定位-路径问题综述

胡大伟; 陈希琼; 高扬

doi:10.19818/j.cnki.1671-1637.2018.01.011

定位-路径问题综述

doi: 10.19818/j.cnki.1671-1637.2018.01.011

长安大学汽车学院, 陕西西安 710064

基金项目:

国家自然科学基金项目 61503043

中央高校基本科研业务费专项资金项目 310822150020

中央高校基本科研业务费专项资金项目 300102228402

详细信息

作者简介:
胡大伟(1963-), 男, 北京人, 长安大学教授, 工学博士, 从事交通运输规划研究

中图分类号: U491.51
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出版历程
- 收稿日期: 2017-09-20
- 刊出日期: 2018-02-25

Review on location-routing problem

School of Automobile, Chang'an University, Xi'an 710064, Shaanxi, China

More Information

Author Bio:
HU Da-wei(1963-), male, professor, PhD, dwhu@chd.edu.cn

摘要

摘要: 研究了定位-路径问题(LRP), 总结了国内外LRP模型及其扩展模型, 比较了LRP模型求解算法的适用性, 分析了LRP测试算例的节点分布和数据规模, 提出了LRP研究的主要方向。研究结果表明: LRP模型从基于基础网络的最简化问题(带容量约束的LRP, CLRP) 向多方向模型进行扩展, 包括基于网络复杂化的LRP扩展, 如特定网络系统的多目标LRP (MOLRP)、同时取送货LRP (LRPSPD)、接驳转运中心LRP (CDCLRP)、两阶段LRP (2E-LRP)、选址-弧路径问题(LARP)、卡车和拖车路径问题(TTRP) 与设施地点为二维连续的LRP (PLRP), 基础网络参数不确定化的LRP, 包括带模糊数据的LRP与多计划周期LRP (MPLRP), 且正在向更切合实际的问题如高度集成、不确定与动态LRP发展; LRP算法方面, 精确算法仅可用于求解小规模LRP, 主要LRP求解算法由早期的智能算法逐渐转向元启发式算法、基于邻域搜索优化的算法与混合算法方向发展, 这些改进算法均基于特定LRP设计, 具有更好的求解性能, 尤其是采用基于多种破坏和修复因子的自适应大邻域搜索算法求解大规模LRP取得了较好的解, 且其改造性极强; 常用LRP测试算例的节点呈现均匀分布、堆分布及均匀与堆混合分布, 且逐渐产生了适用于2E-LRP与LRPSPD等扩展LRP的测试算例; 根据物流市场环境变化和需求, 提出LRP未来扩展研究的主要方向, 包括多阶段LRP的扩展(如2E-LRPSPD、考虑库存的2E-LRP等)、节点二维连续的LRP、客户含优先级的带竞争或盈利LRP、混合不确定LRP等切合实际的问题; 提出了LRP求解算法未来方向, 包括设计新型精确算法求解中、大规模LRP, 设计更准确更高效的组合启发式算法与应用近似算法求解LRP及扩展LRP的最优解。
- 交通运输规划 /
- 物流系统优化 /
- 定位-路径问题 /
- 组合优化问题 /
- 模型构建 /
- 算法设计
Abstract: Location-routing problem (LRP) was studied.The models of LRP and LRP extensions at home and abroad were summarized.The applicability of solving methods to LRP models were compared.The nodes-distributions and data scale of testing instances were analyzed.The main future research directions of LRP were proposed.Analysis result shows that the research of LRP models extends from the mostly simplified problem of basic logistics network (the capacitated LRP, CLRP) to multi-direction: including LRP extensions based on complicated networks such as, multi-objective LRP based on specific network systems, LRP with simultaneous pickup and delivery, LRP with cross-docking center, two-echelon LRP, location arc routing problems, truckand trailer routing problem and Planar LRP; and extensions based on uncertainties such as, LRP with fuzzy factors, multi-period LRP; meanwhile developing to more practical problems such as highly integrated LRPs, LRP with uncertainties and dynamic LRPs.On algorithms for LRPs, the exact algorithm can only be used to solve the small-scale problem.So the main researches on algorithms are gradually turned from intelligent algorithms in earlier times to metaheuristic algorithms, algorithms based on various neighborhood search optimization methods and hybrid algorithms.These algorithms which are designed based on the specific problems have good performance, especially the adaptive large neighbors search with various destruction factors and repair factors obtained better solutions on large-scale instances, and it is highly reusable.Test instances frequently used in the literature reflect that nodes in the instances follow uniform distribution, heap distribution and mix distribution.The instances specifically adapted to 2 ELRP, LRPSPD and other LRP extensions are gradually generated.Finally, the main direction of future research on LRP extensions is put forward according to the change and demand of logistics market environment, which include extensions of multi-echelon LRP such as 2 E-LRPSPD and 2 ELRP with inventory, planar LRP, priority based LRP with profits or competition, LRP with mixed uncertainty.Future directions on solving methods are also proposed: further exploration of exact algorithms for medium and large scale problems, the designation of hybrid heuristic algorithms with higher accuracy and efficiency, and the application of approximate algorithm for solving the optimal solutions of LRP and LRP extensions.
- transportation planning /
- logistics system optimization /
- location-routing problem /
- combination optimization problem /
- modeling /
- algorithm design

HTML全文

图 1 CLRP描述

Figure 1. Description of CLRP

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图 2 2E-LRP比较

Figure 2. Comparison of 2E-LRPs

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图 3 数据分布

Figure 3. Distributions of data

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表 1 LRP扩展问题总结

Table 1. Summary of LRP extension problems

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表 2 元启发式算法

Table 2. Metaheuristics

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表 3 基于邻域的算法比较

Table 3. Comparison of neighborhood based approaches

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表 4 LRP常用标准测试算例

Table 4. Frequently used benchmark test instances of LRP

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参考文献(161)

