<p>Coordinated distribution utilizing trucks and robots is a promising solution for last-mile delivery, yet its potential is often constrained by the complexity of heterogeneous multi-depot integration. This study investigates a novel heterogeneous multi-depot vehicle-robot routing problem, driven by the strict constraints of inventory heterogeneity. The problem synchronizes bidirectional collaborations at the routing level by coupling en-route horizontal transfers that decouple service capability from inventory ownership with vertical robot-assisted delivery acting as mobile hubs. This integration introduces complex spatio-temporal precedence constraints and non-monotonic load fluctuations, necessitating precise coordination to prevent temporal conflicts. We mathematically formulate this problem as a mixed-integer linear programming model. To efficiently solve this problem, we develop an enhanced adaptive large neighborhood search algorithm. It incorporates a topology-based horizontal collaboration feasibility check to rapidly detect infeasible inter-route interactions and a diversity-aware reheating mechanism to prevent stagnation. Computational experiments verify the competitiveness of the algorithm on small-scale instances, its effectiveness on larger-scale problems, and the essential role of horizontal collaboration. Finally, sensitivity analyses reveal that extending truck range is more beneficial in settings with multiple depots and relatively fewer customers, whereas lowering the robot-truck cost ratio is especially effective as customer scale increases.</p>

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Bidirectional collaborative routing: synchronizing en-route transfers and robot-assisted delivery in heterogeneous multi-depot systems

  • Tianyu Mao,
  • Mingrui Yang

摘要

Coordinated distribution utilizing trucks and robots is a promising solution for last-mile delivery, yet its potential is often constrained by the complexity of heterogeneous multi-depot integration. This study investigates a novel heterogeneous multi-depot vehicle-robot routing problem, driven by the strict constraints of inventory heterogeneity. The problem synchronizes bidirectional collaborations at the routing level by coupling en-route horizontal transfers that decouple service capability from inventory ownership with vertical robot-assisted delivery acting as mobile hubs. This integration introduces complex spatio-temporal precedence constraints and non-monotonic load fluctuations, necessitating precise coordination to prevent temporal conflicts. We mathematically formulate this problem as a mixed-integer linear programming model. To efficiently solve this problem, we develop an enhanced adaptive large neighborhood search algorithm. It incorporates a topology-based horizontal collaboration feasibility check to rapidly detect infeasible inter-route interactions and a diversity-aware reheating mechanism to prevent stagnation. Computational experiments verify the competitiveness of the algorithm on small-scale instances, its effectiveness on larger-scale problems, and the essential role of horizontal collaboration. Finally, sensitivity analyses reveal that extending truck range is more beneficial in settings with multiple depots and relatively fewer customers, whereas lowering the robot-truck cost ratio is especially effective as customer scale increases.