不确定性需求下的决策。
(4)区间0-1混合整数规划及双层规划模型与算法
分析了离散型物流网络的不确定性区间需求特征,建立了区间0-1混合整数规划模型与区间双层规划模型,结合物流网络的实际特征,构建适合该两类物流网络结构需求的区间运算及区间数比较法则,通过定义风险系数与最大决策偏差,实现模型的确定性转化,并设计区间递阶优化遗传算法的求解模式。算例运行以及算法比较结果显示,该方法与算法具有区间最优解与情景决策的优越性。
(5)提出不确定性复杂物流网络的区间层次节点递阶三角OD需求模式
分析了不确定性复杂物流网络结构的需求特征,体现为：1)网络费率函数、节点对间配量以及节点费用的不确定性；2)网络中各层次节点间需求的不确定性,指出其需求结构是一种区间层次节点递阶三角OD需求关系,物流链中各层次中的节点与其下游任意层的任何一个节点都可能存在配量需求。
(6)区间多层次、多节点、多商品复杂物流网络规划模型及算法
在分析复杂不确定性物流网络区间层次节点递阶三角OD需求结构下,以两个区间决策变量,结合相应的区间参数约束构建了多层次、多节点、多商品的区间复杂物流网络规划模型,设计问题求解的区间递阶优化遗传算法。并通过算例仿真及算法比较表明其优越性。
本文主要从模型的构建以及算法设计对不确定性物流网络设计问题进行研究,意在拓展一种新的不确定性物流网络规划的思路,同时为物流系统的实际应用提供合理决策服务。
Logistics network design is a basic problem for the scientific rational and sustainable development of modern logistics. With the stable development of national economy, during the powerful support of national macroscopical policy to the revitalization of logistics industry, marketing of logistics industry is deepening and demand potential, the complexity of logistics system and the uncertainty of demand becomes more and more prominent. The research of idea and method of uncertain logistics network design has important theoretical value and practical significance.
In this dissertation, the author applies thought and concept of interval planning to research on the problem of logistics network design under uncertain demand, by analyzing the uncertain demand characteristic about the structure of logistics network, measured uncertain variables and parameters by the form of interval numbers, established interval planning model for logistics network design, and designed interval optimal algorithm. The main research work is as follows:
(1) Superiority demonstration on interval uncertain logistics network design
The uncertain influence factors of logistics demand are analyzed, and the uncertainty of demand characteristics are pointed out which mainly including three aspects:risk of logistics facilities location (node decision); uncertainty of the logistics network structure and uncertainty of distribution route optimization. Currently, stochastic planning and fuzzy planning is the main method to solve the problem of uncertain logistics network design, interval planning is used relatively less, but it has an advantage that it can obtain interval solution, and has superiority of scenario decision. In practice it can give a feasible decision space for final decision.
(2) Present of the interval logistics network planning and the general model
By analyzing the uncertainty of demand, the interval logistics network planning is defined that to the given logistics, constrainted uncertain variables by interval variables or interval parameters to construct planning model adaped the logistics network structure, and combined interval algorithm and optimization algorithm to design the solving model, and with computer program design to solve the problem. Also the general model structure of interval logistics network planning is established.
(3) Model and algorithm for interval continuous logistics network design
Based on the gravity method, the interval planning model of continuous logistics network under multiple commodities and multiple decision nodes and the interval planning model based on regional obstacle constraints are established. A solving model by interval iterative genetic algorithm is designed. It is showed by a tested example that the solving result of the model and algorithm has superiority of interval coordinates, it can meet decision under uncertain demand with anyone viable coordinate in a "limited area".
(4) Model and algorithm of interval0-1mixed integer programming and bi-level programming
The uncertain demand characteristic of discrete logistics network are analyzed, and interval0-1mixed integer programming model and interval bi-level programming model are established. Combined with the actual characteristics of the logistics network, to construct interval arithmetic and interval number comparison adapted the two class logistics network demand structure. By defining the risk coefficient and maximum decision-making deviation to transform the model to certainty, and a hierarchica interval optimization genetic algorithm is designed to solve. The results of examples show that the method and algorithm has the interval optimal solution and the superiority of scenario decision.
(5) Proposed interval levels-nodes hierarchical triangular OD demand model of uncertain complex logistics network
The demand characteristics of uncertain complex logistics network structure are analyzed, as belows:1) uncertainty of network rate function, distributed volumes and fees of nodes;2) demand uncertainty of nodes in each level. The demand structure is an interval levels-nodes hierarchical triangular OD, it also can show that nodes in each level maybe exist demand with any nodes in any level of its downstream in the logistics chain.
(6) Model and algorithm for interval complex logistics network planning with multi-levels, multi-nodes and multi-commodity
Under the analysis of interval levels-nodes hierarchical triangular OD demand structure of complex uncertain logistics network, with two interval decision variables, combined with the corresponding interval parameter constraint to establish the interval complex logistics network planning model with multi-levels, multi-nodes and multi-commodity, an interval hierarchical optimal genetic algorithm is designed to solve the problem. It shows its superiority by a tested example simulation and algorithm comparison.
This dissertation mainly researches on how to establish model and design algorithm for the problem of uncertain logistics network design. The author intends to expant a new idea for the uncertain logistics network planning, and provides a reasonable decision-making service for the application of logistics system.
本文运用区间规划的思想与理论研究不确定性需求下的物流网络设计问题,通过分析物流网络结构的不确定性需求特征,以区间数的形式约束不确定性变量及参数,建立物流网络设计的区间规划模型,并设计区间优化求解算法,主要研究内容有：
(1)区间不确定物流网络设计的优越性论证
分析物流网络需求不确定性的影响因素,指出其不确定性的需求特征主要表现为物流设施选址(节点决策)的风险性；物流网络结构的不确定性以及配送线路优化的不确定性等三个方面。随机规划与模糊规划是当前解决不确定性物流网络设计的主要方法,区间规划相对应用较少,但其优势在于能够得到区间解,同时还具备情景决策的优越性,在实践中为最终决策提供更为广泛的可行决策空间。
(2)区间物流网络规划的提出及一般模型的构建
通过不确定性需求分析,指出区间物流网络规划是对已给定的物流网络,以区间变量或区间参数约束不确定性变量,构建适合物流网络结构特征的规划模型,以区间算法与优化算法相结合设计求解模式,辅以计算机程序设计,对问题求解。同时建立了区间物流网络规划的一般模型结构。
(3)区间连续型物流网络设计模型及算法
以重心法为基础,建立了多商品、多决策节点的连续型物流网络区间规划模型以及考虑区域障碍约束的区间规划模型,设计了区间迭代遗传算法的求解模式。算例测试表明,该模型及算法的求解结果具有区间坐标解的优越性,以一个“有限的区域”范围内的任何一个可行坐标满足不确定性需求下的决策。
(4)区间0-1混合整数规划及双层规划模型与算法
分析了离散型物流网络的不确定性区间需求特征,建立了区间0-1混合整数规划模型与区间双层规划模型,结合物流网络的实际特征,构建适合该两类物流网络结构需求的区间运算及区间数比较法则,通过定义风险系数与最大决策偏差,实现模型的确定性转化,并设计区间递阶优化遗传算法的求解模式。算例运行以及算法比较结果显示,该方法与算法具有区间最优解与情景决策的优越性。
(5)提出不确定性复杂物流网络的区间层次节点递阶三角OD需求模式
分析了不确定性复杂物流网络结构的需求特征,体现为：1)网络费率函数、节点对间配量以及节点费用的不确定性；2)网络中各层次节点间需求的不确定性,指出其需求结构是一种区间层次节点递阶三角OD需求关系,物流链中各层次中的节点与其下游任意层的任何一个节点都可能存在配量需求。
(6)区间多层次、多节点、多商品复杂物流网络规划模型及算法
在分析复杂不确定性物流网络区间层次节点递阶三角OD需求结构下,以两个区间决策变量,结合相应的区间参数约束构建了多层次、多节点、多商品的区间复杂物流网络规划模型,设计问题求解的区间递阶优化遗传算法。并通过算例仿真及算法比较表明其优越性。
本文主要从模型的构建以及算法设计对不确定性物流网络设计问题进行研究,意在拓展一种新的不确定性物流网络规划的思路,同时为物流系统的实际应用提供合理决策服务。
Logistics network design is a basic problem for the scientific rational and sustainable development of modern logistics. With the stable development of national economy, during the powerful support of national macroscopical policy to the revitalization of logistics industry, marketing of logistics industry is deepening and demand potential, the complexity of logistics system and the uncertainty of demand becomes more and more prominent. The research of idea and method of uncertain logistics network design has important theoretical value and practical significance.
