Dominance-Based Feasibility Inference for Packing-Constrained Pickup and Delivery Problems

Abstract

Routing and packing are intrinsically coupled in transport problems, requiring joint planning for cost-efficient and physically realizable solutions. We study a pickup and delivery problem with two-dimensional packing constraints (2P-PDP). Unlike vehicle routing variants where items are loaded before vehicles leave the depot and packing is validated only once, the 2P-PDP induces non-monotonic free-space evolution, substantially increasing feasibility-checking complexity. To address this bottleneck, we propose a generic dominance-based feasibility framework that is embeddable in a broad class of exact and heuristic routing algorithms. Under no-relocation constraints, inferring feasibility from a previously verified packing state requires preserving the pickup and delivery order of onboard items. To this end, we introduce an order-preserving mapping that jointly captures geometric containment and sequence compatibility, enabling dominance-based inference by embedding the new packing state into a verified reference plan. To further reduce dominance-screening overhead, we design three search rules to guide candidate exploration and tailored strategies to store, retrieve, and prioritize verified states. Computational experiments show that the proposed approach reduces feasibility-checking time by up to 42% compared to a benchmark without dominance. The improvement stems from reducing exact packing-procedure calls, shifting verification effort away from the most computationally expensive stage.