Pickup & Delivery with Time Windows and Transfers: combining decomposition with metaheuristics

TL;DR

The Pickup and Delivery Problem with Time Windows and Transfers (PDPT) extends classical routing by allowing load transfers and strict time windows. The authors propose a scalable LBBD exact framework (Branch-and-Check) and a robust, parameter-light LNS metaheuristic, complemented by a public instance generator to benchmark performance. Empirical results show LBBD improves optimality gaps on literature benchmarks up to 30 requests, and rLNS delivers near-optimal solutions and meaningful warm-start gains for larger instances, indicating strong practical impact for urban logistics with transfers. The work advances scalable exact and heuristic approaches for PDPT and provides tools to study transfer-enabled routing at realistic scales.

Abstract

This paper examines the generalisation of the Pickup and Delivery Problem that allows mid-route load exchanges among vehicles and obeys strict time-windows at all locations. We propose a novel Logic-Based Benders Decomposition (LBBD) that improves optimality gaps for all benchmarks in the literature and scales up to handle larger ones. To tackle even larger instances, we introduce a refined Large Neighborhood Search (LNS) algorithm that improves the adaptability of LNS beyond case-specific configurations appearing in related literature. To bridge the gap in benchmark availability, we develop an instance generator that allows for extensive experimentation. For moderate datasets (25 and 50 requests), we evaluate the performance of both LBBD and LNS, the former being able to close the gap and the latter capable of providing near-optimal solutions. For larger instances (75 and 100 requests), we recreate indicative state-of-the-art metaheuristics to highlight the improvements introduced by our LNS refinements, while establishing its scalability.

Figures (1)

• Figure 1: Example of path construction for three requests and two vehicles