In this dissertation, the author applies thought and concept of interval planning to research on the problem of logistics network design under uncertain demand, by analyzing the uncertain demand characteristic about the structure of logistics network, measured uncertain variables and parameters by the form of interval numbers, established interval planning model for logistics network design, and designed interval optimal algorithm. The main research work is as follows:
(1) Superiority demonstration on interval uncertain logistics network design
The uncertain influence factors of logistics demand are analyzed, and the uncertainty of demand characteristics are pointed out which mainly including three aspects:risk of logistics facilities location (node decision); uncertainty of the logistics network structure and uncertainty of distribution route optimization. Currently, stochastic planning and fuzzy planning is the main method to solve the problem of uncertain logistics network design, interval planning is used relatively less, but it has an advantage that it can obtain interval solution, and has superiority of scenario decision. In practice it can give a feasible decision space for final decision.
(2) Present of the interval logistics network planning and the general model
By analyzing the uncertainty of demand, the interval logistics network planning is defined that to the given logistics, constrainted uncertain variables by interval variables or interval parameters to construct planning model adaped the logistics network structure, and combined interval algorithm and optimization algorithm to design the solving model, and with computer program design to solve the problem. Also the general model structure of interval logistics network planning is established.
(3) Model and algorithm for interval continuous logistics network design
Based on the gravity method, the interval planning model of continuous logistics network under multiple commodities and multiple decision nodes and the interval planning model based on regional obstacle constraints are established. A solving model by interval iterative genetic algorithm is designed. It is showed by a tested example that the solving result of the model and algorithm has superiority of interval coordinates, it can meet decision under uncertain demand with anyone viable coordinate in a "limited area".
(4) Model and algorithm of interval0-1mixed integer programming and bi-level programming
The uncertain demand characteristic of discrete logistics network are analyzed, and interval0-1mixed integer programming model and interval bi-level programming model are established. Combined with the actual characteristics of the logistics network, to construct interval arithmetic and interval number comparison adapted the two class logistics network demand structure. By defining the risk coefficient and maximum decision-making deviation to transform the model to certainty, and a hierarchica interval optimization genetic algorithm is designed to solve. The results of examples show that the method and algorithm has the interval optimal solution and the superiority of scenario decision.
(5) Proposed interval levels-nodes hierarchical triangular OD demand model of uncertain complex logistics network
The demand characteristics of uncertain complex logistics network structure are analyzed, as belows:1) uncertainty of network rate function, distributed volumes and fees of nodes;2) demand uncertainty of nodes in each level. The demand structure is an interval levels-nodes hierarchical triangular OD, it also can show that nodes in each level maybe exist demand with any nodes in any level of its downstream in the logistics chain.
(6) Model and algorithm for interval complex logistics network planning with multi-levels, multi-nodes and multi-commodity
Under the analysis of interval levels-nodes hierarchical triangular OD demand structure of complex uncertain logistics network, with two interval decision variables, combined with the corresponding interval parameter constraint to establish the interval complex logistics network planning model with multi-levels, multi-nodes and multi-commodity, an interval hierarchical optimal genetic algorithm is designed to solve the problem. It shows its superiority by a tested example simulation and algorithm comparison.
This dissertation mainly researches on how to establish model and design algorithm for the problem of uncertain logistics network design. The author intends to expant a new idea for the uncertain logistics network planning, and provides a reasonable decision-making service for the application of logistics system.
引文
[1]国家标准《物流术语》GB/T18354-2006.基本概念术语[Z].
[2]胡双增,张明.物流系统工程[M].清华大学出版社.2003.
[3]程国全,柴继峰,王转.物流设施规划与设计[M].北京：中国物资出版社,2003.
[4]PEAT F D.From Certainty to Uncertainty:The story of science and ideas in the twentieth[M] Joseph Henry Press,2002.
[5]POLLACK H N.Untertainty science uncertainty world[M].Cambridge University Press,2003.
[6]KLIR G H.Uncertainty and information:Foundations of generalized information theory[M].John Wiley and Sons,Inc,2006.
[7]胡列格.物流运筹学[M].北京：电子工业出版社,2005.
[8]AIKENS.C.H.Facility location models for distribution planning[J]. European Journal of Operational Re-search,1985,22(2):263-279.
[9]BENAYED.O.A general bi-level linear programming formulation of the network design problem[J]. Transportation Research,1988,22(B):311-318.
[10]TANIGUCHI E.Optimal size and location planning of public logistics terminals[J]. Transportation Research,1999,35(1):207-222.
[11]DAGANZO C F. Logistics System Analysis[M]. Berlin:Springer,1996.
[12]刘海燕,李宗平,叶怀珍.物流配送中心选址模型[J].西南交通大学学报,2000,35(3)：311-314.
[13]胡刚,王淑琴,李铁柱,朱中.针对第三方物流企业的物流中心选址模型研究[J].公路交通科技,2002,19(6)：172-176.
[14]鲁晓春,詹荷生.关于配送中心重心法选址的研究[J].北方交通大学学报,2002,24(6)：108-110.
[15]姜大立,杨西龙.易腐物品配送中心连续选址模型及其遗传算法[J].系统工程理论与实践,2003,(2)：62-67.
[16]李志华,王启富,钟毅芳,周亦波.物流网络设计建模与求解算法研究[J].机械工程学报,2003,39(2)：84-89.
[17]SANJAY M, MARK S. Daskin.Capacitated facility location/network design problems [J]. European Journal of Operational Research,2001,129(2):481-495.
[18]SIDDHARTHA S S. A model and methodologies for the location problem with logistical components[J]. Computers and Operations Research,2002,29(9):1173-1193.
[19]JOVANOVIC D M.Planning of optimal location and sizes of distribution transformers using integer programming[J].Electrical Power and Energy Systems,2003(25):717-723.
[20]VAIDANATHAN J, ANTHONY R. A simulated annealing methodology to distribution network design and management [J]. European Jounral of Operational Research,2003,(14):629-645.
[21]杨波.多品种随机数学模型的物流配送中心选址问题[J].中国管理科学,2003,11(2)：45-49.
[22]田青.离散制造企业物流网络设计方法研究[D].天津大学博士学位论文,2003.
[23]田青,缪立新,郑力.基于运输规划和组合GA的基本物流网络设计[J].清华大学学报,2004,44(11)：1441-1444.
[24]田青,缪立新,郑力,齐二石.基于组合遗传算法的大规模物流网络设计[J].物流技术,2005,(6)：40-42.
[25]张培林,魏巧云.物流配送中心选址模型及其启发式算法[J].交通运输工程学报,2003,13(2)：65-68.
[26]孙会君,高自友.考虑路线安排的物流配送中心选址双层规划模型及求解算法[J].中国公路学报,2003,16(2)：115-119.
[27]孙会君,高自友.基于空间价格均衡的物流中心选址双层规划模型研究[J].土木工程学报,2003,36(7)：40-43.
[28]邹辉霞,高伟.单配送中心的离散选址模型[J].科技进步与对策,2004,(1)：77-78.
[29]吕海峰,马维忠,王衍华.基于网络分析方法的物流配送中心选址的研究[J].运筹与管理,2004,13(6)：80-85.
[30]李尔涛,唐孝飞,胡思继.一个物流网络的双层规划模型[J].系统工程学报,2004,19(1)：8-13.
[31]庞明宝,魏连雨.区域物流线路网络双层规划研究[J].公路交通科技,2005,22(10)：158-162.
[32]姜大元.基于多节点的物流选址规划研究[J].铁道运输与经济,2005,27(8)：24-26.
[33]牟伦英,黄丹.物流网络节点的动态选址研究[J].工业工程与管理,2005,10(2)：102-106.
[34]祝延军,胡纯德,高随祥.单亲进化遗传算法在配送中心选址中的应用[J].计算机工程与设计,2005,26(3)：550-582.
[35]KLOSE A, DREXL A. Facility location models for distribution system design[J]. European Journal of Operational Research,2005,162(1):4-29.
[36]高梦昭.基于供应链的物流网络设计与运作研究[D].北京交通大学博士学位论文, 2005.
[37]吴兵,罗荣桂,彭伟华.基于遗传算法的物流配送中心选址研究[J].武汉理工大学学报,2006,28(1)：89-91.
