Vehicle Routing Problem for Pharmaceutical Logistics Distribution Considering Order Splitting and Time Windows

WANG Yong; WEI Yuanfan; JIN Yan; WEI Yuanhan

doi:10.19554/j.cnki.1001-3563.2026.15.025

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Packaging Engineering ›› 2026, Vol. 47 ›› Issue (15) : 240-253. DOI: 10.19554/j.cnki.1001-3563.2026.15.025

Green Packaging and Circular Economy

Vehicle Routing Problem for Pharmaceutical Logistics Distribution Considering Order Splitting and Time Windows

WANG Yong^1a,b,*, WEI Yuanfan^1a, JIN Yan^1a, WEI Yuanhan²

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Abstract

The work aims to propose a vehicle routing optimization strategy for pharmaceutical logistics distribution that takes into account order splitting and time window constraints, to deal with the high distribution costs and low customer service efficiency in pharmaceutical logistics distribution due to the order splitting demands and time window constraints. First, a bi-objective optimization model was constructed, which minimized the total logistics cost and the number of used vehicles, including vehicle distribution cost, vehicle maintenance cost, leasing cost, time window penalty cost, and order splitting cost. Second, an improved adaptive large neighborhood search algorithm integrating order splitting strategies was proposed to solve the model. Splitting-related disruption operators and splitting order priority repair operators were designed to enhance the optimization ability. The adaptive weight adjustment mechanism of the simulated annealing acceptance criterion was integrated to improve the global optimization ability of the algorithm. At the same time, a global vehicle sharing strategy was designed to achieve the shared scheduling of delivery vehicles. Then, through a comparative analysis with the non-dominated sorting genetic algorithm-II, the multi-objective genetic algorithm and the multi-objective ant colony algorithm, the effectiveness of the proposed model and algorithm was verified. Finally, based on the real-world data, the optimized schemes under different vehicle sharing modes and different order splitting modes were compared and analyzed, and the changes in related indicators such as the total logistics operating cost and the number of used vehicles were discussed. The optimized vehicle routing scheme reduced the number of used vehicles by 7 and saved 47.63% of the total logistics operating cost. The proposed model, algorithm and strategy can reasonably plan the delivery vehicle routes, reduce the total operating cost and vehicle usage, and provide method references and theoretical support for solving the vehicle routing problem of pharmaceutical logistics delivery considering order splitting and time windows.

Key words

pharmaceutical logistics / vehicle routing problem / order splitting / repair operator / improved adaptive large neighborhood search algorithm

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WANG Yong, WEI Yuanfan, JIN Yan, WEI Yuanhan. Vehicle Routing Problem for Pharmaceutical Logistics Distribution Considering Order Splitting and Time Windows[J]. Packaging Engineering. 2026, 47(15): 240-253 https://doi.org/10.19554/j.cnki.1001-3563.2026.15.025