[1]	WATSON-GANDY C D T, DOHRN P J. Depot location with van salesmen—apractical approach[J]. Omega, 1973, 1 (3): 321-329. doi: 10.1016/0305-0483(73)90108-4
[2]	SALHI S, RAND G K. The effect of ignoring routes when locating depots[J]. European Journal of Operational Research, 1989, 39 (2): 150-156. doi: 10.1016/0377-2217(89)90188-4
[3]	GO'SCIE'N R, WALKOWIAK K. Modeling and optimization of data center location and routing and spectrum allocation in survivable elastic optical networks[J]. Optical Switching and Networking, 2017, 23 (2): 129-143.
[4]	杨珺, 冯鹏祥, 孙昊, 等. 电动汽车物流配送系统的换电站选址与路径优化问题研究[J]. 中国管理科学, 2015, 23 (9): 87-96. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGK201509012.htm YANG Jun, FENG Peng-xiang, SUN Hao, et al. Battery exchange station location and vehicle routing problem in electric vehicles distribution system[J]. Chinese Journal of Management Science, 2015, 23 (9): 87-96. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGK201509012.htm
[5]	SCHIFFER M, WALTHER G. The electric location routing problem with time windows and partial recharging[J]. European Journal of Operational Research, 2017, 260 (3): 995-1013. doi: 10.1016/j.ejor.2017.01.011
[6]	HOF J, SCHNEIDER M, GOEKE D. Solving the battery swap station location-routing problem with capacitated electric vehicles using an AVNS algorithm for vehicle-routing problems with intermediate stops[J]. Transportation Research Part B: Methodological, 2017, 97: 102-112. doi: 10.1016/j.trb.2016.11.009
[7]	LAPORTE G. Location-routing problems[C]//Elsevier. Vehicle Routing: Methods and Studies. Studies in Management Science and Systems. Amsterdam: Elsevier, 1988, 16: 163-197.
[8]	MIN H, JAYARAMAN V, SRIVASTAVA R. Combined location-routing problems: a synthesis and future research directions[J]. European Journal of Operational Research, 1998, 108 (1): 1-15. doi: 10.1016/S0377-2217(97)00172-0
[9]	NAGY G, SALHI S. Location-routing: issues, models and methods[J]. European Journal of Operational Research, 2007, 177 (2): 649-672. doi: 10.1016/j.ejor.2006.04.004
[10]	PRODHON C, PRINS C. A survey of recent research on locationrouting problems[J]. European Journal of Operational Research, 2014, 238 (1): 1-17. doi: 10.1016/j.ejor.2014.01.005
[11]	DREXL M, SCHNEIDER M. A survey of variants and extensions of the location-routing problem[J]. European Journal of Operational Research, 2015, 241 (2): 283-308. doi: 10.1016/j.ejor.2014.08.030
[12]	汪寿阳, 赵秋红, 夏国平. 集成物流管理系统中定位-运输路线安排问题的研究[J]. 管理科学学报, 2000, 3 (2): 69-75. doi: 10.3321/j.issn:1007-9807.2000.02.011 WANG Shou-yang, ZHAO Qiu-hong, XIA Guo-ping. Research on combined location-routing problems in integrated logistics systems[J]. Journal of Management Sciences in China, 2000, 3 (2): 69-75. (in Chinese). doi: 10.3321/j.issn:1007-9807.2000.02.011
[13]	张潜, 高立群, 胡祥培. 集成化物流中的定位-运输路线安排问题(LRP) 优化算法评述[J]. 东北大学学报: 自然科学版, 2003, 24 (1): 31-34. https://www.cnki.com.cn/Article/CJFDTOTAL-DBDX202001007.htm ZHANG Qian, GAO Li-qun, HU Xiang-pei. Review on optimal algorithms of location-routing problem (LRP) in integrated logistics[J]. Journal of Northeastern University: Natural Science, 2003, 24 (1): 31-34. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DBDX202001007.htm
[14]	林岩, 胡祥培, 王旭茵. 物流系统优化中的定位-运输路线安排问题(LRP) 研究评述[J]. 管理工程学报, 2004, 18 (4): 45-49. doi: 10.3969/j.issn.1004-6062.2004.04.009 LIN Yan, HU Xiang-pei, WANG Xu-yin. Review on location-routing problems (LRP) in systematic optimization of logistics[J]. Journal of Industrial Engineering/Engineering Management, 2004, 18 (4): 45-49. (in Chinese). doi: 10.3969/j.issn.1004-6062.2004.04.009
[15]	张余华, 张磊. 论集成物流管理系统中定位-运输路线安排问题[J]. 广东外语外贸大学学报, 2006, 17 (4): 35-38. doi: 10.3969/j.issn.1672-0962.2006.04.009 ZHANG Yu-hua, ZHANG Lei. The location-routing problem (LRP) in integrated logistics systems[J]. Journal of Guangdong University of Foreign Studies, 2006, 17 (4): 35-38. (in Chinese). doi: 10.3969/j.issn.1672-0962.2006.04.009
[16]	万凤娇. 集成物流管理系统中定位-运输路线安排问题评述[J]. 物流技术, 2012, 31 (10): 124-126. https://www.cnki.com.cn/Article/CJFDTOTAL-WLJS201219039.htm WAN Feng-jiao. Review of location-VRP in integrated logistics management system[J]. Logistics Technology, 2012, 31 (10): 124-126. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-WLJS201219039.htm
[17]	BASHIRI M, RASOULINEJAD Z, FALLAHZADE E. A new approach on auxiliary vehicle assignment in capacitated location routing problem[J]. International Journal of Systems Science, 2016, 47 (4): 886-902. doi: 10.1080/00207721.2014.906770
[18]	罗耀波, 孙延明, 刘小龙. 多约束选址-路径问题的改进混合遗传算法研究[J]. 计算机应用研究, 2013, 30 (8): 2283-2287. doi: 10.3969/j.issn.1001-3695.2013.08.011 LUO Yao-bo, SUN Yan-ming, LIU Xiao-long. Hybrid genetic algorithm for capacitated location-routing problem[J]. Application Research of Computers, 2013, 30 (8): 2283-2287. (in Chinese). doi: 10.3969/j.issn.1001-3695.2013.08.011
[19]	石兆, 符卓. 配送选址-多车型运输路径优化问题及求解算法[J]. 计算机科学, 2015, 42 (5): 245-250. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJA201505050.htm SHI Zhao, FU Zhuo. Distribution location-routing problem of heterotypic vehicles and its algorithms[J]. Computer Science, 2015, 42 (5): 245-250. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JSJA201505050.htm
[20]	宋强, 刘凌霞. 多行程车辆路径问题和配送中心定位问题的研究[J]. 数学的实践与认识, 2016, 46 (7): 103-113. https://www.cnki.com.cn/Article/CJFDTOTAL-SSJS201607014.htm SONG Qiang. LIU Ling-xia. Research on multi-trip vehicle routing problem and distribution center location problem[J]. Mathematics in Practice and Theory, 2016, 46 (7): 103-113. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-SSJS201607014.htm