[38]秦进.多商品物流网络设计相关优化模型及算法研究[D].中南大学博士学位论文,2006.
[39]秦进,史峰.多级物流配送网络设计的优化模型及算法[J].武汉理工大学学报,2007,31(5)：819-822.
[40]秦进,倪玲霖,缪立新.多级多商品流物流网络设计的优化模型与组合模拟退火算法[J].计算机应用研究,2010,27(9)：3348-3351.
[41]姜春艳,徐大川.带惩罚的动态设施选址问题的近似算法[J].应用数学学报,2009,32(6)：988-995.
[42]XU D C, DU D L. The k-level facility location game[J].Operations Research Letters, 2006,34(4):421-426.
[43]XU D C, YANG R. A cost-sharing method for an economic lot-sizing game[J]. Operations Research Letters,2009,(37):107-110.
[44]XU D C, ZHANG S. Approximation algorithm for facility location with service installation costs[J]. Operations Research Letters,2008,36(1):46-50.
[45]AROSTEGUI M A, KADIPASAOGLU S N, KHUMAWALA B M. An empirical comparison of tabu search,simulated annealing,and genitic alfotithms for facilities location problems[J]. Inernational Journal of Production Economics,2006,103(2): 742-754.
[46]邱法聚,张予川,易荃.物流配送中心连续型选址模型的推广[J].物流科技,2007,(1)：16-19.
[47]杨茂盛,李霞.改进重心法在物流配送中心选址中的应用[J].物流技术,2007,(6)：60-62.
[48]辜勇,高东旭.重心法在油库选址问题中的应用[J].物流技术,2007,(2)：108-111.
[49]彭扬,伍蓓.物流系统优化与仿真[M].北京：中国物质出版社,2006.
[50]彭扬.物流配送网路设计模型与算法研究[D].中国科学技术大学博士学位论文,2007.
[51]索晨霞,张志慧,张志红,董琳媛,赵剑峰.多产品物流网络设计模型[J].北京石油化工学院学报,2008,16(1)：57-61.
[52]童明荣,薛恒新.基于遗传算法的城市物流网络设计研究[J].运筹与管理,2008,17(5)：69-72.
[53]童明荣.基于遗传算法的城市闭环物流网络设计研究[J].公路交通科技,2009,26(6)：129-132.
[54]CORDEAU J F, LAPORTE G, PASIN F. An interated local search heuristic for the logistics network design problem with single assignment[J]. International Journal of Prodution Economics,2008,113(2):626-640.
[55]ABOOLIAN R, BERMAN O, KRASS D. Competitive facility location and design problem[J]. European Journal of Operational Research,2009,182(1):40-62.
[56]刘沛,刘超.基于遗传算法的轴辐式物流网络设计研究[J].物流技术,2009,28(12)：101-103.
[57]管小俊,王喜富,王翠华,闫亚娜.基于竞争的物流中心选址双层规划模型及算法研究[J].武汉理工大学学报,2009,33(5)：956-959.
[58]孙杨,宋瑞,何世伟.分层物流网络设计及启发式算法求解研究[J].物流技术,2009,28(1)：55-59.
[59]花本高,丛雪.基于遗传算法物流配送路线优化研究与实现[J].电脑知识与技术,2010,6(24)：6834-6839.
[60]张纪会,高齐圣.复杂物流系统工程[J].青岛大学学报,2002,15(2)：74-77.
[61]朱卫峰,费奇.复杂物流系统仿真及研究现状[J].系统仿真学报,2003,15(3)：353-356.
[62]朱卫峰,费奇.一种集成的复杂物流系统仿真结构[J].华中科技大学学报,2004,32(7)：24-26.
[63]戎晓霞,崔玉泉,马建华.不确定环境下的物流配送中心选址模型[J].山东大学学报,2004,39(6)：72-77.
[64]卞文良,鞠颂东.物流复杂网络模型探究[A].21世纪数量经济学(第6卷)[M].北京：方志出版社,2006：425-432.
[65]李晔,陈燕.基于随机需求的多级供应链网络优化模型的研究[J].计算机集成制造,2004,(10)：25-29.
[66]SANTOSO T, AHMED S, GOETSCHALCKX M, et al. A stochastic programming approach for supply chain network design under uncertainty [J]. European Journal of Operational Research,2005,(167):96-115.
[67]MARIA I G S, ANA P B P,AUGUSTO Q N. An optimization model for the design of a capacitated multi-product teverse logistics network with uncertainty [J]. European Journal of Operational Research,2006,172(2):456-465.
[68]ZHANG Y, LI J, LI X H. Integrated logistics facilities network design for 3pls under uncertainty [J]. Jourmal of Southe University,2006,22(4):570-576.
[69]计小宇,邵震.基于不确定规划的供应链网络设计模型与算法[J].系统工程理论与实践,2007,(2)：118-121.
[70]刘海龙.不确定性环境下物流中心选址研究[D].哈尔滨理工大学硕士学位论文,2007.
[71]姚九存.不确定环境下多层有容量的设备选址问题[D].南京理工大学硕士学位论文,2007.
[72]张勇,蒋琦.不确定环境下的物流配送中心选址方法研究[J].兰州交通大学学报,2007,26(1)：135-137.
[73]陈超,王明春.供应链网络设计不确定规划模型及应用[J].经济研究导刊,2008,(11)：126-127.
[74]王保华,何世伟.不确定环境下物流中心选址鲁棒优化[J].交通运输系统工程与信息,2009,9(2)：69-74.
[75]覃儒展,李天华,唐贤健.基于复杂网络的物流网络构建初探[J].信息系统工程,2009,9：104-107.
[76]毛海军,芮维娜,李旭宏.基于不确定条件的再制造物流网络优化设计[J].东南大学学报,2010,40(2)：425-430.
[77]ATAMTURK A, ZHANG M. Two-Stage robust network flow and design under demand uncertainty[J]. Operations Research.2007,55(4):662-673.
[78]UKKUSURIi S V. Robust transportation network design under demand uncertainty [J]. Computer-Aided Civil and Infrastructure Engineering.2007,(22):6-18.
[79]MUDCHANATONGSUK S, ORDONEZ F, LIU J. Robust solutions for network design under transportation cost and demand uncertainty[J]. Journal of the Operational Research Society.2008,59(5):652-662.
[80]WATTS D J, STEVEN S H.Collective dynamics of "small-world" networks[J].Nature 1998,393:440-442.
[81]GILL R.Scenario Planning:Managing for the Future[M], John Wiley & Sons.2006.
[82]刘宝碇,赵瑞清.不确定规划及进一步的研究问题[J].系统工程理论与实践,1999,10(6)：1-6.
[83]LIU B D. Theory and Practice of Uncertain Programming[M].Physica-Verlag, Heidelberg,2002.
[84]彭锦,刘宝碇.不确定规划的研究现状及其发展前景[J].运筹与管理,2002,11(2)：1-9.
[85]刘宝碇,赵瑞清,王纲.不确定规划及应用[M].北京：清华大学出版社,2003.
[86]赵瑞清.不确定规划：现状与将来[A].中国运筹学会第六届学术交流会论文集,2000,255-263.
[87]ZADEH L A, Fuzzy sets as a basis for a theory of possibility [J],Fuzzy Sets and Systems,1978,(1):3-28.
[88]DUBOIS D, PRADE H. Possibility theory:An approach to computerized processing of uncertainty plenum,NewYork,1988.
[89]DUBOIS D, PRADE H. Fuzzy numbers:An overview,in analysis of fuzzy information, Bezdek JC(Ed.),CRC Press,Boca Raton,1988,(2):3-39.
[90]高雷阜.不确定规划模型及其算法研究[J].辽宁工程技术大学学报,2003,22(3)：413-415.
[91]高金伍.不确定多层规划模型与算法[D].清华大学博士学位论文,2004.
[92]蒋峥,刘斌.不确定优化问题的研究动向[J].武汉科技大学学报,2006,29(9)：599-602.
[93]MOORE R.YANG C. Interval Analysis[R].Technical Document.Lockheed Missiles and Space Division.Number LMSD-285875.1959.
[94]MOORE R. Interval Analysis[M].Englewood:Pretice-Hall,1966.
[95]MOORE R.Method and application of interval analysis[M].London:Prentice-Hall, 1979.
[96]沈祖和.区间分析方法及其应用[J].应用数学与计算数学,1983,(2)：1-27.
