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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2023, Vol. 57 Issue (11): 2200-2209    DOI: 10.3785/j.issn.1008-973X.2023.11.007
    
Robust closed-loop supply chain network design model considering complexity
Yu-yin WANG1(),Yan-wei ZHANG1,*(),Mei-mei ZHENG2
1. School of Transportation and Logistics Engineering, Wuhan University of Technology, Wuhan 430063, China
2. School of Mechanical and Power Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
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Abstract  

A nonlinear mixed integer programming model was established with the optimization objective of minimizing closed-loop supply chain operation cost and maintenance cost with considering the complexity of network structure, aiming at the closed-loop network design problems under the uncertainty of customer demand and the failure of some facility nodes. The robust counterpart theory and the scenario analysis of robust optimization were used to deal with the demand uncertainty and the interruption uncertainty of a single facility node. The information entropy theory was used to quantify the network structure complexity and a piecewise linearization was used to make linear construction of structural complexity. A robust optimization model under the influence of mixed uncertainties was constructed. The Gurobi solver was used to make node opening or not and traffic allocation decisions. The case study shows that, when considering the network structure complexity, the fluctuation amplitude of the objective function value of robust optimization model under uncertain scenarios is significantly reduced compared with that of the stochastic programming model, and it is proved that the established model has a good ability to resist external risks.

Key words： closed-loop supply chain (CLSC)      supply chain network design      facility node disruption      uncertainty      structure complexity      robust optimization     
Received: 04 December 2022      Published: 11 December 2023
CLC:  F 274  
Fund:  国家自然科学基金资助项目（72271162）
Corresponding Authors: Yan-wei ZHANG     E-mail: wangyuyin7476@163.com;zywtg@whut.edu.cn
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Yu-yin WANG
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Cite this article:

Yu-yin WANG,Yan-wei ZHANG,Mei-mei ZHENG. Robust closed-loop supply chain network design model considering complexity. Journal of ZheJiang University (Engineering Science), 2023, 57(11): 2200-2209.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2023.11.007     OR     https://www.zjujournals.com/eng/Y2023/V57/I11/2200


考虑复杂度的鲁棒闭环供应链网络设计模型

针对顾客需求不确定和部分设施节点失效情况下闭环供应链网络设计问题，考虑网络结构复杂度，以最小化闭环供应链运营成本和维护成本为优化目标，构建非线性混合整数规划模型. 采用鲁棒对等式理论处理需求不确定性，采用情景分析方法处理单一设施节点中断不确定性；采用信息熵理论量化网络结构复杂度并采用分段线性逼近方法进行结构复杂度线性重构，构建混合不确定因素影响下的鲁棒优化模型，利用Gurobi求解进行节点开放及流量分配决策. 针对算例，将鲁棒优化模型与随机规划模型进行对比，结果显示，考虑网络结构复杂度进行网络设计，与随机规划模型相比，鲁棒优化模型的目标函数值在不确定情景下的波动幅度显著减小，表明模型具有较好的抵抗外部风险的能力.


