Vehicle Routing Problem with Resource-Constrained Pickup and Delivery: A Heuristic-Informed BRKGA with Pattern-Based Analysis

Abstract

We introduce the Vehicle Routing Problem with Resource-Constrained Pickup and Delivery (VRP-RPD), where agents deploy finite identical resources at customer locations for processing before retrieval and redeployment. Applications include portable medical equipment, tool rental, and disaster relief. Unlike classical pickup-and-delivery variants, VRP-RPD permits different agents to perform dropoff and pickup for the same customer—creating inter-route dependencies absent from standard formulations. We provide a complete mixed-integer linear programming formulation and demonstrate that exact methods are intractable even for small instances. Problems with 16 customers cannot be solved to optimality within two hours of computational time. We develop a Biased Random-Key Genetic Algorithm (BRKGA) with a four-gene-per-customer encoding. Two genes assign dropoff and pickup agents independently, while two priority keys determine sequencing. A simulation decoder guarantees feasibility by deferring operations until resources become available. Experiments on 14 TSPlib-derived benchmarks across five variants of processing time (base, 2X, 5X, 1R10, 1R20) compare four configurations. Warm-start BRKGA achieves 13–67% makespan reduction over the heuristics, with larger gains on higher-resource instances. Ablation tests show warm-start initialization is the primary driver of performance. Friedman tests (p < 0.01) confirm warm-start BRKGA superiority across all instance variants.