Capacitated Vehicle Routing with Target Geometric Constraints

TL;DR

This paper addresses a novel variant of the vehicle routing problem where customer locations are regions rather than points, proposing efficient algorithms that outperform greedy methods and are optimal for convex regions.

Contribution

The paper introduces the CVRG problem, extending CVRP to regional customer locations, and develops fast, high-quality algorithms with optimality guarantees for convex regions.

Findings

Algorithms compute solutions for hundreds of regions

Proposed methods outperform greedy approaches

Solutions are optimal for convex customer regions

Abstract

We investigate the capacitated vehicle routing problem (CVRP) under a robotics context, where a vehicle with limited payload must complete delivery (or pickup) tasks to serve a set of geographically distributed customers with varying demands. In classical CVRP, a customer location is modeled as a point. In many robotics applications, however, it is more appropriate to model such "customer locations" as 2D regions. For example, in aerial delivery, a drone may drop a package anywhere in a customer's lot. This yields the problem of CVRG (Capacitated Vehicle Routing with Target Geometric Constraints). Computationally, CVRP is already strongly NP-hard; CVRG is therefore more challenging. Nevertheless, we develop fast algorithms for CVRG, capable of computing high quality solutions for hundreds of regions. Our algorithmic solution is guaranteed to be optimal when customer regions are convex. Numerical evaluations show that our proposed methods significantly outperform greedy best-first approaches. Comprehensive simulation studies confirm the effectiveness of our methods.