[97]张乃良,王海鹰等.非线性规划的区间方法[J].河海大学学报,1992,20(3)：97-103.
[98]ISHIHUCHI H, TANAKA M. Multiobjective programming in optimization of the interval objective function[J]. European Journal of Operation Research,1990, (48): 219-225.
[99]CSALLNER A E, CSENDES T. The convergence speed of interval methods for global optimization[J]. Computers & Mathematics with Applications.1996,31(4): 173-178.
[100]CHANAS S, KUCHTA D. Multiobjective programming in optimization of interval objective functions—a generalized approach[J].European Journal of Operational Research,1996, (94):594-598.
[101]GEN M, CHENG R. Optimal design of system reliability using interval programming and genetic algorithm[J]. Com-puters and Industrial Engineering,1996,31(1): 237-240.
[102]SHEN Z H, HUANG Z Y, WOLFE M A. An interval maximum entropy method for a discrete minimax problem[J].Appl.Math. and Comput,1997,(87):49-68.
[103]DARLINGTON J, PANTELIDES C C, RUSTEM B, et al. Decreasing the sensitivity of openloop optimal solutions in decision making under uncertainty [J]. European Journal of Operational Research,2000,121(2):343-362.
[104]ZHANG J J, FAN Y Y. The optimality conditions of interval number linear programming problem [J].Opera-tions Research and Management Science,2003, 12(2):44-47.
[105]刘新旺,达庆利.一种区间数线性规划的满意解[J].系统工程学报,1999,14(2)：123-128.
[106]刘兴旺,达庆利,韩世莲.区间数运输问题模型及其模糊目标规划求解方法[J].管理工程学报,1999,13(4)：6-9.
[107]张兴芳,张兴伟.区间数的排序及其在系统决策中的应用[J].系统工程理论与实践,1999,(7)：112-115.
[108]王海鹰,张乃良.带约束条件的离散Minmax问题的区间极大熵方法[J].应用数学学报,2000,15(3)：369-376.
[109]仝凌云,杨钊.区间数和泛灰数在区间分析中的比较[J].河北工业大学学报,2001,30(4)：93-96.
[110]胡承毅,徐山鹰,杨晓光.区间算法简介[J].系统工程理论与实践[J],2003(4)：59-62.
[111]郑泳凌,马龙华,钱积新.一类参数不确定规划的三目标规划解集方法[J].系统工程理论与实践,2003(5)：59-64.
[112]郭均鹏,吴育华.区间线性规划的标准型及其求解[J].系统工程,2003,21(3)：79-82.
[113]韦兰用,韦振中.区间数判断矩阵中区间数的运算[J].数学的实践与认识,2003,33(9)：75-79.
[114]吴江,黄登仕.区间数排序方法研究综述[J].系统工程,2004,22(8)：1-4.
[115]谢凡荣.需求区间型运输问题的求解算法[J].运筹与管理,2005,14(1)：23-27.
[116]蒋峥,戴连奎,吴铁军.区间非线性规划问题的确定化描述及其递阶求解[J].系统工程理论与实践,2005,(1)：100-116.
[117]史加荣,刘三阳,熊文涛.区间数线性规划的一种新解法[J].系统工程理论与实践,2005,(2)：101-106.
[118]沈家骅,严振祥.基于区间分析的组合预测系数确定方法[J].武汉理工大学学报,2006,30(6)：1077-1080.
[119]彭瑞.区间分析在极大极小全局优化和鲁棒控制中的应用[D].同济大学博士学位论文,2006.
[120]冯向前.区间数不确定多属性决策方法研究[D].南京航空航天大学博士学位论文,2006.
[121]KASPERSKI A, ZIELINSKI P. An approximation algorithm for interval data minmax regret combinatorial optimization problems [J]. Information Processing Letters.2006,97(5):177-180.
[122]JIANG C, HAN X, LIU G R, et al. A nonlinear interval number programming method for uncertain optimization problems [J]. European Journal of Operational Research. 2008,188(1):1-13.
[123]彭涛.含区间参数的非线性规划问题及算法研究[D].重庆大学硕士学位论文,2007.
[124]曾霁,张先君,叶俊.运输问题的区间规划模型[J].四川理工学院学报,2008,21(2)：30-32.
[125]肖峻,林立鹏,何丽薇,方国雄.基于区间分析的建设项目经济评估方法研究[J].天津大学学报,2008,41(4)：401-406.
[126]王建忠,杜纲.区间线性双层规划的最好最优解[J].系统工程,2009,27(4)：100-103.
[127]牛彦涛,黄国和,张晓萱,杨勇平.区间数线性规划及其区间解的研究[J].运筹与管理,2010,19(3)：23-29.
[128]WANG J Z, DU G. A solution to interval linear bi-level programming and its application in decentralized supply chain planning[J],proceedings of 2008 IEEE International Conference on Service Operations and Logistics,and Informatics, 2008(2):2035-2038.
[129]赵晓煜,汪定伟,供应链中分销中心布局问题的区间规划模型及解法,系统工程,2004,22(8)：28-32.
[130]曹洪医.动态联盟中伙伴选择问题的区间规划模型及其求解[J].中国管理科学.2006,14(6)：86-91.
[131]刘金荣.供应链管理中的不确定性因素及其解决对策[J].衡阳师范高等专科学校学报,2004,24(6)：129-131.
[132]胡翠红,杜文.供应链中不确定性因素分析[J].商业研究,2007(3)：69-70.
[133]MANOLIS C.NYGAARDA,LILLERND B.Uncertainly and vertical control:an inlc malional investigation[J]. International Business Review,1997,6(5):501-518.
[134]BEALE E M L. On minimizing a convex function subject to linear inequalities [J]. Journal of the Royal Statistical Society,1955,17B,173-184.
[135]DANTZIG G B.Linear programming under uncertainty [J]. Management Science,1955, 1,197-206.
[136]TINTNER,G.Stochastic linear programming with applications to agricultural economics[D].Proceedings of the Second Symposium in Linear Programming, National Bureau of Standard,Washington, DC.1955,197-228.
[137]BELLMAN R E.Dynamic programming[M].Princetion,PA:Princetion University Press,1957.
[138]BELLMAN R E,ZADEH L A.Decision-making in a fuzzy environment[J]. Management Science,1970,17,141-161.
[139]CHARNES A,COOPER W W.Chance-constrained programming[J].Management Science,1959,6,73-79.
[140]CHARNES A,COOPER W W,SYMONDS G H.Cost horizons and certainty equivalents:An approach to stochastic programming of heating oil[J]. Management Science,1958,6,235-263.
[141]KALLP W S. Stochastic Programming[M].Chichester:Wiley,1994.
[142]HOMER P. Planning under uncertainty[J].ORMS Today.1999,(26):26-30.
[143]KALL P WALLACE S. Stochastic Programming.Wiley,New York,1994.Online available.
[144]PAWLAK Z. Rough sets[J].Int J Comput Inform Sei.1982,11(5):341-356.
[145]PAWLAK Z. Rough sets:theortical aspects of reasoning about data[M]. Dordrecht: Kluwer Academic Publishers,1991.
[146]ALEFELD G, HERZBERGER J. Introductionto Interval Computions[M].New York: Academic Press,1983.
[147]王光远.未确知信息及其数学处理[J].哈尔滨建筑大学学报.1990,23(4)：1-9.
[148]朱道立,龚国华,罗齐.物流和供应链管理[M].上海：复旦大学出版社,2002.
[149]MOORE R E.Interval arithmetic and automatic error analysis in digital computing[D].Ph.D.Dissertation,Stanford University,October 1962.
[150]ALEFELD G, HERZBERGER J. Introductionto Interval Computions[M].New York: Academic Press,1983.
[151]NEUMAIER A. Inerval methods for systems of equations[M].New York:Cambridge University Press.1990.
[152]KEARFOTT R. Interval computations:Introduction, uses and resources euromath [J]. Bulletin,1996,2(1):95-112.
[153]WOLFE M A. Interval mathematics,algebraic equations and optimization[J]. Comput. Appl.Math,2000,(124):263-280.
[154]SHARY S. A new technique in systems analysis under interval uncertainty and ambiguity[J].Reliab.Comp,2002,(8):321-418.
[155]HANSEN E, WILLIAM G W.Global optimization using interval analysis[M]. New York:Marcel Dekker,2004.
