A hybrid framework for multi-depot vehicle routing under stochastic demand: integrating adaptive redispatching with joint distribution

Jingshuai Yang; Zhengyu Liu; Zixin Zhou; Huan Pang; Minghui Xie; Deyin Jiang; Jingshuai Yang; Zhengyu Liu; Zixin Zhou; Huan Pang; Minghui Xie; Deyin Jiang

doi:10.3934/jimo.2026119

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 7: 3252-3283. doi: 10.3934/jimo.2026119

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Research article

A hybrid framework for multi-depot vehicle routing under stochastic demand: integrating adaptive redispatching with joint distribution

School of Automobile, Chang'an University, Xi'an 710018, China

Received: 17 April 2026 Revised: 04 June 2026 Accepted: 12 June 2026 Published: 22 June 2026
90B06, 90C29

E-commerce and last-mile growth intensify routing demands, while deterministic demand, independent distribution, and single-mode rescheduling hinder efficiency and realism. To address these issues, we proposed a multi-depot capacity-constrained vehicle routing problem with stochastic demands and joint distribution (MCVRPSD-JD), embedding adaptive skip, reassigning, and redistributing redispatching strategies for failed delivery points. The model integrates chance-constrained programming with cooperative scheduling mechanisms to enhance vehicle utilization and mitigate capacity imbalance under stochastic demand. A hybrid variable neighborhood descent scatter search (HVNDSS) algorithm is developed to balance global search and local refinement across optimization stages. Experimental results demonstrated that the proposed method outperformed baseline algorithms, reducing solution error to 0.17% while achieving notable distribution cost savings. Compared with independent distribution, the joint distribution model lowered costs by an average of 15.91% and reduced failure points. This study contributes a scalable framework for stochastic logistics, offering practical insights for cost-efficient urban distribution systems.
- urban logistics,
- vehicle routing problem,
- stochastic demand,
- joint distribution,
- hybrid optimization model
Citation: Jingshuai Yang, Zhengyu Liu, Zixin Zhou, Huan Pang, Minghui Xie, Deyin Jiang. A hybrid framework for multi-depot vehicle routing under stochastic demand: integrating adaptive redispatching with joint distribution[J]. Journal of Industrial and Management Optimization, 2026, 22(7): 3252-3283. doi: 10.3934/jimo.2026119

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Abstract

E-commerce and last-mile growth intensify routing demands, while deterministic demand, independent distribution, and single-mode rescheduling hinder efficiency and realism. To address these issues, we proposed a multi-depot capacity-constrained vehicle routing problem with stochastic demands and joint distribution (MCVRPSD-JD), embedding adaptive skip, reassigning, and redistributing redispatching strategies for failed delivery points. The model integrates chance-constrained programming with cooperative scheduling mechanisms to enhance vehicle utilization and mitigate capacity imbalance under stochastic demand. A hybrid variable neighborhood descent scatter search (HVNDSS) algorithm is developed to balance global search and local refinement across optimization stages. Experimental results demonstrated that the proposed method outperformed baseline algorithms, reducing solution error to 0.17% while achieving notable distribution cost savings. Compared with independent distribution, the joint distribution model lowered costs by an average of 15.91% and reduced failure points. This study contributes a scalable framework for stochastic logistics, offering practical insights for cost-efficient urban distribution systems.

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