[21]	郑斌, 马祖军, 方涛. 应急物流系统中的模糊多目标定位-路径问题[J]. 系统工程, 2009, 27 (8): 21-25. doi: 10.3969/j.issn.1001-2362.2009.08.010 ZHENG Bin, MA Zu-jun, FANG Tao. Fuzzy multi-objective location-routing problem in emergency logistics systems[J]. Systems Engineering, 2009, 27 (8): 21-25. (in Chinese). doi: 10.3969/j.issn.1001-2362.2009.08.010
[22]	王绍仁, 马祖军. 震后随机动态LRP多目标优化模型及算法[J]. 计算机应用研究, 2010, 27 (9): 3283-3286, 3293. doi: 10.3969/j.issn.1001-3695.2010.09.021 WANG Shao-ren, MA Zu-jun. Stochastic dynamic multiobjective optimization location-routing model and algorithm in post-earthquake[J]. Application Research of Computers, 2010, 27 (9): 3283-3286, 3293. (in Chinese). doi: 10.3969/j.issn.1001-3695.2010.09.021
[23]	孙华丽, 王循庆, 薛耀锋. 随机需求应急物流多阶段定位-路径鲁棒优化研究[J]. 运筹与管理, 2013, 22 (6): 45-51. doi: 10.3969/j.issn.1007-3221.2013.06.008 SUN Hua-li, WANG Xun-qing, XUE Yao-feng. Robust optimization for multi-stage location-routing problem with stochastic demand under emergency logistics[J]. Operations Research and Management Science, 2013, 22 (6): 45-51. (in Chinese). doi: 10.3969/j.issn.1007-3221.2013.06.008
[24]	赵佳虹, 彭艳梅. 危险废物回收物流的选址-路径多目标模型[J]. 交通运输工程与信息学报, 2011, 9 (2): 25-29. doi: 10.3969/j.issn.1672-4747.2011.02.005 ZHAO Jia-hong, PENG Yan-mei. A new multi-objective model for the combined location-routing problem in hazardous waste recycling logistics[J]. Journal of Transportation Engineering and Information, 2011, 9 (2): 25-29. (in Chinese). doi: 10.3969/j.issn.1672-4747.2011.02.005
[25]	李双琳, 马祖军, 邹坤. 危险品物流中的多目标定位-路径问题[J]. 运筹与管理, 2014, 23 (3): 8-15. doi: 10.3969/j.issn.1007-3221.2014.03.002 LI Shuang-lin, MA Zu-jun, ZOU Kun. Multi-objective location-routing problem for hazardous materials logistics[J]. Operations Research and Management Science, 2014, 23 (3): 8-15. (in Chinese). doi: 10.3969/j.issn.1007-3221.2014.03.002
[26]	赵佳虹, 丁宏飞, 胡鹏. 基于环境风险控制的危险废物选址-路径问题研究[J]. 公路交通科技, 2015, 32 (3): 135-141. doi: 10.3969/j.issn.1002-0268.2015.03.022 ZHAO Jia-hong, DING Hong-fei, HU Peng. Study of location-routing of hazardous waste based on controlling environmental risks[J]. Journal of Highway and Transportation Research and Development, 2015, 32 (3): 135-141. (in Chinese). doi: 10.3969/j.issn.1002-0268.2015.03.022
[27]	王海燕, 张岐山. 废弃物收运网络周期性选址-路径问题多目标优化模型及算法[J]. 系统工程理论与实践, 2013, 33 (8): 1998-2006. doi: 10.3969/j.issn.1000-6788.2013.08.012 WANG Hai-yan, ZHANG Qi-shan. Multi-objective optimization of periodic location routing problem for waste logistics network in cities[J]. Systems Engineering—Theory and Practice, 2013, 33 (8): 1998-2006. (in Chinese). doi: 10.3969/j.issn.1000-6788.2013.08.012
[28]	CABALLERO R, GONZ'ALEZ M, GUERRERO F M, et al. Solving a multiobjective location routing problem with a metaheuristic based on tabu search. Application to a real case in Andalusia[J]. European Journal of Operational Research, 2007, 177 (3): 1751-1763. doi: 10.1016/j.ejor.2005.10.017
[29]	ZHAO J, VERTER V. A bi-objective model for the used oil location-routing problem[J]. Computers and Operations Research, 2015, 62: 157-168. doi: 10.1016/j.cor.2014.10.016
[30]	罗耀波, 孙延明. 基于模糊时间窗的带容积约束选址路径问题[J]. 系统工程, 2014, 32 (1): 19-25. doi: 10.3969/j.issn.1001-2362.2014.01.006 LUO Yao-bo, SUN Yan-ming. Capacitated location routing problem based on fuzzy time windows[J]. Systems Engineering, 2014, 32 (1): 19-25. (in Chinese). doi: 10.3969/j.issn.1001-2362.2014.01.006
[31]	TAVAKKOLI-MOGHADDAM R, MAKUI A, MAZLOOMI Z. A new integrated mathematical model for a bi-objective multidepot location-routing problem solved by a multi-objective scatter search algorithm[J]. Journal of Manufacturing Systems, 2010, 29 (2): 111-119.
[32]	RATH S, GUTJAHR W J. A math-heuristic for the warehouse location-routing problem in disaster relief[J]. Computers and Operations Research, 2014, 42 (2): 25-39.
[33]	王道平, 徐展, 杨岑. 基于竞争环境的截流设施选址与车辆路径问题[J]. 控制与决策, 2015, 30 (6): 1053-1058. https://www.cnki.com.cn/Article/CJFDTOTAL-KZYC201506014.htm WANG Dao-ping, XU Zhan, YANG Cen. Flow interception facility location and vehicle routing problem based on competitive conditions[J]. Control and Decision, 2015, 30 (6): 1053-1058. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-KZYC201506014.htm
[34]	GOETSCHALCKX M, JACOBS-BLECHA C. The vehicle routing problem with backhauls[J]. European Journal of Operational Research, 1987, 42 (1): 39-51.
[35]	MIN H. The multiple vehicle routing problem with simultaneous delivery and pick-up points[J]. Transportation Research Part A: General, 1989, 23 (5): 377-386. doi: 10.1016/0191-2607(89)90085-X
[36]	胡大伟, 陈诚, 郭晓汾. 带集货和配送的多站点VRP优化算法研究[J]. 数学的实践与认识, 2007, 37 (2): 98-104. doi: 10.3969/j.issn.1000-0984.2007.02.017 HU Da-wei, CHEN Cheng, GUO Xiao-fen. Research on optimal algorithm for multi-depot vehicle routing problem with pickups and deliveries[J]. Mathematics in Practice and Theory, 2007, 37 (2): 98-104. (in Chinese). doi: 10.3969/j.issn.1000-0984.2007.02.017
[37]	胡大伟, 陈诚, 王来军. 带硬时间窗车辆路线问题的混合遗传启发式算法[J]. 交通运输工程学报, 2007, 7 (5): 112-117. doi: 10.3321/j.issn:1671-1637.2007.05.024 HU Da-wei, CHEN Cheng, WANG Lai-jun. Hybrid-geneticheuristic algorithm of vehicle routing problem with hard timewindows[J]. Journal of Traffic and Transportation Engineering, 2007, 7 (5): 112-117. (in Chinese). doi: 10.3321/j.issn:1671-1637.2007.05.024
[38]	KARAOGLAN I, ALTIPARMAK F, KARA I, et al. A branch and cut algorithm for the location-routing problem with simultaneous pickup and delivery[J]. European Journal of Operational Research, 2011, 211 (2): 318-332. doi: 10.1016/j.ejor.2011.01.003
[39]	KARAOGLAN I, ALTIPARMAK F, KARA I, et al. The location-routing problem with simultaneous pickup and delivery: formulations and a heuristic approach[J]. Omega, 2012, 40 (4): 465-477. doi: 10.1016/j.omega.2011.09.002
[40]	YU V F, LIN S W. Multi-start simulated annealing heuristic for the location routing problem with simultaneous pickup and delivery[J]. Applied Soft Computing, 2014, 24: 284-290. doi: 10.1016/j.asoc.2014.06.024