[156]NAKAHARA Y, SASAKI M, GEN M.On the linear programming problems with interval coefficients[J].International Journal of Computer Industrial Engineering, 1992, (23):301-304.
[157]张全,樊治平,潘德惠.不确定性多属性决策中区间数的一种排序方法[J].系统工程理论与实践,1999,19(5)：129-133.
[158]徐泽水,达庆利.区间数的排序方法研究[J].系统工程,2001,19(6)：94-96.
[159]曾文艺.区间数的综合决策模型[J].系统工程理论与实践,1997,17(11)：48-50.
[160]刘进生,王绪柱.区间数排序[J].工程数学学报,2001,18(4)：103-109.
[161]张兴芳,管恩瑞,孟广武.区间值模糊综合评判及其应用[J].系统工程理论与实践,2001,21(12)：81-84.
[162]张吉军.区间线性规划问题的最优解[J].系统工程与电子技术,2001,23(9)：53-55.
[163]WU H C. On interval-valued nonlinear programming problems[J] Journal of Mathematical analysis and applications,Operational Research,2008,338(1):299-316.
[164]INUIGUCHI M, KUME Y.,Goal programming problems with interval coefficients and target intervals[J], European Journal of Operational Research,1991,52(3):345-360.
[165]INUIGUCHI M, SAKAWA M. Minimax regret solution to linear programming problems with an interval objective function[J],European Journal of Operational Research,1995,86(3):526-536.
[166]INUIGUCHI M, SAKAWA M. Maximum regret analysis in linear programs with an interval objective function[C],In Proceedings of IWSCI'96,1996,308-317.
[167]MAUSSER H E, LAGUNA M. A new mixed integer formulation for the maximum regret problem[J]. International Transactions in Operational Research, 1998,5(5):389-403.
[168]MAUSSER H E, LAGUNA M. A heuristic to minimax absolute regret for linear programs with interval objective function coefficients [J]. European Journal of Operational Research,1999,117(l):157-174.
[169]AVERBAKH I, LEBEDEV V. Interval data minmax regret network optimization problems[J]. Discrete Applied Mathematics,2004,138(3):289-301.
[170]AVERBAKH I, LEBEDEV V. On the complexity of minmax regret linear programming[J]. European Journal of Operational Research,2005,160(1):227-231.
[171]AVERBAKH I, LEBEDEV V. Complexity of minimizing the total flow time with interval data and minmax regret criterion[J]. Discrete Applied Mathematics,2006,154(15):2167-2177.
[172]NIKAS I A, GRAPSA T N. Bounding the zeros of an interval equation[J].Appl. Math. Comput,2009.
[173]KRAWCZYK R. Newton-algorithmen zur bestimmung von nullstellen mit fehlerschranken[J].Computing,1969,(4):197-201.
[174]HANSEN E. Interval forms of Newton's method[J].Computing,1978,20(2):153-163.
[175]韩超,曹德欣.非线性方程的最佳Krawczyk-Hansen算子[J].大学数学,2010,26(1)：53-56.
[176]马龙华.不确定系统的鲁棒优化方法及其研究[D].浙江大学博士学位论文,2002.
[177]程志强,戴连奎,孙优贤.区间参数不确定性系统优化的可行性分析[J].自动化学报,2004,30(3)：455-459.
[178]JIANG C, HAN X, LIU G R.Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval[J].Computer Methods in Applied Mechanics and Engineering,2007,(196):4791-4800.
[179]WU H C.The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function[J]. European Jounral of Operational Research,2007,(176):46-59.
[180]TAKAO Y, MITSUO G, YINXIU L,et al. A genetic algorithm for interval nonlinear integer programming problem[J]. Computers & Industrial Engineering,1996,31 (3/4):913-917.
[181]TAKEAKI T, KENICHI I, MITSEO G. Method for solving nonlinear goal programming with interval coefficients using genetic algorithm [J]. Computers & Industrial Engineering,1997,33 (3/4):597-600.
[182]TAKEAKI T, TAKAO Y. Optimal design problem of system reliability with interval coefficient using improved genetic algorithms [J]. Computers & Industrial Engineering, 1999,37(1/2):145-149.
[183]BHUNIA A K, SAHOO L, ROY D.Reliability stochastic optimization for a series system with interval component reliability via genetic algorithm[J].Applied Mathematics and Computation,2010,216(3):929-939.
[184]JIRI R.An algorithm for computing the hull of the solution set of interval linear equations [J].,Linear Algebra and Its Applications,2011,435(2):193-201.
[185]LAXMINARAYAN S,ASOKE K B, PARMAD K K. Genetic algorithm based multi-objective reliability optimization in interval environment[J]. Computers & Industrial Engineering,2012,62(1):152-160.
[186]肖剑,陈义华.DEA评价下的配送中心再选址模型及求解[J].系统工程学报,2006,21(4)：442-445.
[187]王欢连.改进的DEA在物流中心选址中的应用[J].赣南师范学院学报,2007,(3)：85-87.
[188]张学成,何去非.基于AHP-GP的物流中心选址方法[J].重庆工学院学报,2007,21(9)：111-113.
[189]ERDOS P, RENYI A.On the evaluation of random graphs[J].Publ Math Inst Hungar Acad Sci.1960,(5):17-61.
[190]李靖,张永安.复杂网络理论在物流网络研究中的应用[J].中国流通经济,2011,(5)：38-42.
[191]徐娟.基于复杂网络的物流网络度分布[J].物流科技.2011,(6)：89-91.
[192]曾云,刘宗武.基于复杂网络理论的物流配送路径优化研究[J].物流技术.2011,30(9)：113-116.
[193]赵勇,曾勇,贾春华,简三军.基于改进蚁群算法的物流配送复杂路径优化问题研究[J].中国市场.2011,(28)：6-10.
[194]刘利军.基于供应链复杂系统理论的煤炭物流网络特性研究[J].煤炭经济研究.2009,(10)：46-48.
[195]后锐,杨建梅,姚灿中.物流产业竞争关系复杂网络模型研究[J].管理学报.2010,7(3)：406-411.
[196]万志成,慕静.物流系统的复杂适应性研究[J].物流科技.2010,(2)：1-4.
[2]胡双增,张明.物流系统工程[M].清华大学出版社.2003.
[3]程国全,柴继峰,王转.物流设施规划与设计[M].北京：中国物资出版社,2003.
[4]PEAT F D.From Certainty to Uncertainty:The story of science and ideas in the twentieth[M] Joseph Henry Press,2002.
[5]POLLACK H N.Untertainty science uncertainty world[M].Cambridge University Press,2003.
[6]KLIR G H.Uncertainty and information:Foundations of generalized information theory[M].John Wiley and Sons,Inc,2006.
[7]胡列格.物流运筹学[M].北京：电子工业出版社,2005.
[8]AIKENS.C.H.Facility location models for distribution planning[J]. European Journal of Operational Re-search,1985,22(2):263-279.
[9]BENAYED.O.A general bi-level linear programming formulation of the network design problem[J]. Transportation Research,1988,22(B):311-318.
[10]TANIGUCHI E.Optimal size and location planning of public logistics terminals[J]. Transportation Research,1999,35(1):207-222.
[11]DAGANZO C F. Logistics System Analysis[M]. Berlin:Springer,1996.
[12]刘海燕,李宗平,叶怀珍.物流配送中心选址模型[J].西南交通大学学报,2000,35(3)：311-314.
[13]胡刚,王淑琴,李铁柱,朱中.针对第三方物流企业的物流中心选址模型研究[J].公路交通科技,2002,19(6)：172-176.
[14]鲁晓春,詹荷生.关于配送中心重心法选址的研究[J].北方交通大学学报,2002,24(6)：108-110.
[15]姜大立,杨西龙.易腐物品配送中心连续选址模型及其遗传算法[J].系统工程理论与实践,2003,(2)：62-67.
[16]李志华,王启富,钟毅芳,周亦波.物流网络设计建模与求解算法研究[J].机械工程学报,2003,39(2)：84-89.
[17]SANJAY M, MARK S. Daskin.Capacitated facility location/network design problems [J]. European Journal of Operational Research,2001,129(2):481-495.
[18]SIDDHARTHA S S. A model and methodologies for the location problem with logistical components[J]. Computers and Operations Research,2002,29(9):1173-1193.
[19]JOVANOVIC D M.Planning of optimal location and sizes of distribution transformers using integer programming[J].Electrical Power and Energy Systems,2003(25):717-723.
