Service capacity guarantee under the disruption risk of supply chain is a key challenge for the coordinated development of Beijing-Tianjin-Hebei region. Aiming at the characteristics of both random and fuzzy uncertainty of transportation time, this paper proposes an equilibrium optimization model of single allocation hub location based on ambiguous probability distribution. Firstly, by introducing the equilibrium value-at-risk constraint, the uncertainty of transportation time is quantified in the joint form of credibility distribution and probability distribution to ensure that the path transportation time meets the service level requirement. Secondly, the equilibrium optimization model is constructed to minimize the total average transportation time. It is equivalently converted to mixed integer linear programming to realize the efficient solution of the model under trapezoidal fuzzy parameters and normal probability distribution. The case study based on 15 nodes in Beijing-Tianjin-Hebei region shows that compared with the traditional stochastic optimization method, the proposed method can optimize the hub location scheme under dual uncertainty, and the sensitivity of the optimal hub location to the change of confidence level and transportation time limit is significantly improved.The research results provide effective decision support for- DOI:10.3969/j.issn.1000-1565.2025.03.001京津冀供应链中断风险下保障服务能力的枢纽选址策略陈艳菊,殷方浩,刘彦奎(河北大学 数学与信息科学学院,河北 保定 071002)摘 要:供应链中断风险下的服务能力保障是京津冀协同发展的关键挑战.针对运输时间兼具随机与模糊双重不确定性的特征,提出一种基于非精确概率分布的单分配枢纽选址平衡优化模型.首先,通过引入平衡风险值约束,将运输时间的不确定性用可信分布与概率分布的联合形式进行量化,确保路径运输时间满足服务水平要求;其次,以总平均运输时间最小化为目标,构建平衡优化模型,并在梯形模糊参数与正态概率分布下等价转换为混合整数线性规划以实现高效求解.京津冀地区15个节点的案例研究表明:相较于传统随机优化方法,本文方法在双重不确定性下能够有效优化枢纽选址方案,最优枢纽位置对置信水平与运输期限的变化敏感度显著提升.研究结果为复杂不确定环境下区域物流网络优化提供了有效的决策支持.关键词:枢纽选址;平衡优化;双重不确定性;非精确概率分布;京津冀供应链中图分类号:C934 文献标志码:A 文章编号:1000-1565(2025)03-0225-10Hub location strategy for ensuring service capability of supply chain in Beijing-Tianjin-Hebei region under disruption riskCHEN Yanju, YIN Fanghao, LIU Yankui(College of Mathematics and Information Science, Hebei University, Baoding 071002, China)Abstract: Service capacity guarantee under the disruption risk of supply chain is a key challenge for the coordinated development of Beijing-Tianjin-Hebei region. Aiming at the characteristics of both random and fuzzy uncertainty of transportation time, this paper proposes an equilibrium optimization model of single allocation hub location based on ambiguous probability distribution. Firstly, by introducing the equilibrium value-at-risk constraint, the uncertainty of transportation time is quantified in the joint form of credibility distribution and probability distribution to ensure that the path transportation time meets the service level requirement. Secondly, the equilibrium optimization model is constructed to minimize the total average transportation time. It is equivalently converted to mixed integer linear programming to realize the efficient solution of the model under trapezoidal fuzzy parameters and normal probability distribution. The case study based on 15 nodes in Beijing-Tianjin-Hebei region shows that compared with the traditional stochastic optimization method, the proposed method can optimize the hub location scheme under dual uncertainty, and the sensitivity of the optimal hub location to the change of confidence level and transportation time limit is significantly improved.The research results provide effective decision support for- 收稿日期:2024-05-04;修回日期:2024-12-27 基金项目:河北省社科基金资助项目(HB21YJ029) 第一作者:陈艳菊(1978—),女,河北大学副教授,主要从事随机优化、平衡优化及其应用方向研究.E-mail:yanjuchen@hbu.edu.cn 通信作者:刘彦奎(1963—),男,河北大学教授,博士生导师,主要从事不确定性最优化理论方向研究.E-mail:yliu@hbu.edu.cn 第3期陈艳菊等:京津冀供应链中断风险下保障服务能力的枢纽选址策略河北大学学报(自然科学版) 第45卷regional logistics network optimization in complex and uncertain environment.
CHEN Yanju
,
YIN Fanghao
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LIU Yankui
. Hub location strategy for ensuring service capability of supply chain in Beijing-Tianjin-Hebei region under disruption risk[J]. Journal of Hebei University(Natural Science Edition), 2025
, 45(3)
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DOI: 10.3969/j.issn.1000-1565.2025.03.001
[1] ALUMUR S A, CAMPBELL J F, CONTRERAS I, et al. Perspectives on modeling hub location problems[J]. Eur J Oper Res, 2021, 291(1): 1-17. DOI: 10.1016/j.ejor.2020.09.039.
[2] O’KELLY M E. The location of interacting hub facilities[J]. Transp Sci, 1986, 20(2): 92-106. DOI: 10.1287/trsc.20.2.92.
[3] O’KELLY M E. A quadratic integer program for the location of interacting hub facilities[J]. Eur J Oper Res, 1987, 32(3): 393-404. DOI: 10.1016/S0377-2217(87)80007-3.
[4] CAMPBELL J F. Hub location and the p-hub Median problem[J]. Oper Res, 1996, 44(6): 923-935. DOI: 10.1287/opre.44.6.923.
