目的 针对城市末端配送路径规划中包装安全因素考虑不足的问题,探究将包装损伤暴露纳入路径决策后的优化效果。方法 在带时间窗车辆路径问题的框架下,引入包装脆弱系数、车辆装载状态和归一化累计运输距离,构建以配送成本、延误惩罚和包装损伤暴露最小化为目标的三目标配送规划模型,采用NSGA-II算法求解。基于Solomon标准算例,从模型对比、客户规模扩展、算法对比和参数敏感性分析4个方面开展实验验证。结果 与不考虑包装损伤暴露目标的模型相比,所提模型在25个客户代表方案中使包装损伤暴露降低6.42%~14.18%;客户规模扩展至50、100个客户后,包装损伤暴露仍保持降低趋势,降幅为6.34%~23.37%。在成本与时效方面,配送成本以下降为主,主要代价体现为延误增加。算法对比结果表明,NSGA-II在各类实例中均能获得具有竞争力的折中解。敏感性分析表明,高脆弱客户占比和装载敏感参数变化会影响包装损伤暴露水平,而时效响应具有明显场景差异。结论 将包装损伤暴露显式纳入末端配送路径优化目标,可在所选算例上有效改善包装安全表现并揭示包装安全与配送时效之间随配送条件变化的权衡关系,为易损品配送中的包装—物流协同优化提供了方法参考。
Abstract
The work aims to investigate the optimization effect of incorporating packaging damage exposure into routing decision-making, to address the insufficient consideration of packaging safety in urban last-mile delivery routing. Within the framework of the vehicle routing problem with time windows (VRPTW), a three-objective optimization model was developed by integrating packaging fragility coefficient, vehicle load condition, and normalized cumulative transportation distance, with the objectives of minimizing delivery cost, delay penalty, and packaging damage exposure. The model was solved using the NSGA-II algorithm and evaluated on Solomon benchmark instances from four aspects: model comparison, customer-scale extension, algorithm comparison, and parameter sensitivity analysis. Compared with the model that did not consider the packaging damage exposure objective, the proposed model reduced packaging damage exposure by 6.42%-14.18% in representative 25-customer solutions. When the customer scale was extended to 50 and 100 customers, packaging damage exposure still showed a decreasing trend, with reductions of 6.34%-23.37%. In terms of cost and timeliness, delivery cost mainly decreased, while the main trade-off was increased delay. Algorithm comparison showed that NSGA-II could obtain competitive compromise solutions across all tested instances. Sensitivity analysis indicated that the proportion of high-fragility customers and the loading sensitivity parameter affected packaging damage exposure, whereas timeliness responses exhibited clear scenario differences. Explicitly incorporating packaging damage exposure into last-mile delivery routing optimization can effectively improve packaging safety performance in the tested instances and reveal the trade-off between packaging safety and delivery timeliness under varying delivery conditions, providing a methodological reference for packaging-logistics collaborative optimization in fragile goods distribution.
关键词
城市末端配送 /
包装损伤暴露 /
多目标优化 /
车辆路径问题 /
NSGA-II
Key words
urban last-mile delivery /
packaging damage exposure /
multi-objective optimization /
vehicle routing problem /
NSGA-II
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] SHUAIBU A S, MAHMOUD A S, SHELTAMI T R.A Review of Last-Mile Delivery Optimization: Strategies, Technologies, Drone Integration, and Future Trends[J]. Drones, 2025, 9(3): 158.
[2] 雷宇翔, 杨中华. 国内外物流末端配送研究现状与进展[J]. 物流科技, 2024, 47(17): 47-51.
LEI Y X, YANG Z H.Research on Terminal Distribution Process: Recent Advances and Future Prospects[J]. Logistics Sci-Tech, 2024, 47(17): 47-51.
[3] BÖRÖCZ P, NÉMETH Z. Review Paper on the Field Measurement of Parcel Packaging Drop for Testing Purposes[J]. Packaging Technology and Science, 2025, 38(5): 345-357.
[4] KIM S, HORVATH L, LEE S, et al.Measurement and Analysis of Last-Mile Parcel Delivery Truck Vibration Levels in Korea[J]. Applied Sciences, 2024, 14(8): 3245.
[5] ČIŽIŪNIENĖ K, BATARLIENĖ N, et al. Analysis of Parcel Delivery Issues at “State Parcel Company”[J]. Logistics, 2025, 9(1): 16.
[6] SOLOMON M M.Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints[J]. Operations Research, 1987, 35(2): 254-265.
[7] BRÄYSY O, GENDREAU M. Vehicle Routing Problem with Time Windows, Part I: Route Construction and Local Search Algorithms[J]. Transportation Science, 2005, 39(1): 104-118.
[8] LIU X, CHEN Y L, POR L Y, KU C S.A Systematic Literature Review of Vehicle Routing Problems with Time Windows[J]. Sustainability, 2023, 15(15): 12004.