[41]	YU V F, LIN S Y. Solving the location-routing problem with simultaneous pickup and delivery by simulated annealing[J]. International Journal of Production Research, 2016, 54 (2): 526-549. doi: 10.1080/00207543.2015.1085655
[42]	ZHOU L, WANG X, NI L, et al. Location-routing problem with simultaneous home delivery and customer's pickup for city distribution of online shopping purchases[J]. Sustainability, 2016, 8 (8): 1-20.
[43]	KARTAL Z, HASGUL S, ERNST A T. Single allocation p-hub median location and routing problem with simultaneous pick-up and delivery[J]. Transportation Research Part E: Logistics and Transportation Review, 2017, 108: 141-159. doi: 10.1016/j.tre.2017.10.004
[44]	孙青伟, 张杨. 带同时取送货的选址-多车型路径问题研究[J]. 交通运输工程与信息学报, 2017, 15 (2): 100-104, 118. doi: 10.3969/j.issn.1672-4747.2017.02.015 SUN Qing-wei, ZHANG Yang. Study on location-routing problem with simultaneous pickup and delivery[J]. Journal of Transportation Engineering and Information, 2017, 15 (2): 100-104, 118. (in Chinese). doi: 10.3969/j.issn.1672-4747.2017.02.015
[45]	CAMARGO R S D, MIRANDA G D, LOKKETANGEN A. A new formulation and an exact approach for the many-tomany hub location-routing problem[J]. Applied Mathematical Modelling, 2013, 37 (12/13): 7465-7480.
[46]	RIECK J, EHRENBERG C, ZIMMERMANN J. Many-tomany location-routing with inter-hub transport and multicommodity pickup-and-delivery[J]. European Journal of Operational Research, 2014, 236 (3): 863-878. doi: 10.1016/j.ejor.2013.12.021
[47]	KARAOGLAN I, ALTIPARMAK F. A memetic algorithm for the capacitated location-routing problem with mixed backhauls[J]. Computers and Operations Research, 2015, 55: 200-216. doi: 10.1016/j.cor.2014.06.009
[48]	LEE Y H, JUNG J W, LEE K M. Vehicle routing scheduling for cross-docking in the supply chain[J]. Computers and Industrial Engineering, 2006, 51 (2): 247-256. doi: 10.1016/j.cie.2006.02.006
[49]	MOUSAVI S M, TAVAKKOLI-MOGHADDAM R. A hybrid simulated annealing algorithm for location and routing scheduling problems with cross-docking in the supply chain[J]. Journal of Manufacturing Systems, 2013, 32 (2): 335-347. doi: 10.1016/j.jmsy.2012.12.002
[50]	MOUSAVI S M, VAHDANI B, TAVAKKOLI-MOGHADDAM R, et al. Location of cross-docking centers and vehicle routing scheduling under uncertainty: a fuzzy possibilisticstochastic programming model[J]. Applied Mathematical Modelling, 2014, 38 (7/8): 2249-2264.
[51]	MOKHTARINEJAD M, AHMADI A, KARIMI B, et al. A novel learning based approach for a new integrated locationrouting and scheduling problem within cross-docking considering direct shipment[J]. Applied Soft Computing, 2015, 34 (C): 274-285.
[52]	MACEDO R, ALVES C, HANAFI S, et al. Skewed general variable neighborhood search for the location routing scheduling problem[J]. Computers and Operations Research, 2015, 61 (C): 143-152.
[53]	GOODARZI A H, ZEGORDI S H. A location-routing problem for cross-docking networks: a biogeography-based optimization algorithm[J]. Computers and Industrial Engineering, 2016, 102: 132-146. doi: 10.1016/j.cie.2016.10.023
[54]	LI J, CHU F, PRINS C. Lower and upper bounds for a capacitated plant location problem with multicommodity flow[J]. Computers and Operations Research, 2009, 36 (11): 3019-3030. doi: 10.1016/j.cor.2009.01.012
[55]	GENDRON B, SEMET F. Formulations and relaxations for a multi-echelon capacitated location-distribution problem[J]. Computers and Operations Research, 2009, 36 (5): 1335-1355. doi: 10.1016/j.cor.2008.02.009
[56]	LIN J R, LEI H C. Distribution systems design with twolevel routing considerations[J]. Annals of Operations Research, 2009, 172 (1): 329-347. doi: 10.1007/s10479-009-0628-y
[57]	BOCCIA M, CRAINIC T G, SFORZA A, et al. A metaheuristic for a two echelon location-routing problem[C]//FESTA P. International Symposium on Experimental Algorithms. Berlin: Springer, 2010: 288-301.
[58]	BOCCIA M, CRAINIC T G, SFORZA A, et al. Locationrouting models for designing a two-echelon freight distribution system[R]. Montréal: University of Montréal, 2011.
[59]	NGUYEN V P, PRINS C, PRODHON C. Solving the twoechelon location routing problem by a GRASP reinforced by a learning process and path relinking[J]. European Journal of Operational Research, 2012, 216 (1): 113-126. doi: 10.1016/j.ejor.2011.07.030
[60]	NGUYEN V P, PRINS C, PRODHON C. A multi-start iterated local search with tabu list and path relinking for the two-echelon location-routing problem[J]. Engineering Applications of Artificial Intelligence, 2012, 25 (1): 56-71. doi: 10.1016/j.engappai.2011.09.012
[61]	CONTARDO C, HEMMELMAYR V, CRAINIC T G. Lower and upper bounds for the two-echelon capacitated location-routing problem[J]. Computers and Operations Research, 2012, 39 (12): 3185-3199. doi: 10.1016/j.cor.2012.04.003
[62]	DALFARD V M, KAVEH M, NOSRATIAN N E. Two meta-heuristic algorithms for two-echelon location-routing problem with vehicle fleet capacity and maximum route length constraints[J]. Neural Computing and Applications, 2013, 23 (7/8): 2341-2349.
[63]	GOVINDAN K, JAFARIAN A, KHODAVERDI R, et al. Two-echelon multiple-vehicle location-routing problem with time windows for optimization of sustainable supply chain network of perishable food[J]. International Journal of Production Economics, 2014, 152 (2): 9-28.
[64]	VIDOVI'C M, RATKOVI'C B, BJELI'CN, et al. A two-echelon location-routing model for designing recycling logistics networks with profit: MILP and heuristic approach[J]. Expert Systems with Applications, 2016, 51 (C): 34-48.
[65]	RAHMANI Y, CHERIF-KHETTAF W R, OULAMARA A. The two-echelon multi-products location-routing problem with pickup and delivery: formulation and heuristic approaches[J]. International Journal of Production Research, 2016, 54 (4): 1-21.