[5] CAMPBELL J F. Integer programming formulations of discrete hub location problems[J]. Eur J Oper Res, 1994, 72(2): 387-405. DOI: 10.1016/0377-2217(94)90318-2.
[6] ROSTAMI B, CHITSAZ M, ARSLAN O, et al. Single allocation hub location with heterogeneous economies of scale[J]. Oper Res, 2022, 70(2): 766-785. DOI: 10.1287/opre.2021.2185.
[7] 康凯,毕海玲,张旭涛.弹性视角下战略投送网络枢纽选址策略[J].系统工程, 2018, 36(3): 151-154.
[8] 申皓,张锦,孙文杰,等.基于货物时间价值的空铁联运转运枢纽选址优化[J].交通运输系统工程与信息, 2023, 23(1): 48-57. DOI: 10.16097/j.cnki.1009-6744.2023.01.006.
[9] SNYDER L V. Facility location under uncertainty: a review[J]. IIE Trans, 2006, 38(7): 547-564. DOI: 10.1080/07408170500216480.
[10] AMIN-NASERI M R, YAZDEKHASTI A, SALMASNIA A. Robust bi-objective optimization of uncapacitated single allocation p-hub Median problem using a hybrid heuristic algorithm[J]. Neural Comput Appl, 2018, 29(9): 511-532. DOI: 10.1007/s00521-016-2520-4.
[11] MARIANOV V, SERRA D. Location models for airline hubs behaving as M/D/c queues[J]. Comput Oper Res, 2003, 30(7): 983-1003. DOI: 10.1016/S0305-0548(02)00052-7.
[12] YANG K, LIU Y K, YANG G Q. Optimizing fuzzy p-hub center problem with generalized value-at-risk criterion[J]. Appl Math Model, 2014, 38(15/16): 3987-4005. DOI: 10.1016/j.apm.2014.01.009.
[13] SIM T, LOWE T J, THOMAS B W. The stochastic p-hub center problem with service-level constraints[J]. Comput Oper Res, 2009, 36(12): 3166-3177. DOI: 10.1016/j.cor.2008.11.020.
[14] LIU YK, LIU B D. Random fuzzy programming with chance measures defined by fuzzy integrals[J]. Math Comput Model, 2002, 36(4/5): 509-524. DOI: 10.1016/S0895-7177(02)00180-2.
[15] LIU Y K, LIU B D. Expected value operator of random fuzzy variable and random fuzzy expected value models[J]. Int J Uncertain Fuzziness Knowl Based Syst, 2003, 11(2): 195-215. DOI: 10.1142/S0218488503002016.
[16] 刘彦奎,陈艳菊,杨国庆.平衡优化理论与应用[M].北京:科学出版社, 2018.
[17] MIŠKOVIC' S, STANIMIROVIC' Z. A hybrid metaheuristic method for the deterministic and robust uncapacitated multiple allocation p-hub centre problem[J]. Eur J Ind Eng, 2017, 11(5): 631. DOI: 10.1504/ejie.2017.087705.
[18] RAHMATI R, BASHIRI M, NIKZAD E, et al. A two-stage robust hub location problem with accelerated Benders decomposition algorithm[J]. Int J Prod Res, 2022, 60(17): 5235-5257. DOI: 10.1080/00207543.2021.1953179.
[19] 郑建风,管玉静,曾雄超,等.不确定的班轮运输枢纽港选址问题[J].工业工程与管理, 2023, 28(6): 25-36. DOI: 10.19495/j.cnki.1007-5429.2023.06.003.
[20] LIU B D, LIU Y K. Expected value of fuzzy variable and fuzzy expected value models[J]. IEEE Trans Fuzzy Syst, 2002, 10(4): 445-450. DOI: 10.1109/TFUZZ.2002.800692.
[21] EYDI A, SHIRINBAYAN P. Multi-modal and multi-product hierarchical hub location problem with fuzzy demands[J]. Eng Appl Artif Intell, 2023, 123: 106282. DOI: 10.1016/j.engappai.2023.106282.
[22] DHYANI BHATT S, JAYASWAL S, SINHA A, et al. Alternate second order conic program reformulations for hub location under stochastic demand and congestion[J]. Ann Oper Res, 2021, 304(1): 481-527. DOI: 10.1007/s10479-021-03993-6.
[23] GHAFFARINASAB N, KARA B Y. A conditional β-mean approach to risk-averse stochastic multiple allocation hub location problems[J]. Transp Res Part E Logist Transp Rev, 2022, 158: 102602. DOI: 10.1016/j.tre.2021.102602.
[24] 乐美龙,郑文娟,吴明功,等.不确定需求下航空公司枢纽网络优化设计[J].北京航空航天大学学报, 2020, 46(4): 674-682. DOI: 10.13700/j.bh.1001-5965.2019.0319.
[25] YIN F H, CHEN Y J, SONG F X, et al. A new distributionally robust p-hub Median problem with uncertain carbon emissions and its tractable approximation method[J]. Appl Math Model, 2019, 74: 668-693. DOI: 10.1016/j.apm.2019.04.056.
[26] YIN F H, LIU Y K, CHEN Y J. Distributionally robust optimisation model for multi-objective hub location problem via considering ambiguousness[J]. Transp A Transp Sci, 2023, 19(3): 2094494. DOI: 10.1080/23249935.2022.2094494.
[27] 刘彦奎,刘颖.鲁棒可信性优化的新进展[J].河北大学学报(自然科学版), 2021, 41(5): 457-462. DOI: 10.3969/j.issn.1000-1565.2021.05.002. (