References

[1] HE H, ZHAN Y Z, HUO B F, et al.The Impact of National Centralized Drug Procurement Policy on Firm Performance: Evidence from Chinese Pharmaceutical Firms[J]. Transportation Research Part E: Logistics and Transportation Review, 2025, 200: 104225.
[2] 邓发珩, 梁卓斌, 秦虎, 等. 考虑冷链-常温货品混合配送的路径优化问题[J]. 系统工程学报, 2024, 39(2): 258-271.
DENG F H, LIANG Z B, QIN H, et al.Vehicle Routing Optimization for the Mixed Distribution of Refrigerated and Ambient Products[J]. Journal of Systems Engineering, 2024, 39(2): 258-271.
[3] 唐坚强, 祁超, 王红卫. 带时间窗的多仓库订单拆分与异构车辆路径联合优化方法[J]. 系统工程理论与实践, 2023, 43(5): 1446-1464.
TANG J Q, QI C, WANG H W.Integrated Optimization Approach to Multi-Depot Order Splitting and Heterogeneous Vehicle Routing with Time Windows[J]. Systems Engineering-Theory & Practice, 2023, 43(5): 1446-1464.
[4] LEE S J, KIM B S.Vehicle Routing and Scheduling Problem with Order Acceptance for Pharmaceutical Refrigerated Logistics[J]. Applied Soft Computing, 2024, 164: 111983.
[5] SIKKING C, DINH T T, CRUL M, et al.Analysis of the Formation of (Sub)Visual Particles in Ready-to-Administer Trastuzumab Infusion Bags during Transport from the Hospital Pharmacy to Patients at Home[J]. Journal of Pharmaceutical Sciences, 2026, 115(3): 104164.
[6] 王勇, 魏远晗, 蒋琼, 等. 三维装载约束下基于运输资源共享的车辆路径问题[J]. 计算机集成制造系统, 2023, 29(9): 3153-3170.
WANG Y, WEI Y H, JIANG Q, et al.Vehicle Routing Problem Based on Transportation Resource Sharing under Three-Dimensional Loading Constraints[J]. Computer Integrated Manufacturing Systems, 2023, 29(9): 3153-3170.
[7] ZHEN L, MA C L, WANG K, et al.Multi-Depot Multi-Trip Vehicle Routing Problem with Time Windows and Release Dates[J]. Transportation Research Part E: Logistics and Transportation Review, 2020, 135: 101866.
[8] WANG S H, SUN W, HUANG M.An Adaptive Large Neighborhood Search for the Multi-Depot Dynamic Vehicle Routing Problem with Time Windows[J]. Computers & Industrial Engineering, 2024, 191: 110122.
[9] CHEN T T, CHU F, ZHANG J T, et al.Sustainable Collaborative Strategy in Pharmaceutical Refrigerated Logistics Routing Problem[J]. International Journal of Production Research, 2024, 62(14): 5036-5060.
[10] XU B, SUN J, ZHANG Z M, et al.Research on Cold Chain Logistics Transportation Scheme under Complex Conditional Constraints[J]. Sustainability, 2023, 15(10): 8431.
[11] GAMST M, LUSBY R M, ROPKE S.Exact and Heuristic Methods for the Split Delivery Vehicle Routing Problem[J]. Transportation Science, 2024, 58(4): 741-760.
[12] KOU S H, GOLDEN B, BERTAZZI L.Estimating Optimal Split Delivery Vehicle Routing Problem Solution Values[J]. Computers & Operations Research, 2024, 168: 106714.
[13] FERREIRA K M, DE QUEIROZ T A, MUNARI P, et al. A Variable Neighborhood Search for the Green Vehicle Routing Problem with Two-Dimensional Loading Constraints and Split Delivery[J]. European Journal of Operational Research, 2024, 316(2): 597-616.
[14] BECKER C, SCHNEIDER M.An A-Priori-Splitting- Based Heuristic for the Split Delivery Vehicle Routing Problem with Time Windows[J]. Networks, 2025, 86(4): 468-516.
[15] 吴瑶, 周愉峰, 李峰. 订单可拆分的低碳冷链配送选址与多车舱路径优化[J]. 计算机工程与应用, 2025, 61(8): 339-350.
WU Y, ZHOU Y F, LI F.Optimization of Low-Carbon Location and Routing Problem with Multi-Compartment for Cold Chain Distribution Considering Order Splitting[J]. Computer Engineering and Applications, 2025, 61(8): 339-350.
[16] XU X, LI F, WU T, et al.Location-Routing Optimization Problem of Pharmaceutical Cold Chain Logistics with Oil-Electric Mixed Fleets under Uncertainties[J]. Computers & Industrial Engineering, 2025, 201: 110932.
[17] ZHANG J, LI Y F, LU Z Y.Multi-Period Vehicle Routing Problem with Time Windows for Drug Distribution in the Epidemic Situation[J]. Transportation Research Part C: Emerging Technologies, 2024, 160: 104484.
[18] 江云倩, 杨慧敏, 彭程, 等. 考虑碳排放和时间窗的冷链物流配送路径优化研究[J]. 包装工程, 2024, 45(3): 262-268.
JIANG Y Q, YANG H M, PENG C, et al.Optimization of Cold Chain Logistics Distribution Route Considering Carbon Emission and Time Window[J]. Packaging Engineering, 2024, 45(3): 262-268.
[19] 王勇, 王静媛, 苟梦圆, 等. 基于时间窗和多仓温控的生鲜商品配送车辆路径优化问题[J]. 包装工程, 2024, 45(5): 263-275.
WANG Y, WANG J Y, GOU M Y, et al.Fresh Commodity Distribution Vehicle Routing Optimization Based on Time Windows and Multi-Compartment Temperature Control[J]. Packaging Engineering, 2024, 45(5): 263-275.
[20] DENG J W, ZHANG J H, YANG S X.An Improved Adaptive Large Neighborhood Search Algorithm for Integrated Scheduling of Distributed Production and Distribution Systems[J]. Memetic Computing, 2025, 18(1): 4.
[21] KUO R J, EDBERT E, ZULVIA F E, et al.Applying NSGA-II to Vehicle Routing Problem with Drones Considering Makespan and Carbon Emission[J]. Expert Systems with Applications, 2023, 221: 119777.
[22] ZHANG X, HAO Y C, ZHANG L Y, et al.Application of Improved Genetic Algorithm to Vehicle Routing Problem Considering the Environmental Self-Regulation of the Freight Companies[J]. Expert Systems with Applications, 2025, 274: 127010.
[23] SONG C Y, CHEN S W.A Solid Waste Recycling Vehicle Routing Optimization Model under Online Appointment-Based Mode Using MOACO-ET Algorithm[J]. Case Studies on Transport Policy, 2025, 19: 101373.
[24] SOLOMON M M.Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints[J]. Operations Research, 1987, 35(2): 254-265.