关键词： 闭环供应链(CLSC),  供应链网络设计,  设施节点中断,  不确定性,  结构复杂度,  鲁棒优化 
Fig.1 Closed-loop supply chain network structure
参数 数值
${C_i}$/元 [80000，85000，83000，78000]
${C_j}$/元 [18000，14000，17000，16000，20000，15000]
${C_r}$/元 [27000，26000，28000，23000，29000，35000]
${D_k}$/件 [[190,200]，[310,330]，[270,290]，[250,350]，[250,270]，[300,330]]
$c_k^u$/元 [480，560，550，540，560，500]
${N_i}$/件 [750，800，780，850]
${N_j}$/件 [510，490，505，500，560，520]
${N_r}$/件 [430，425，435，420，440，410]
Nm/件 [330，300]
${\text{A}}{{\text{M}}_r}$ 0.8
${\text{A}}{{\text{R}}_k}$ 0.5
${b_s}$ [0.2，0.1，0.1，0.1，0.1，0.1，0.1，0.1，0.1]
Tab.1 Parameter setting related to alternative facility nodes
节点 ${J_1}$ ${J_2}$ $ {J_3} $ ${J_4}$ ${J_5}$ ${J_6}$
${I_1}$ 33.4 36.9 34.7 39.4 35.0 36.6
${I_2}$ 30.7 38.5 40.8 31.4 40.0 30.0
${I_3}$ 32.0 31.2 36.1 37.6 32.0 35.8
$ {I_4} $ 30.0 31.1 29.8 32.0 28.0 32.4
Tab.2 Unit operating costs parameter setting from manufacturing plant to distribution center 元
节点 ${K_1}$ ${K_2}$ ${K_3}$ ${K_4}$ ${K_5}$ ${K_6}$
${J_1}$ 5.1 3.8 4.0 5.7 4.2 3.8
${J_2}$ 5.4 3.9 4.1 3.2 3.6 4.7
$ {J_3} $ 4.6 4.8 5.2 4.3 4.8 3.7
${J_4}$ 3.3 5.9 6.0 4.2 3.9 3.4
${J_5}$ 6.0 4.5 4.8 5.2 4.7 5.9
${J_6}$ 4.5 4.8 5.2 4.9 4.0 4.6
Tab.3 Unit operating costs parameter setting from distribution center to customer 元
节点 ${R_1}$ ${R_2}$ ${R_3}$ ${R_4}$ ${R_5}$ ${R_6}$
${K_1}$ 12.5 10.9 13.1 14.2 12.9 13.0
${K_2}$ 9.7 14.8 9.0 9.5 11.9 11.5
${K_3}$ 14.5 12.4 13.4 11.2 9.6 10.0
${K_4}$ 10.6 11.2 14.9 10.4 12.2 10.5
${K_5}$ 13.7 9.2 10.8 12.6 11.0 11.2
${K_6}$ 10.7 13.7 10.3 13.6 13.1 9.8
Tab.4 Unit operating costs parameter setting from customer to recycling center 元
节点 ${I_1}$ ${I_2}$ ${I_3}$ $ {I_4} $
${R_1}$ 7.6 8.2 8.5 6.8
${R_2}$ 6.6 7.1 7.4 7.2
${R_3}$ 7.2 6.2 8.4 8.5
${R_4}$ 8.6 7.5 6.6 6.9
${R_5}$ 8.9 8.0 8.7 7.2
${R_6}$ 5.9 7.5 6.6 9.0
Tab.5 Unit operating costs parameter setting from recycling centers to manufacturing plants 元
节点 ${R_1}$ ${R_2}$ ${R_3}$ ${R_4}$ ${R_5}$ ${R_6}$
$ {M}_{1} $ 3.9 4.6 5.4 4.3 5.1 4.7
$ {M}_{2} $ 4.2 4.9 3.5 3.8 4.4 5.2
Tab.6 Unit operating costs parameter setting from recycling centers to other processing points 元
${\varGamma _k} = \varGamma _k^1$ $p_{\rm{ub} }$ $ p_{\rm{lb}} $
0.0 1.1226 0.3634
0.2 1.0974 0.3419
0.4 1.0749 0.3341
0.6 1.0524 0.3258
0.8 1.0311 0.3182
1.0 1.0113 0.3110
Tab.7 Values of regret value limiting coefficient at different uncertainty levels
$p$ $z$/元 $p$ $z$/元
0.3633 491734.8 0.8000 481515.7
0.3700 481541.5 1.1000 478868.0
0.5000 481515.7 1.2000 477892.4
Tab.8 Changes of objective function under different regret value limiting coefficients
Fig.2 Trend of objective function value under different regret value limiting coefficients
不同场景 $z_s^*$/元 $z_0^s$/元 ${z^s}$/元 ${\text{DI}}{{\text{F}}_0}$/% $z_1^s$/元 ${\text{DI}}{{\text{F}}_1}$/%
$ {S}_{0} $ 364794.2 364796.2 473823.3 29.89 391617.2 7.35