[20]VAIDANATHAN J, ANTHONY R. A simulated annealing methodology to distribution network design and management [J]. European Jounral of Operational Research,2003,(14):629-645.
[21]杨波.多品种随机数学模型的物流配送中心选址问题[J].中国管理科学,2003,11(2)：45-49.
[22]田青.离散制造企业物流网络设计方法研究[D].天津大学博士学位论文,2003.
[23]田青,缪立新,郑力.基于运输规划和组合GA的基本物流网络设计[J].清华大学学报,2004,44(11)：1441-1444.
[24]田青,缪立新,郑力,齐二石.基于组合遗传算法的大规模物流网络设计[J].物流技术,2005,(6)：40-42.
[25]张培林,魏巧云.物流配送中心选址模型及其启发式算法[J].交通运输工程学报,2003,13(2)：65-68.
[26]孙会君,高自友.考虑路线安排的物流配送中心选址双层规划模型及求解算法[J].中国公路学报,2003,16(2)：115-119.
[27]孙会君,高自友.基于空间价格均衡的物流中心选址双层规划模型研究[J].土木工程学报,2003,36(7)：40-43.
[28]邹辉霞,高伟.单配送中心的离散选址模型[J].科技进步与对策,2004,(1)：77-78.
[29]吕海峰,马维忠,王衍华.基于网络分析方法的物流配送中心选址的研究[J].运筹与管理,2004,13(6)：80-85.
[30]李尔涛,唐孝飞,胡思继.一个物流网络的双层规划模型[J].系统工程学报,2004,19(1)：8-13.
[31]庞明宝,魏连雨.区域物流线路网络双层规划研究[J].公路交通科技,2005,22(10)：158-162.
[32]姜大元.基于多节点的物流选址规划研究[J].铁道运输与经济,2005,27(8)：24-26.
[33]牟伦英,黄丹.物流网络节点的动态选址研究[J].工业工程与管理,2005,10(2)：102-106.
[34]祝延军,胡纯德,高随祥.单亲进化遗传算法在配送中心选址中的应用[J].计算机工程与设计,2005,26(3)：550-582.
[35]KLOSE A, DREXL A. Facility location models for distribution system design[J]. European Journal of Operational Research,2005,162(1):4-29.
[36]高梦昭.基于供应链的物流网络设计与运作研究[D].北京交通大学博士学位论文, 2005.
[37]吴兵,罗荣桂,彭伟华.基于遗传算法的物流配送中心选址研究[J].武汉理工大学学报,2006,28(1)：89-91.
[38]秦进.多商品物流网络设计相关优化模型及算法研究[D].中南大学博士学位论文,2006.
[39]秦进,史峰.多级物流配送网络设计的优化模型及算法[J].武汉理工大学学报,2007,31(5)：819-822.
[40]秦进,倪玲霖,缪立新.多级多商品流物流网络设计的优化模型与组合模拟退火算法[J].计算机应用研究,2010,27(9)：3348-3351.
[41]姜春艳,徐大川.带惩罚的动态设施选址问题的近似算法[J].应用数学学报,2009,32(6)：988-995.
[42]XU D C, DU D L. The k-level facility location game[J].Operations Research Letters, 2006,34(4):421-426.
[43]XU D C, YANG R. A cost-sharing method for an economic lot-sizing game[J]. Operations Research Letters,2009,(37):107-110.
[44]XU D C, ZHANG S. Approximation algorithm for facility location with service installation costs[J]. Operations Research Letters,2008,36(1):46-50.
[45]AROSTEGUI M A, KADIPASAOGLU S N, KHUMAWALA B M. An empirical comparison of tabu search,simulated annealing,and genitic alfotithms for facilities location problems[J]. Inernational Journal of Production Economics,2006,103(2): 742-754.
[46]邱法聚,张予川,易荃.物流配送中心连续型选址模型的推广[J].物流科技,2007,(1)：16-19.
[47]杨茂盛,李霞.改进重心法在物流配送中心选址中的应用[J].物流技术,2007,(6)：60-62.
[48]辜勇,高东旭.重心法在油库选址问题中的应用[J].物流技术,2007,(2)：108-111.
[49]彭扬,伍蓓.物流系统优化与仿真[M].北京：中国物质出版社,2006.
[50]彭扬.物流配送网路设计模型与算法研究[D].中国科学技术大学博士学位论文,2007.
[51]索晨霞,张志慧,张志红,董琳媛,赵剑峰.多产品物流网络设计模型[J].北京石油化工学院学报,2008,16(1)：57-61.
[52]童明荣,薛恒新.基于遗传算法的城市物流网络设计研究[J].运筹与管理,2008,17(5)：69-72.
[53]童明荣.基于遗传算法的城市闭环物流网络设计研究[J].公路交通科技,2009,26(6)：129-132.
[54]CORDEAU J F, LAPORTE G, PASIN F. An interated local search heuristic for the logistics network design problem with single assignment[J]. International Journal of Prodution Economics,2008,113(2):626-640.
[55]ABOOLIAN R, BERMAN O, KRASS D. Competitive facility location and design problem[J]. European Journal of Operational Research,2009,182(1):40-62.
[56]刘沛,刘超.基于遗传算法的轴辐式物流网络设计研究[J].物流技术,2009,28(12)：101-103.
[57]管小俊,王喜富,王翠华,闫亚娜.基于竞争的物流中心选址双层规划模型及算法研究[J].武汉理工大学学报,2009,33(5)：956-959.
[58]孙杨,宋瑞,何世伟.分层物流网络设计及启发式算法求解研究[J].物流技术,2009,28(1)：55-59.
[59]花本高,丛雪.基于遗传算法物流配送路线优化研究与实现[J].电脑知识与技术,2010,6(24)：6834-6839.
[60]张纪会,高齐圣.复杂物流系统工程[J].青岛大学学报,2002,15(2)：74-77.
[61]朱卫峰,费奇.复杂物流系统仿真及研究现状[J].系统仿真学报,2003,15(3)：353-356.
[62]朱卫峰,费奇.一种集成的复杂物流系统仿真结构[J].华中科技大学学报,2004,32(7)：24-26.
[63]戎晓霞,崔玉泉,马建华.不确定环境下的物流配送中心选址模型[J].山东大学学报,2004,39(6)：72-77.
[64]卞文良,鞠颂东.物流复杂网络模型探究[A].21世纪数量经济学(第6卷)[M].北京：方志出版社,2006：425-432.
[65]李晔,陈燕.基于随机需求的多级供应链网络优化模型的研究[J].计算机集成制造,2004,(10)：25-29.
[66]SANTOSO T, AHMED S, GOETSCHALCKX M, et al. A stochastic programming approach for supply chain network design under uncertainty [J]. European Journal of Operational Research,2005,(167):96-115.
[67]MARIA I G S, ANA P B P,AUGUSTO Q N. An optimization model for the design of a capacitated multi-product teverse logistics network with uncertainty [J]. European Journal of Operational Research,2006,172(2):456-465.
[68]ZHANG Y, LI J, LI X H. Integrated logistics facilities network design for 3pls under uncertainty [J]. Jourmal of Southe University,2006,22(4):570-576.
[69]计小宇,邵震.基于不确定规划的供应链网络设计模型与算法[J].系统工程理论与实践,2007,(2)：118-121.
[70]刘海龙.不确定性环境下物流中心选址研究[D].哈尔滨理工大学硕士学位论文,2007.
[71]姚九存.不确定环境下多层有容量的设备选址问题[D].南京理工大学硕士学位论文,2007.
[72]张勇,蒋琦.不确定环境下的物流配送中心选址方法研究[J].兰州交通大学学报,2007,26(1)：135-137.
[73]陈超,王明春.供应链网络设计不确定规划模型及应用[J].经济研究导刊,2008,(11)：126-127.
[74]王保华,何世伟.不确定环境下物流中心选址鲁棒优化[J].交通运输系统工程与信息,2009,9(2)：69-74.
[75]覃儒展,李天华,唐贤健.基于复杂网络的物流网络构建初探[J].信息系统工程,2009,9：104-107.
[76]毛海军,芮维娜,李旭宏.基于不确定条件的再制造物流网络优化设计[J].东南大学学报,2010,40(2)：425-430.
[77]ATAMTURK A, ZHANG M. Two-Stage robust network flow and design under demand uncertainty[J]. Operations Research.2007,55(4):662-673.
[78]UKKUSURIi S V. Robust transportation network design under demand uncertainty [J]. Computer-Aided Civil and Infrastructure Engineering.2007,(22):6-18.