[9] CAI Y, LIN Z, CHENG M, et al.Solving Multi-Objective Vehicle Routing Problems with Time Windows: A Decomposition-Based Multiform Optimization Approach[J]. Tsinghua Science and Technology, 2024, 29(2): 305-324.
[10] LI J K, LI J Q, XU Y.An Improved Multiobjective Evolutionary Algorithm for Time-Dependent Vehicle Routing Problem with Time Windows[J]. Egyptian Informatics Journal, 2024, 28: 100574.
[11] ZHOU Y, LI Z, CAI Y, et al.A Multiobjective Edge-Based Learning Algorithm for the Vehicle Routing Problem with Time Windows[J]. Information Sciences, 2025, 689: 121525.
[12] 凌帅, 杨娟, 孙鹏, 等. 多目标协同下的即时配送路径优化[J]. 交通运输工程与信息学报, 2025, 23(4): 123-137.
LING S, YANG J, SUN P, et al.Multi-Objective Instant-Delivery Routing Problem Considering the Labor Rights and Safety[J]. Journal of Transportation Engineering and Information, 2025, 23(4): 123-137.
[13] 樊双蛟, 张佳傲, 张雨晴. 考虑剩余货架期的生鲜物流配送路径干扰管理研究[J]. 包装工程, 2026, 47(1): 64-71.
FAN S J, ZHANG J A, ZHANG Y Q.Interference Management of Fresh Produce Logistics and Distribution Routes Considering Remaining Shelf-Life[J]. Packaging Engineering, 2026, 47(1): 64-71.
[14] 于水源, 曾台英, 丁逸秋. 基于运输环境的包装系统疲劳损伤分析[J]. 包装工程, 2020, 41(13): 118-123.
YU S Y, ZENG T Y, DING Y Q.Fatigue Damage of Packaging System Based on the Transportation Environment[J]. Packaging Engineering, 2020, 41(13): 118-123.
[15] 王立军, 宋海燕, 王志伟. 运输包装加速随机振动试验研究综述[J]. 振动与冲击, 2022, 41(8): 277-286.
WANG L J, SONG H Y, WANG Z W.A Review on an Accelerated Random Vibration Test of Transport Packaging[J]. Journal of Vibration and Shock, 2022, 41(8): 277-286.
[16] FERNANDO I, FEI J, STANLEY R.Measurement and Analysis of Vibration and Mechanical Damage to Bananas During Long-Distance Interstate Transport by Multi-Trailer Road Trains[J]. Postharvest Biology and Technology, 2019, 158: 110977.
[17] FERNANDO I, FEI J, STANLEY R, ENSHAEI H.Measurement and Evaluation of the Effect of Vibration on Fruits in Transit—Review[J]. Packaging Technology and Science, 2018, 31(11): 723-738.
[18] LÉPINE J, ROUILLARD V, SEK M. Review Paper on Road Vehicle Vibration Simulation for Packaging Testing Purposes[J]. Packaging Technology and Science, 2015, 28(8): 672-682.
[19] WANG L J, ZHANG Q, SONG H Y, et al.Mechanical Damage of ‘Huangguan’ Pear Using Different Packaging under Random Vibration[J]. Postharvest Biology and Technology, 2022, 187: 111847.
[20] WANG L, XIE Z, WU Y, et al.Effects of Packaging Constraints on Vibration Damage of ‘Huangguan’ Pear During Simulated Transport[J]. Horticulturae, 2025, 11(7): 749.
[21] WANG L J, LAI Y Z, WANG Z W.Fatigue Failure and Grms-N Curve of Corrugated Paperboard Box[J]. Journal of Vibration and Control, 2020, 26(11-12): 1028-1041.
[22] BUELVAS PADILLA M P, NISPERUZA CANABAL P A, LÓPEZ PEREIRA J M, et al. Vehicle Routing Problem for the Minimization of Perishable Food Damage Considering Road Conditions[J]. Logistics Research, 2018, 11(2): 1-18.
[23] POLLARIS H, BRAEKERS K, CARIS A, et al.Vehicle Routing Problems with Loading Constraints: State-of-the-Art and Future Directions[J]. OR Spectrum, 2015, 37(2): 297-330.
[24] KREBS C, EHMKE J F, KOCH H.Advanced Loading Constraints for 3D Vehicle Routing Problems[J]. OR Spectrum, 2021, 43(4): 835-875.
[25] FERNANDO I, FEI J, STANLEY R, ENSHAEI H, ROUILLARD V.Developing an Accelerated Vibration Simulation Test for Packaged Bananas[J]. Postharvest Biology and Technology, 2021, 173: 111400.
[26] DEB K, PRATAP A, AGARWAL S, et al.A Fast and Elitist Multi-Objective Genetic Algorithm: NSGA-II[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197.
PDF(702 KB)
渝公网安备 50010702501716号 渝ICP备15012534号-2
