Novel Tour Construction Heuristic for Pick-Up and Delivery Routing Problems

TL;DR

This paper introduces an adapted convex hull heuristic for pick-up and delivery routing problems with precedence constraints, outperforming traditional nearest neighbor methods on benchmark datasets.

Contribution

It develops a novel heuristic tailored for precedence-constrained routing, filling a gap in existing heuristic approaches for such problems.

Findings

The new heuristic outperforms nearest neighbor in all tested instances.

It is especially effective when pickups are peripheral and deliveries are central.

The approach is validated on TSPLIB benchmark data.

Abstract

In logistic applications that require the pickup and delivery of items, route optimization problems can be modeled as precedence constrained traveling salesperson problems. The combinatorial nature of this problem restricts the application of exact algorithms to small instances, and heuristics are largely preferred for tractability. However, due to precedence constraints that restrict the order in which locations can be visited, heuristics outside of the nearest neighbor algorithm have been neglected in literature. While the convex hull cheapest insertion heuristic is known to produce good solutions in the absence of precedence constraints, i.e., when locations can be visited in any order, it has not been adapted for pick-up and delivery considerations. This paper presents an adapted convex hull cheapest insertion heuristic that accounts for precedence constraints and compares its solutions with the nearest neighbor heuristic using the TSPLIB benchmark data set. The proposed algorithm is particularly suited to cases where pickups are located in the periphery and deliveries are centrally located, outperforming the Nearest Neighbor algorithm in every examined instance.