A decomposition-based approach for large-scale pickup and delivery problems

TL;DR

The paper tackles very large-scale offline pickup and delivery with time windows, pooling, and vehicle-to-request dispatching. It introduces a decomposition-based matheuristic to solve up to about $5{,}000$ requests rapidly and an ${ILS}$-based metaheuristic to handle instances with more than $20{,}000$ requests, plus a hybrid warm-start approach that combines both. Through extensive computational experiments on NYC-derived data and established PDPTW benchmarks, the authors show competitive performance, deliver numerous best-known solutions, and provide practical insights on fleet sizing and passenger delay tolerance. The findings demonstrate that pooling and dispatching decisions can achieve substantial service improvements, with modest time-window flexibilities sometimes matching large increases in fleet size and reducing overall travel while maintaining customer satisfaction.

Abstract

With the advent of self-driving cars, experts envision autonomous mobility-on-demand services in the near future to cope with overloaded transportation systems in cities worldwide. Efficient operations are imperative to unlock such a system's maximum improvement potential. Existing approaches either consider a narrow planning horizon or ignore essential characteristics of the underlying problem. In this paper, we develop an algorithmic framework that allows the study of very large-scale pickup and delivery routing problems with more than 20 thousand requests, which arise in the context of integrated request pooling and vehicle-to-request dispatching. We conduct a computational study and present comparative results showing the characteristics of the developed approaches. Furthermore, we apply our algorithm to related benchmark instances from the literature to show the efficacy. Finally, we solve very large-scale instances and derive insights on upper-bound improvements regarding fleet sizing and customer delay acceptance from a practical perspective.

Figures (18)

• Figure 1: Outline of the sequential pooling and dispatching approach.
• Figure 2: Dispatching graph transformed into a k-disjoint shortest path problem
• Figure 3: Example of a run of the recombination procedure.
• Figure 4: Sequences considered when inserting request $r=(p,d)$ between nodes $i,j$ and the concatenation operations to evaluate them.
• Figure 5: Graph $G^*$ with $k=3$ and $\vartheta^{}=\{v{}, p_{1}, p_{2}, d_{1}, p_{3}, d_{2},d_{3}\}$ (Nodes contain the corresponding pickup or delivery node for visualization). Arcs in black show the path of permutation $\pi = \{v{}, p_{1}, d_{1}, p_{3}, p_{2}, d_{3}, d_{2}\}$. Note that the dashed arc from Layer 1, Node 1 to Layer 2, Node 4 is invalid as the resulting sequence would violate the precedence constraint.