[66]	WU X, NIE L, XU M. Designing an integrated distribution system for catering services for high-speed railways: a threeechelon location routing model with tight time windows and time deadlines[J]. Transportation Research Part C: Emerging Technologies, 2017, 74: 212-244. doi: 10.1016/j.trc.2016.11.006
[67]	金莉, 朱云龙, 申海. 三级物流网络选址-路径问题建模与求解算法研究[J]. 控制与决策, 2010, 25 (8): 1195-1200, 1206. https://www.cnki.com.cn/Article/CJFDTOTAL-KZYC201008016.htm JIN Li, ZHU Yun-long, SHEN Hai. Research on modeling and algorithm for three-layer distribution network locationrouting problem[J]. Control and Decision, 2010, 25 (8): 1195-1200, 1206. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-KZYC201008016.htm
[68]	王绍仁, 马祖军. 震害紧急响应阶段应急物流系统中的LRP[J]. 系统工程理论与实践, 2011, 31 (8): 1497-1507. https://www.cnki.com.cn/Article/CJFDTOTAL-XTLL201108012.htm WANG Shao-ren, MA Zu-jun. Location-routing problem in emergency logistics system for post-earthquake emergency relief response[J]. Systems Engineering—Theory and Practice, 2011, 31 (8): 1497-1507. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-XTLL201108012.htm
[69]	李守英, 运士伟. 物流系统中基于改进遗传算法的定位-路径问题研究[J]. 物流技术, 2013, 32 (7): 253-256, 280. doi: 10.3969/j.issn.1005-152X.2013.07.082 LI Shou-ying, YUN Shi-wei. Study on location-routing problem of logistics systems using improved GA[J]. Logistics Technology, 2013, 32 (7): 253-256, 280. (in Chinese). doi: 10.3969/j.issn.1005-152X.2013.07.082
[70]	陈久梅, 龚英. 求解两级定位-路径问题的粒子群算法[J]. 计算机应用, 2013, 33 (8): 2261-2264, 2268. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJY201308044.htm CHEN Jiu-mei, GONG Ying. Particle swarm optimization for two-echelon location-routing problem[J]. Journal of Computer Applications, 2013, 33 (8): 2261-2264, 2268. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JSJY201308044.htm
[71]	陈久梅. 两级定位-路径问题的人工蜂群算法[J]. 计算机工程, 2014, 40 (1): 172-176. doi: 10.3969/j.issn.1000-3428.2014.01.036 CHEN Jiu-mei. Artificial bee colony algorithm for twoechelon location-routing problem[J]. Computer Engineering, 2014, 40 (1): 172-176. (in Chinese). doi: 10.3969/j.issn.1000-3428.2014.01.036
[72]	陈久梅, 龚英. 两级定位-路径问题的变邻域人工蜂群算法[J]. 计算机工程与应用, 2014, 50 (6): 25-30, 34. doi: 10.3778/j.issn.1002-8331.1309-0335 CHEN Jiu-mei, GONG Ying. Artificial bee colony algorithm with variable neighborhood search for two-echelon locationrouting problem[J]. Computer Engineering and Applications, 2014, 50 (6): 25-30, 34. (in Chinese). doi: 10.3778/j.issn.1002-8331.1309-0335
[73]	陈久梅, 曾波. 两级定位-路径问题的路径重连变邻域搜索人工蜂群算法[J]. 计算机集成制造系统, 2014, 20 (5): 1228-1236. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJJ201405027.htm CHEN Jiu-mei, ZENG Bo. Artificial bee colony algorithm with variable neighborhood search and path relinking for twoechelon location routing problem[J]. Computer Integrated Manufacturing Systems, 2014, 20 (5): 1228-1236. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JSJJ201405027.htm
[74]	陈久梅, 邱晗光. 两级定位-路径问题模型及变邻域粒子群算法[J]. 运筹与管理, 2014, 23 (3): 38-44. doi: 10.3969/j.issn.1007-3221.2014.03.006 CHEN Jiu-mei, QIU Han-guang. A mathematical model and particle swarm optimization with variable neighborhood search for two location-routing problem[J]. Operations Research and Management Science, 2014, 23 (3): 38-44. (in Chinese). doi: 10.3969/j.issn.1007-3221.2014.03.006
[75]	LEVY L, BODIN L. The arc oriented location routing problem[J]. INFOR: Information Systems and Operational Research, 1989, 27 (1): 74-94. doi: 10.1080/03155986.1989.11732083
[76]	AMAYA A, LANGEVIN A, TR'EPANIER M. The capacitated arc routing problem with refill points[J]. Operations Research Letters, 2007, 35 (1): 45-53. doi: 10.1016/j.orl.2005.12.009
[77]	PIA A D, FILIPI C. A variable neighborhood descent algorithm for a real waste collection problem with mobile depots[J]. International Transactions in Operational Research, 2006, 13 (2): 125-141. doi: 10.1111/j.1475-3995.2006.00539.x
[78]	DOULABI S H H, SEIFI A. Lower and upper bounds for location-arc routing problems with vehicle capacity constraints[J]. European Journal of Operational Research, 2013, 224 (1): 189-208. doi: 10.1016/j.ejor.2012.06.015
[79]	ARBIB C, SERVILIO M, ARCHETTI C, et al. The directed profitable location rural postman problem[J]. European Journal of Operational Research, 2014, 236 (3): 811-819. doi: 10.1016/j.ejor.2013.07.018
[80]	LOPES R B, PLASTRIA F, FERREIRA C, et al. Location-arc routing problem: heuristic approaches and test instances[J]. Computers and Operations Research, 2014, 43 (3): 309-317.
[81]	RIQUELME-RODR'IGUEZ J P, GAMACHE M, LANGEVIN A. Location arc routing problem with inventory constraints[J]. Computers and Operations Research, 2016, 76: 84-94. doi: 10.1016/j.cor.2016.06.012
[82]	彭锦环, 马慧民. 带容量约束的弧路径问题: 文献综述[J]. 物流科技, 2015, 38 (1): 63-66. doi: 10.3969/j.issn.1002-3100.2015.01.019 PENG Jin-huan, MA Hui-min. Review of literature about capacitated arc routing problem[J]. Logistics Sci-Tech, 2015, 38 (1): 63-66. (in Chinese). doi: 10.3969/j.issn.1002-3100.2015.01.019
[83]	CHAO I M. A tabu search method for the truck and trailer routing problem[J]. Computers and Operations Research, 2002, 29 (1): 33-51. doi: 10.1016/S0305-0548(00)00056-3
[84]	SCHEUERER S. A tabu search heuristic for the truck and trailer routing problem[J]. Computers and Operations Research, 2006, 33 (4): 894-909. doi: 10.1016/j.cor.2004.08.002
[85]	CARAMIA M, GUERRIERO F. A heuristic approach for the truck and trailer routing problem[J]. Journal of the Operational Research Society, 2010, 61 (7): 1168-1180. doi: 10.1057/jors.2009.59
