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Operations optimization in multi-modal relay-based delivery systems: Plan-based model and nested exact algorithm
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DOI：10.1016/j.trb.2026.103618.png)
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Abstract
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This study investigates the operational optimization of an on-demand, multi-modal relay-based delivery system comprising dispersed unmanned hub stations and fleets of drones and unmanned vehicles. We formulate a plan-based model to coordinate and synchronize heterogeneous delivery modes, ensuring timely and cost-effective fulfillment of customer orders. The proposed model determines which orders to accept in each arriving batch, allocates drones and vehicles to execute these orders, and schedules their movements to guarantee on-time deliveries. A nested exact algorithm, integrating logic-based Benders decomposition (LBBD), column-and-row generation (CRG), and branch-and-price (BP), efficiently solves typical instances in approximately 70 seconds. The algorithmic novelty lies in that a CRG & BP based exact algorithm is embedded in an LBBD to solve the LBBD’s subproblem. Computational experiments, based on realistic scenarios, demonstrate the effectiveness of our proposed methodology and provide several managerial insights. Factors such as average delivery distance, time-window flexibility, and fleet composition are shown to significantly impact system profitability and service quality. The results offer practical guidance on batch sizing, fleet configuration, and operational conditions under which multi-modal relay-based delivery systems outperform traditional courier-based models.
Keywords:
Multi-modal delivery
Relay
Drones
Exact algorithm
Nested algorithm
Column-and-row generation
Logic-based Benders decomposition
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