Vehicle Routing Problem with Resource-Constrained Pickup and Delivery

Abstract

We introduce the Vehicle Routing Problem with Resource-Constrained Pickup and Delivery (VRP-RPD), where vehicles transport finite identical resources to customer locations for autonomous processing before retrieval and redeployment. Unlike classical pickup-and-delivery problems where the same vehicle must perform both operations for each customer, VRP-RPD permits different vehicles to handle dropoff and pickup at the same location, creating inter-route dependencies absent from standard formulations. This decoupling reflects practical scenarios in autonomous robotics deployment, portable medical equipment distribution, disaster relief operations, construction tool rental, and agricultural sensor networks, where transport vehicles are the scarce resource and need not wait during processing. The objective is to minimize makespan, defined as the time when the last vehicle returns after all resources are deployed, processed, and retrieved. Although makespan objectives are typical in scheduling problems, the significant transportation times relative to processing durations and the resource capacity constraints fundamentally alter optimization considerations. We demonstrate that exact methods are computationally intractable for instances beyond 16 customers. We develop a sequential two-stage metaheuristic pipeline: a GPU-accelerated Adaptive Large Neighborhood Search (ALNS) is run first to obtain a high-quality incumbent, which is then encoded as a warm-start seed for a Biased Random-Key Genetic Algorithm (BRKGA) that refines the solution through evolutionary search. Evaluated on TSPlib-derived benchmarks (17-1000 nodes) across multiple processing time variants (base, 2x, 5x, 1R10, 1R20), the pipeline consistently achieves the best solutions across all instance sizes, reducing makespan by up to 74% over baseline heuristics.