[86]	LIN S W, YU V F, CHOU S Y. Solving the truck and trailer routing problem based on a simulated annealing heuristic[J]. Computers and Operations Research, 2009, 36 (5): 1683-1692. doi: 10.1016/j.cor.2008.04.005
[87]	VILLEGAS J G, PRINS C, PRODHON C, et al. A GRASP with evolutionary path relinking for the truck and trailer routing problem[J]. Computers and Operations Research, 2011, 38 (9): 1319-1334. doi: 10.1016/j.cor.2010.11.011
[88]	VILLEGAS J G, PRINS C, PRODHON C, et al. A matheuristic for the truck and trailer routing problem[J]. European Journal of Operational Research, 2013, 230 (2): 231-244. doi: 10.1016/j.ejor.2013.04.026
[89]	TAN K C, CHEW Y H, LEE L H. A hybrid multi-objective evolutionary algorithm for solving truck and trailer vehicle routing problems[J]. European Journal of Operational Research, 2006, 172 (3): 855-885. doi: 10.1016/j.ejor.2004.11.019
[90]	DREXL M. Branch-and-price and heuristic column generation for the generalized truck-and-trailer routing problem[J]. Revista De Métodos Cuantitativos Para La Economía Y La Empresa, 2011, 12 (1): 5-38.
[91]	LIN S W, YU V F, LU C C. A simulated annealing heuristic for the truck and trailer routing problem with time windows[J]. Expert Systems with Applications, 2011, 38 (12): 15244-15252. doi: 10.1016/j.eswa.2011.05.075
[92]	DERIGS U, PULLMANN M, VOGEL U. Truck and trailer routing—problems, heuristics and computational experience[J]. Computers and Operations Research, 2013, 40 (2): 536-546. doi: 10.1016/j.cor.2012.08.007
[93]	BATSYN M, PONOMARENKO A. Heuristic for a real-life truck and trailer routing problem[J]. Procedia Computer Science, 2014, 31: 778-792. doi: 10.1016/j.procs.2014.05.328
[94]	温旖旎. 甩挂运输的运作模式设计及其车辆调度问题研究[D]. 广州: 华南理工大学, 2012. WEN Yi-ni. Operation mode design and vehicle routing problem research for"truck-trailer"[D]. Guangzhou: South China University of Technology, 2012. (in Chinese).
[95]	ZARANDI M H F, HEMMATI A, DAVARI S, et al. Capacitated location-routing problem with time windows under uncertainty[J]. Knowledge-Based Systems, 2013, 37 (2): 480-489.
[96]	GHAFFARI-NASAB N, AHARI S G, GHAZANFARI M. A hybrid simulated annealing based heuristic for solving the location-routing problem with fuzzy demands[J]. Scientia Iranica, 2013, 20 (3): 919-930.
[97]	MEHRJERDI Y Z, NADIZADEH A. Using greedy clustering method to solve capacitated location-routing problem with fuzzy demands[J]. European Journal of Operational Research, 2013, 229 (1): 75-84. doi: 10.1016/j.ejor.2013.02.013
[98]	NADIZADEH A, NASAB H H. Solving the dynamic capacitated location-routing problem with fuzzy demands by hybrid heuristic algorithm[J]. European Journal of Operational Research, 2014, 238 (2): 458-470. doi: 10.1016/j.ejor.2014.04.012
[99]	ZARANDI M H F, HEMMATI A, DAVARI S. The multidepot capacitated location-routing problem with fuzzy travel times[J]. Expert Systems with Applications, 2011, 38 (8): 10075-10084. doi: 10.1016/j.eswa.2011.02.006
[100]	GOLOZARI F, JAFARI A, AMIRI M. Application of a hybrid simulated annealing-mutation operator to solve fuzzy capacitated location-routing problem[J]. International Journal of Advanced Manufacturing Technology, 2013, 67 (5-8): 1791-1807. doi: 10.1007/s00170-012-4609-y
[101]	王迎春. 配送中心动态选址-路线安排问题研究[D]. 哈尔滨: 哈尔滨工业大学, 2007. WANG Ying-chun. Research on dynamic location-routing problem of distribution center[D]. Harbin: Harbin Institute of Technology, 2007. (in Chinese).
[102]	王海军, 杜丽敬, 胡蝶, 等. 不确定条件下的应急物资配送选址-路径问题[J]. 系统管理学报, 2015, 24 (6): 828-834. https://www.cnki.com.cn/Article/CJFDTOTAL-XTGL201506006.htm WANG Hai-jun, DU Li-jing, HU Die, et al. Locationrouting problem for relief distribution in emergency logistics under uncertainties[J]. Journal of Systems and Management, 2015, 24 (6): 828-834. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-XTGL201506006.htm
[103]	张晓楠, 范厚明, 李剑锋. 变动补偿的多模糊选址-路径机会约束模型及算法[J]. 系统工程理论与实践, 2016, 36 (2): 442-453. https://www.cnki.com.cn/Article/CJFDTOTAL-XTLL201602016.htm ZHANG Xiao-nan, FAN Hou-ming, LI Jian-feng. Chanceconstrained model and algorithm for LRP with multiple fuzzy variable under change-reward[J]. Systems Engineering—Theory and Practice, 2016, 36 (2): 442-453. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-XTLL201602016.htm
[104]	PRODHON C. A metaheuristic for the periodic locationrouting problem[C]//Springer. Proceedings of the Annual International Conference of the German Operations Research Society (GOR). Berlin: Springer, 2008: 159-164.
[105]	PRODHON C, PRINS C. A memetic algorithm with population management (MA\|PM) for the periodic location-routing problem[C]//BLESA M, BLUM C, COTTA C, et al. Hybrid Metaheuristics. Berlin: Springer, 2008: 43-57.
[106]	PRODHON C. A hybrid evolutionary algorithm for the periodic location-routing problem[J]. European Journal of Operational Research, 2011, 210 (2): 204-212. doi: 10.1016/j.ejor.2010.09.021
[107]	ALBAREDA-SAMBOLA M, FERNANDEZ E, NICKEL S. Multiperiod location-routing with decoupled time scales[J]. European Journal of Operational Research, 2012, 217 (2): 248-258. doi: 10.1016/j.ejor.2011.09.022
[108]	HEMMELMAYR V C. Sequential and parallel large neighborhood search algorithms for the periodic location routing problem[J]. European Journal of Operational Research, 2015, 243 (1): 52-60. doi: 10.1016/j.ejor.2014.11.024
[109]	胡大伟. 设施定位和车辆路线问题模型及其启发式算法研究[D]. 西安: 长安大学, 2008. HU Da-wei. Study of model and heuristic algorithms for location routing problems[D]. Xi'an: Chang'an University, 2008. (in Chinese).
[110]	JAVID A A, AZAD N. Incorporating location, routing and inventory decisions in supply chain network design[J]. Transportation Research Part E: Logistics and Transportation Review, 2010, 46 (5): 582-597. doi: 10.1016/j.tre.2009.06.005