[79]MUDCHANATONGSUK S, ORDONEZ F, LIU J. Robust solutions for network design under transportation cost and demand uncertainty[J]. Journal of the Operational Research Society.2008,59(5):652-662.
[80]WATTS D J, STEVEN S H.Collective dynamics of "small-world" networks[J].Nature 1998,393:440-442.
[81]GILL R.Scenario Planning:Managing for the Future[M], John Wiley & Sons.2006.
[82]刘宝碇,赵瑞清.不确定规划及进一步的研究问题[J].系统工程理论与实践,1999,10(6)：1-6.
[83]LIU B D. Theory and Practice of Uncertain Programming[M].Physica-Verlag, Heidelberg,2002.
[84]彭锦,刘宝碇.不确定规划的研究现状及其发展前景[J].运筹与管理,2002,11(2)：1-9.
[85]刘宝碇,赵瑞清,王纲.不确定规划及应用[M].北京：清华大学出版社,2003.
[86]赵瑞清.不确定规划：现状与将来[A].中国运筹学会第六届学术交流会论文集,2000,255-263.
[87]ZADEH L A, Fuzzy sets as a basis for a theory of possibility [J],Fuzzy Sets and Systems,1978,(1):3-28.
[88]DUBOIS D, PRADE H. Possibility theory:An approach to computerized processing of uncertainty plenum,NewYork,1988.
[89]DUBOIS D, PRADE H. Fuzzy numbers:An overview,in analysis of fuzzy information, Bezdek JC(Ed.),CRC Press,Boca Raton,1988,(2):3-39.
[90]高雷阜.不确定规划模型及其算法研究[J].辽宁工程技术大学学报,2003,22(3)：413-415.
[91]高金伍.不确定多层规划模型与算法[D].清华大学博士学位论文,2004.
[92]蒋峥,刘斌.不确定优化问题的研究动向[J].武汉科技大学学报,2006,29(9)：599-602.
[93]MOORE R.YANG C. Interval Analysis[R].Technical Document.Lockheed Missiles and Space Division.Number LMSD-285875.1959.
[94]MOORE R. Interval Analysis[M].Englewood:Pretice-Hall,1966.
[95]MOORE R.Method and application of interval analysis[M].London:Prentice-Hall, 1979.
[96]沈祖和.区间分析方法及其应用[J].应用数学与计算数学,1983,(2)：1-27.
[97]张乃良,王海鹰等.非线性规划的区间方法[J].河海大学学报,1992,20(3)：97-103.
[98]ISHIHUCHI H, TANAKA M. Multiobjective programming in optimization of the interval objective function[J]. European Journal of Operation Research,1990, (48): 219-225.
[99]CSALLNER A E, CSENDES T. The convergence speed of interval methods for global optimization[J]. Computers & Mathematics with Applications.1996,31(4): 173-178.
[100]CHANAS S, KUCHTA D. Multiobjective programming in optimization of interval objective functions—a generalized approach[J].European Journal of Operational Research,1996, (94):594-598.
[101]GEN M, CHENG R. Optimal design of system reliability using interval programming and genetic algorithm[J]. Com-puters and Industrial Engineering,1996,31(1): 237-240.
[102]SHEN Z H, HUANG Z Y, WOLFE M A. An interval maximum entropy method for a discrete minimax problem[J].Appl.Math. and Comput,1997,(87):49-68.
[103]DARLINGTON J, PANTELIDES C C, RUSTEM B, et al. Decreasing the sensitivity of openloop optimal solutions in decision making under uncertainty [J]. European Journal of Operational Research,2000,121(2):343-362.
[104]ZHANG J J, FAN Y Y. The optimality conditions of interval number linear programming problem [J].Opera-tions Research and Management Science,2003, 12(2):44-47.
[105]刘新旺,达庆利.一种区间数线性规划的满意解[J].系统工程学报,1999,14(2)：123-128.
[106]刘兴旺,达庆利,韩世莲.区间数运输问题模型及其模糊目标规划求解方法[J].管理工程学报,1999,13(4)：6-9.
[107]张兴芳,张兴伟.区间数的排序及其在系统决策中的应用[J].系统工程理论与实践,1999,(7)：112-115.
[108]王海鹰,张乃良.带约束条件的离散Minmax问题的区间极大熵方法[J].应用数学学报,2000,15(3)：369-376.
[109]仝凌云,杨钊.区间数和泛灰数在区间分析中的比较[J].河北工业大学学报,2001,30(4)：93-96.
[110]胡承毅,徐山鹰,杨晓光.区间算法简介[J].系统工程理论与实践[J],2003(4)：59-62.
[111]郑泳凌,马龙华,钱积新.一类参数不确定规划的三目标规划解集方法[J].系统工程理论与实践,2003(5)：59-64.
[112]郭均鹏,吴育华.区间线性规划的标准型及其求解[J].系统工程,2003,21(3)：79-82.
[113]韦兰用,韦振中.区间数判断矩阵中区间数的运算[J].数学的实践与认识,2003,33(9)：75-79.
[114]吴江,黄登仕.区间数排序方法研究综述[J].系统工程,2004,22(8)：1-4.
[115]谢凡荣.需求区间型运输问题的求解算法[J].运筹与管理,2005,14(1)：23-27.
[116]蒋峥,戴连奎,吴铁军.区间非线性规划问题的确定化描述及其递阶求解[J].系统工程理论与实践,2005,(1)：100-116.
[117]史加荣,刘三阳,熊文涛.区间数线性规划的一种新解法[J].系统工程理论与实践,2005,(2)：101-106.
[118]沈家骅,严振祥.基于区间分析的组合预测系数确定方法[J].武汉理工大学学报,2006,30(6)：1077-1080.
[119]彭瑞.区间分析在极大极小全局优化和鲁棒控制中的应用[D].同济大学博士学位论文,2006.
[120]冯向前.区间数不确定多属性决策方法研究[D].南京航空航天大学博士学位论文,2006.
[121]KASPERSKI A, ZIELINSKI P. An approximation algorithm for interval data minmax regret combinatorial optimization problems [J]. Information Processing Letters.2006,97(5):177-180.
[122]JIANG C, HAN X, LIU G R, et al. A nonlinear interval number programming method for uncertain optimization problems [J]. European Journal of Operational Research. 2008,188(1):1-13.
[123]彭涛.含区间参数的非线性规划问题及算法研究[D].重庆大学硕士学位论文,2007.
[124]曾霁,张先君,叶俊.运输问题的区间规划模型[J].四川理工学院学报,2008,21(2)：30-32.
[125]肖峻,林立鹏,何丽薇,方国雄.基于区间分析的建设项目经济评估方法研究[J].天津大学学报,2008,41(4)：401-406.
[126]王建忠,杜纲.区间线性双层规划的最好最优解[J].系统工程,2009,27(4)：100-103.
[127]牛彦涛,黄国和,张晓萱,杨勇平.区间数线性规划及其区间解的研究[J].运筹与管理,2010,19(3)：23-29.
[128]WANG J Z, DU G. A solution to interval linear bi-level programming and its application in decentralized supply chain planning[J],proceedings of 2008 IEEE International Conference on Service Operations and Logistics,and Informatics, 2008(2):2035-2038.
[129]赵晓煜,汪定伟,供应链中分销中心布局问题的区间规划模型及解法,系统工程,2004,22(8)：28-32.
[130]曹洪医.动态联盟中伙伴选择问题的区间规划模型及其求解[J].中国管理科学.2006,14(6)：86-91.
[131]刘金荣.供应链管理中的不确定性因素及其解决对策[J].衡阳师范高等专科学校学报,2004,24(6)：129-131.
[132]胡翠红,杜文.供应链中不确定性因素分析[J].商业研究,2007(3)：69-70.
[133]MANOLIS C.NYGAARDA,LILLERND B.Uncertainly and vertical control:an inlc malional investigation[J]. International Business Review,1997,6(5):501-518.
[134]BEALE E M L. On minimizing a convex function subject to linear inequalities [J]. Journal of the Royal Statistical Society,1955,17B,173-184.
[135]DANTZIG G B.Linear programming under uncertainty [J]. Management Science,1955, 1,197-206.
[136]TINTNER,G.Stochastic linear programming with applications to agricultural economics[D].Proceedings of the Second Symposium in Linear Programming, National Bureau of Standard,Washington, DC.1955,197-228.