$ {S}_{1} $ 374201.9 739112.1 502124.3 34.19 767870.7 105.20
$ {S}_{2} $ 393537.6 764631.7 524913.0 33.38 794655.0 101.93
$ {S}_{3} $ 368170.4 422142.7 474285.6 28.82 425729.2 15.63
$ {S}_{4} $ 365216.0 429216.4 474191.6 29.84 391617.2 7.23
$ {S}_{5} $ 366298.4 427175.3 473823.3 29.35 431002.0 17.66
$ {S}_{6} $ 368152.6 437854.3 475414.3 29.14 440803.0 19.73
$ {S}_{7} $ 365672.5 724292.6 474290.7 29.70 392080.9 7.22
$ {S}_{8} $ 368613.6 720096.6 474257.5 28.66 392053.0 6.36
期望成本 369948.7 539199.1 482094.7 30.33 481904.5 32.04
Tab.9 Comparison of solution performance of different models
层级 节点选址结果
生产中心 [0, 1, 0, 1]
配送中心 [0, 1, 0, 1, 1, 1]
回收中心 [0, 1, 0, 1, 0, 0]
Tab.10 Node routing result
${\varGamma _k} = \varGamma _k^1$ $\theta $ ${\pi ^0}$ $z_0^*\left( {L_{\rm{c}}^0} \right)$/元
0 0 262.9 355721.8
0.4 0 262.9 374064.2
0.8 0 252.3 392371.7
1.0 0 252.7 401719.0
Tab.11 Values of objective function value at different uncertainty levels without disruption
Fig.3 Trend of objective function value of different uncertainty levels under interruption scenario
${\varGamma _k} = \varGamma _k^1$ $\theta $ ${\pi ^0}$ $z_0^*$/元 $L_{\rm{c}}^0$/元
0 0 270.9 355721.8 355721.8
0 1 262.9 355984.7 355721.8
0 10 260.9 358350.8 355741.8
0 100 247.7 381706.2 356936.0
0 1000 245.7 602637.9 356936.0
Tab.12 Values of related cost under different complexity cost adjustment coefficient
${\varGamma _k} = \varGamma _k^1$ $p = 0.5$
$\theta $ ${z^*}$/元 $z_{\rm{c}}^*$/元 ${\pi ^*}$ ${z_{\rm{a}}}$/元 $z_{\rm{c} }^{\rm{a}}$/元 ${\pi ^{\rm{a}}}$ ${\text{DIF}}(z)$ ${{{\text{DIF}}(\pi )}}$
0.2 0 369686.3 369686.3 259.3 481775.6 481775.6 314.0 30.3350 21.1525
0.2 1 369945.3 369686.9 258.5 482094.9 481783.3 311.6 30.3301 20.6826
0.2 10 372281.3 369700.1 258.1 484985.8 482185.9 278.0 30.8309 8.6850
0.2 50 382622.1 370297.3 246.5 496225.6 482356.8 277.4 30.2401 12.6057
0.2 100 394954.5 370456.0 245.0 510139.0 482312.5 278.3 29.6758 13.6540
Tab.13 Comparison of expected cost of robust programming with expected cost of optimal solution
Fig.4 Trend of robust planning cost with complexity cost adjustment coefficient
Fig.5 Trend of complexity relative regret value with complexity cost adjustment coefficient
[1]   SHEN Z J M, ZHAN R L, ZHANG J The reliable facility location problem: formulations, heuristics, and approximation algorithms[J]. INFORMS Journal on Computing, 2011, 23 (3): 470- 482
doi: 10.1287/ijoc.1100.0414
[2]   王珂, 杨艳, 周建 基于在险价值的物流网络规划模糊两阶段模型与精确求解方法[J]. 运筹与管理, 2020, 29 (2): 88- 96
WANG Ke, YANG Yan, ZHOU Jian Value-at-risk-based fuzzy two-stage model for logistics planning and its accurate solution approach[J]. Operations Research and Management Science, 2020, 29 (2): 88- 96
[3]   杨晓华, 郭健全 模糊环境下多周期多决策生鲜闭环物流网络[J]. 计算机应用, 2019, 39 (7): 2168- 2174