[111]	SAJJADI S R, CHERAGHI S H. Multi-products location routing problem integrated with inventory under stochastic demand[J]. International Journal of Industrial and Systems Engineering, 2011, 7 (4): 454-476. doi: 10.1504/IJISE.2011.039670
[112]	唐艳, 马祖军, 赵娟娟. 基于CMI的废旧轮胎回收系统多周期LRIP[J]. 计算机集成制造系统, 2011, 17 (2): 397-403. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJJ201102026.htm TANG Yan, MA Zu-jun, ZHAO Juan-juan. Multi-period location-routing-inventory problem based on collector managed inventory in scrap tires recycling systems[J]. Computer Integrated Manufacturing Systems, 2011, 17 (2): 397-403. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JSJJ201102026.htm
[113]	GUERRERO W J, PRODHON C, VELASCO N, et al. Hybrid heuristic for the inventory location-routing problem with deterministic demand[J]. International Journal of Production Economics, 2013, 146 (1): 359-370. doi: 10.1016/j.ijpe.2013.07.025
[114]	NEKOOGHADIRLI N, MOGHADDAM R T, GHEZAVATI V R, et al. Solving a new bi-objective location-routing-inventory problem in a distribution network by meta-heuristics[J]. Computers and Industrial Engineering, 2014, 76 (C): 204-221.
[115]	崔飞涛. 动态环境下的选址-库存-路径问题集成优化模型与算法研究[D]. 武汉: 华中师范大学, 2012. CUI Fei-tao. Research on integrated optimization model and algorithm for location-inventory-routing problem taking dynamic environment into consideration[D]. Wuhan: Central China Normal University, 2012. (in Chinese).
[116]	杜丽敬, 李延晖. 选址-库存-路径问题模型及其集成优化算法[J]. 运筹与管理, 2014, 23 (4): 70-79. doi: 10.3969/j.issn.1007-3221.2014.04.010 DU Li-jing, LI Yan-hui. Integrated models and approach for location inventory and routing problem[J]. Operations Research and Management Science, 2014, 23 (4): 70-79. (in Chinese). doi: 10.3969/j.issn.1007-3221.2014.04.010
[117]	GHORBANI A, JOKAR M R A. A hybrid imperialist competitivesimulated annealing algorithm for a multisource multi-product location-routing-inventory problem[J]. Computers and Industrial Engineering, 2016, 101: 116-127. doi: 10.1016/j.cie.2016.08.027
[118]	TAVAKKOLI-MOGHADDAM R, RAZIEI Z. A new bi-objective location-routing-inventory problem with fuzzy demands[J]. IFAC-papers Online, 2016, 49 (12): 1116-1121. doi: 10.1016/j.ifacol.2016.07.646
[119]	崔广彬, 李一军. 基于双层规划的物流系统集成定位-运输路线安排-库存问题研究[J]. 系统工程理论与实践, 2007, 27 (6): 49-55. doi: 10.3321/j.issn:1000-6788.2007.06.008 CUI Guang-bin, LI Yi-jun. Study on the combined location routing and inventory problem in logistics system based on bilevel programming[J]. Systems Engineering—Theory and Practice, 2007, 27 (6): 49-55. (in Chinese). doi: 10.3321/j.issn:1000-6788.2007.06.008
[120]	王超峰, 帅斌. 带有横向调度的维修备件选址库存路径问题研究[J]. 计算机工程与应用, 2013, 49 (14): 10-14. doi: 10.3778/j.issn.1002-8331.1211-0152 WANG Chao-feng, SHUAI Bin. Location-inventory-routing problem of maintenance spare parts logistics system with lateral transshipment[J]. Computer Engineering and Applications, 2013, 49 (14): 10-14. (in Chinese). doi: 10.3778/j.issn.1002-8331.1211-0152
[121]	郭昊. 考虑退货的选址-库存-路径问题集成优化模型与算法研究[D]. 武汉: 华中师范大学, 2013. GUO Hao. Research on integrated optimization model and algorithm for location-inventory-routing problem taking returns into consideration[D]. Wuhan: Central China Normal University, 2013. (in Chinese).
[122]	HIASSAT A, DIABAT A, RAHWAN I. A genetic algorithm approach for location-inventory-routing problem with perishable products[J]. Journal of Manufacturing Systems, 2017, 42: 93-103. doi: 10.1016/j.jmsy.2016.10.004
[123]	SCHWARDT M, DETHLOFF J. Solving a continuous location-routing problem by use of a self-organizing map[J]. International Journal of Physical Distribution and Logistics Management, 2005, 35 (6): 390-408. doi: 10.1108/09600030510611639
[124]	SALHI S, NAGY G. Local improvement in planar facility location using vehicle routing[J]. Annals of Operations Research, 2009, 167 (1): 287-296. doi: 10.1007/s10479-007-0223-z
[125]	MANZOUR-AL-AJDAD S M H, TORABI S A, SALHI S. A hierarchical algorithm for the planar single-facility location routing problem[J]. Computers and Operations Research, 2012, 39 (2): 461-470. doi: 10.1016/j.cor.2011.05.013
[126]	AKCA Z, BERGER R T, RALPHS T K. A branch-and-price algorithm for combined location and routing problems under capacity restrictions[C]//CHINNECK J W, CRISTJANSSON B, SALTSMAN M J. Operations Research and CyberInfrastructure. Berlin: Springer, 2009: 309-330.
[127]	RODR'IGUEZ-MART'IN I, SALAZAR-GONZ'ALEZ J J, YAMAN H. A branch-and-cut algorithm for the hub location and routing problem[J]. Computers and Operations Research, 2014, 50 (10): 161-174.
[128]	BELENGUER J M, BENAVENT E, PRINS C, et al. A branch-and-cut method for the capacitated location-routing problem[J]. Computers and Operations Research, 2011, 38 (6): 931-941. doi: 10.1016/j.cor.2010.09.019
[129]	BALDACCI R, MINGOZZI A, CALVO R W. An exact method for the capacitated location-routing problem[J]. Operations Research, 2011, 59 (5): 1284-1296. doi: 10.1287/opre.1110.0989
[130]	CONTARDO C, CORDEAU J F, GENDRON B. A branchand-cut-and-price algorithm for the capacitated locationrouting problem[J]. INFORMS Journal on Computing, 2013, 26 (1): 88-102.
[131]	CESELLI A, RIGHINI G, TRESOLDI E. Combined location and routing problems for drug distribution[J]. Discrete Applied Mathematics, 2014, 165 (2): 130-145.
[132]	PONBOON S, QURESHI A G, TANIGUCHI E. Branchand-price algorithm for the location-routing problem with time windows[J]. Transportation Research Part E: Logistics and Transportation Review, 2016, 86: 1-19. doi: 10.1016/j.tre.2015.12.003
[133]	LOPES R B, FERREIRA C, SANTOS B S. A simple and effective evolutionary algorithm for the capacitated locationrouting problem[J]. Computers and Operations Research, 2016, 70 (C): 155-162.