[137]BELLMAN R E.Dynamic programming[M].Princetion,PA:Princetion University Press,1957.
[138]BELLMAN R E,ZADEH L A.Decision-making in a fuzzy environment[J]. Management Science,1970,17,141-161.
[139]CHARNES A,COOPER W W.Chance-constrained programming[J].Management Science,1959,6,73-79.
[140]CHARNES A,COOPER W W,SYMONDS G H.Cost horizons and certainty equivalents:An approach to stochastic programming of heating oil[J]. Management Science,1958,6,235-263.
[141]KALLP W S. Stochastic Programming[M].Chichester:Wiley,1994.
[142]HOMER P. Planning under uncertainty[J].ORMS Today.1999,(26):26-30.
[143]KALL P WALLACE S. Stochastic Programming.Wiley,New York,1994.Online available.
[144]PAWLAK Z. Rough sets[J].Int J Comput Inform Sei.1982,11(5):341-356.
[145]PAWLAK Z. Rough sets:theortical aspects of reasoning about data[M]. Dordrecht: Kluwer Academic Publishers,1991.
[146]ALEFELD G, HERZBERGER J. Introductionto Interval Computions[M].New York: Academic Press,1983.
[147]王光远.未确知信息及其数学处理[J].哈尔滨建筑大学学报.1990,23(4)：1-9.
[148]朱道立,龚国华,罗齐.物流和供应链管理[M].上海：复旦大学出版社,2002.
[149]MOORE R E.Interval arithmetic and automatic error analysis in digital computing[D].Ph.D.Dissertation,Stanford University,October 1962.
[150]ALEFELD G, HERZBERGER J. Introductionto Interval Computions[M].New York: Academic Press,1983.
[151]NEUMAIER A. Inerval methods for systems of equations[M].New York:Cambridge University Press.1990.
[152]KEARFOTT R. Interval computations:Introduction, uses and resources euromath [J]. Bulletin,1996,2(1):95-112.
[153]WOLFE M A. Interval mathematics,algebraic equations and optimization[J]. Comput. Appl.Math,2000,(124):263-280.
[154]SHARY S. A new technique in systems analysis under interval uncertainty and ambiguity[J].Reliab.Comp,2002,(8):321-418.
[155]HANSEN E, WILLIAM G W.Global optimization using interval analysis[M]. New York:Marcel Dekker,2004.
[156]NAKAHARA Y, SASAKI M, GEN M.On the linear programming problems with interval coefficients[J].International Journal of Computer Industrial Engineering, 1992, (23):301-304.
[157]张全,樊治平,潘德惠.不确定性多属性决策中区间数的一种排序方法[J].系统工程理论与实践,1999,19(5)：129-133.
[158]徐泽水,达庆利.区间数的排序方法研究[J].系统工程,2001,19(6)：94-96.
[159]曾文艺.区间数的综合决策模型[J].系统工程理论与实践,1997,17(11)：48-50.
[160]刘进生,王绪柱.区间数排序[J].工程数学学报,2001,18(4)：103-109.
[161]张兴芳,管恩瑞,孟广武.区间值模糊综合评判及其应用[J].系统工程理论与实践,2001,21(12)：81-84.
[162]张吉军.区间线性规划问题的最优解[J].系统工程与电子技术,2001,23(9)：53-55.
[163]WU H C. On interval-valued nonlinear programming problems[J] Journal of Mathematical analysis and applications,Operational Research,2008,338(1):299-316.
[164]INUIGUCHI M, KUME Y.,Goal programming problems with interval coefficients and target intervals[J], European Journal of Operational Research,1991,52(3):345-360.
[165]INUIGUCHI M, SAKAWA M. Minimax regret solution to linear programming problems with an interval objective function[J],European Journal of Operational Research,1995,86(3):526-536.
[166]INUIGUCHI M, SAKAWA M. Maximum regret analysis in linear programs with an interval objective function[C],In Proceedings of IWSCI'96,1996,308-317.
[167]MAUSSER H E, LAGUNA M. A new mixed integer formulation for the maximum regret problem[J]. International Transactions in Operational Research, 1998,5(5):389-403.
[168]MAUSSER H E, LAGUNA M. A heuristic to minimax absolute regret for linear programs with interval objective function coefficients [J]. European Journal of Operational Research,1999,117(l):157-174.
[169]AVERBAKH I, LEBEDEV V. Interval data minmax regret network optimization problems[J]. Discrete Applied Mathematics,2004,138(3):289-301.
[170]AVERBAKH I, LEBEDEV V. On the complexity of minmax regret linear programming[J]. European Journal of Operational Research,2005,160(1):227-231.
[171]AVERBAKH I, LEBEDEV V. Complexity of minimizing the total flow time with interval data and minmax regret criterion[J]. Discrete Applied Mathematics,2006,154(15):2167-2177.
[172]NIKAS I A, GRAPSA T N. Bounding the zeros of an interval equation[J].Appl. Math. Comput,2009.
[173]KRAWCZYK R. Newton-algorithmen zur bestimmung von nullstellen mit fehlerschranken[J].Computing,1969,(4):197-201.
[174]HANSEN E. Interval forms of Newton's method[J].Computing,1978,20(2):153-163.
[175]韩超,曹德欣.非线性方程的最佳Krawczyk-Hansen算子[J].大学数学,2010,26(1)：53-56.
[176]马龙华.不确定系统的鲁棒优化方法及其研究[D].浙江大学博士学位论文,2002.
[177]程志强,戴连奎,孙优贤.区间参数不确定性系统优化的可行性分析[J].自动化学报,2004,30(3)：455-459.
[178]JIANG C, HAN X, LIU G R.Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval[J].Computer Methods in Applied Mechanics and Engineering,2007,(196):4791-4800.
[179]WU H C.The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function[J]. European Jounral of Operational Research,2007,(176):46-59.
[180]TAKAO Y, MITSUO G, YINXIU L,et al. A genetic algorithm for interval nonlinear integer programming problem[J]. Computers & Industrial Engineering,1996,31 (3/4):913-917.
[181]TAKEAKI T, KENICHI I, MITSEO G. Method for solving nonlinear goal programming with interval coefficients using genetic algorithm [J]. Computers & Industrial Engineering,1997,33 (3/4):597-600.
[182]TAKEAKI T, TAKAO Y. Optimal design problem of system reliability with interval coefficient using improved genetic algorithms [J]. Computers & Industrial Engineering, 1999,37(1/2):145-149.
[183]BHUNIA A K, SAHOO L, ROY D.Reliability stochastic optimization for a series system with interval component reliability via genetic algorithm[J].Applied Mathematics and Computation,2010,216(3):929-939.
[184]JIRI R.An algorithm for computing the hull of the solution set of interval linear equations [J].,Linear Algebra and Its Applications,2011,435(2):193-201.
[185]LAXMINARAYAN S,ASOKE K B, PARMAD K K. Genetic algorithm based multi-objective reliability optimization in interval environment[J]. Computers & Industrial Engineering,2012,62(1):152-160.
[186]肖剑,陈义华.DEA评价下的配送中心再选址模型及求解[J].系统工程学报,2006,21(4)：442-445.
[187]王欢连.改进的DEA在物流中心选址中的应用[J].赣南师范学院学报,2007,(3)：85-87.
[188]张学成,何去非.基于AHP-GP的物流中心选址方法[J].重庆工学院学报,2007,21(9)：111-113.
[189]ERDOS P, RENYI A.On the evaluation of random graphs[J].Publ Math Inst Hungar Acad Sci.1960,(5):17-61.
[190]李靖,张永安.复杂网络理论在物流网络研究中的应用[J].中国流通经济,2011,(5)：38-42.
[191]徐娟.基于复杂网络的物流网络度分布[J].物流科技.2011,(6)：89-91.
[192]曾云,刘宗武.基于复杂网络理论的物流配送路径优化研究[J].物流技术.2011,30(9)：113-116.
[193]赵勇,曾勇,贾春华,简三军.基于改进蚁群算法的物流配送复杂路径优化问题研究[J].中国市场.2011,(28)：6-10.
[194]刘利军.基于供应链复杂系统理论的煤炭物流网络特性研究[J].煤炭经济研究.2009,(10)：46-48.
[195]后锐,杨建梅,姚灿中.物流产业竞争关系复杂网络模型研究[J].管理学报.2010,7(3)：406-411.
[196]万志成,慕静.物流系统的复杂适应性研究[J].物流科技.2010,(2)：1-4.