YANG Xiao-hua, GUO Jian-quan Multi-period multi-decision closed-loop logistics network for fresh product with fuzzy variables[J]. Journal of Computer Applications, 2019, 39 (7): 2168- 2174
doi: 10.11772/j.issn.1001-9081.2018122434
[4]   FATTAHI M, GOVINDAN K Integrated forward/reverse logistics network design under uncertainty with pricing for collection of used products[J]. Annals of Operations Research, 2017, 253 (1): 193- 225
doi: 10.1007/s10479-016-2347-5
[5]   HATEFI S M, JOLAI F Robust and reliable forward-reverse logistics network design under demand uncertainty and facility disruptions[J]. Applied Mathematical Modelling, 2014, 38 (9/10): 2630- 2647
[6]   PENG P, SNYDER L V, LIM A, et al Reliable logistics networks design with facility disruptions[J]. Transportation Research Part B: Methodological, 2011, 45 (8): 1190- 1211
doi: 10.1016/j.trb.2011.05.022
[7]   BOZARTH C C, WARSING D P, FlYNN B B, et al The impact of supply chain complexity on manufacturing plant performance[J]. Journal of Operations Management, 2009, 27 (1): 78- 93
doi: 10.1016/j.jom.2008.07.003
[8]   GIANNOCCARO I, NAIR A, CHOI T The impact of control and complexity on supply network performance: an empirically informed investigation using NK simulation analysis[J]. Decision Sciences, 2018, 49 (4): 625- 659
doi: 10.1111/deci.12293
[9]   WANG H, GU T, JIN M Z, et al The complexity measurement and evolution analysis of supply chain network under disruption risks[J]. Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science, 2018, 116: 72- 78
[10]   LIN Y H, WANG Y, LEE L H, et al Robust facility location with structural complexity and demand uncertainty[J]. Flexible Services and Manufacturing Journal, 2021, 33 (2): 485- 507
doi: 10.1007/s10696-020-09382-8
[11]   OLIVARES AGUILA J, ElMARAGHY W Structural complexity and robustness of supply chain networks based on product architecture[J]. International Journal of Production Research, 2018, 56 (20): 6701- 6718
doi: 10.1080/00207543.2018.1489158
[12]   SNYDER L V, DASKIN M S Stochastic p-robust location problems[J]. IIE Transactions, 2006, 38 (11): 971- 985
[13]   BERTSIMAS D, SIM M The price of robustness[J]. Operations Research, 2004, 52 (1): 35- 53
doi: 10.1287/opre.1030.0065
[14]   BERTSIMAS D, SIM M Robust discrete optimization and network flows[J]. Mathematical Programming, 2003, 98 (1−3): 49- 71
doi: 10.1007/s10107-003-0396-4
[15]   LIN Y H, WANG Y, LEE L H, et al Consistency matters: revisiting the structural complexity for supply chain networks[J]. Physica A: Statistical Mechanics and its Applications, 2021, 572: 125862
doi: 10.1016/j.physa.2021.125862
[16]   代颖, 马祖军, 刘飞 再制造闭环物流网络优化设计模型[J]. 中国机械工程, 2006, 17 (8): 809- 814
DAI Ying, MA Zu-jun, LIU Fei Optimization model for closed-loop logistics network design in a remanufacturing environment[J]. China Mechanical Engineering, 2006, 17 (8): 809- 814
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