[134]	YU V F, LIN S W, LEE W, et al. A simulated annealing heuristic for the capacitated location routing problem[J]. Computers and Industrial Engineering, 2010, 58 (2): 288-299. doi: 10.1016/j.cie.2009.10.007
[135]	JOKAR A, SAHRAEIAN R. A heuristic based approach to solve a capacitated location-routing problem[J]. Journal of Management and Sustainability, 2012, 2 (2): 219-226.
[136]	YU V F, LIN S W. Multi-start simulated annealing heuristic for the location routing problem with simultaneous pickup and delivery[J]. Applied Soft Computing, 2014, 24: 284-290. doi: 10.1016/j.asoc.2014.06.024
[137]	PRINS C, PRODHON C, RUIZ A, et al. Solving the capacitated location-routing problem by a cooperative Lagrangean relaxation-granular tabu search heuristic[J]. Transportation Science, 2007, 41 (4): 470-483. doi: 10.1287/trsc.1060.0187
[138]	TING C J, CHEN C H. A multiple ant colony optimization algorithm for the capacitated location routing problem[J]. International Journal of Production Economics, 2013, 141 (1): 34-44. doi: 10.1016/j.ijpe.2012.06.011
[139]	ESCOBAR J W, LINFATI R, TOTH P. A two-phase hybrid heuristic algorithm for the capacitated location-routing problem[J]. Computers and Operations Research, 2013, 40 (1): 70-79. doi: 10.1016/j.cor.2012.05.008
[140]	SHAW P. Using constraint programming and local search methods to solve vehicle routing problems[C]//Springer. International Conference on Principles and Practice of Constraint Programming. Berlin: Springer, 1998: 417-431.
[141]	ROPKE S, PISINGER D. An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows[J]. Transportation Science, 2006, 40 (4): 455-472. doi: 10.1287/trsc.1050.0135
[142]	PRINS C, PRODHON C, CALVO R W. Solving the capacitated location-routing problem by a GRASP complemented by a learning process and a path relinking[J]. European Journal of Operational Research, 2012, 216 (1): 113-126. doi: 10.1016/j.ejor.2011.07.030
[143]	PIRKWIESER S, RAIDL G R. Variable neighborhood search coupled with ILP-based very large neighborhood searches for the (periodic) location-routing problem[C]//Springer. International Workshop on Hybrid Metaheuristics. Berlin: Springer, 2010: 174-189.
[144]	JABAL-AMELI M S, ARYANEZHAD M B, GHAFFARINASAB N. A variable neighborhood descent based heuristic to solve the capacitated location-routing problem[J]. International Journal of Industrial Engineering Computations, 2011, 2 (1): 141-154. doi: 10.5267/j.ijiec.2010.06.003
[145]	SCHWENGERER M, PIRKWIESER S, RAIDL G R. A variable neighborhood search approach for the two-echelon locationrouting problem[C]//Springer. European Conference on Evolutionary Computation in Combinatorial Optimization. Berlin: Springer, 2012: 13-24.
[146]	JARBOUI B, DERBEL H, HANAFI S, et al. Variable neighborhood search for location routing[J]. Computers and Operations Research, 2013, 40 (1): 47-57. doi: 10.1016/j.cor.2012.05.009
[147]	HEMMELMAYR V C, CORDEAU J F, CRAINIC T G. An adaptive large neighborhood search heuristic for two-echelon vehicle routing problems arising in city logistics[J]. Computers and Operations Research, 2012, 39 (12): 3215-3228. doi: 10.1016/j.cor.2012.04.007
[148]	NGUYEN V P, PRINS C, PRODHON C. Solving the twoechelon location routing problem by a GRASP reinforced by a learning process and path relinking[J]. European Journal of Operational Research, 2012, 216 (1): 113-126. doi: 10.1016/j.ejor.2011.07.030
[149]	DUHAMEL C, LACOMME P, PRINS C, et al. A GRASP×ELS approach for the capacitated location-routing problem[J]. Computers and Operations Research, 2010, 37 (11): 1912-1923. doi: 10.1016/j.cor.2009.07.004
[150]	CONTARDO C, CORDEAU J F, GENDRON B. A GRASP+ILP-based metaheuristic for the capacitated location-routing problem[J]. Journal of Heuristics, 2014, 20 (1): 1-38. doi: 10.1007/s10732-013-9230-1
[151]	VILLEGAS J G, PRINS C, PRODHON C, et al. A GRASP with evolutionary path relinking for the truck and trailer routing problem[J]. Computers and Operations Research, 2011, 38 (9): 1319-1334. doi: 10.1016/j.cor.2010.11.011
[152]	SÖRENSEN K, SEVAUX M. MA\|PM: memetic algorithms with population management[J]. Computers and Operations Research, 2006, 33 (5): 1214-1225. doi: 10.1016/j.cor.2004.09.011
[153]	PRINS C, PRODHON C, CALVO R W. A memetic algorithm with population management (MA\|PM) for the capacitated location-routing problem[C]//Springer. European Conference on Evolutionary Computation in Combinatorial Optimization. Berlin: Springer, 2006: 183-194.
[154]	DERBEL H, JARBOUI B, HANAFI S, et al. An iterated local search for solving a location-routing problem[J]. Electronic Notes in Discrete Mathematics, 2010, 36 (3): 875-882.
[155]	DERBEL H, JARBOUI B, HANAFI S, et al. Genetic algorithm with iterated local search for solving a location-routing problem[J]. Expert Systems with Applications, 2012, 39 (3): 2865-2871. doi: 10.1016/j.eswa.2011.08.146
[156]	PERL J. A unified warehouse location-routing analysis[D]. Illinois: Northwestern University, 1983.
[157]	BARRETO S D S. Análise e modelizaca"o de problemas de localizaca"o-distribuica"o[D]. Aveiro: Universidade de Aveiro, 2004.
[158]	PRINS C, PRODHON C, CALVO R W. Nouveaux algorithmes pour le problème de localisation et routage sous contraintes de capacité[J]. Psicologia Educativa, 2004, 8 (5): 5-20.
[159]	TUZUN D, BURKE L I. A two-phase tabu search approach to the location routing problem[J]. European Journal of Operational Research, 1999, 116 (1): 87-99. doi: 10.1016/S0377-2217(98)00107-6
[160]	ALBAREDA-SAMBOLA M, D'LAZ J A, FERN'ANDEZ E. A compact model and tight bounds for a combined locationrouting problem[J]. Computers and Operations Research, 2005, 32 (3): 407-428. doi: 10.1016/S0305-0548(03)00245-4
[161]	PRODHON C. Le problème de localisation-routage[D]. Troyes: Troyes University of Technology, 2006.