Constraint Programming models for the parallel drone scheduling vehicle routing problem

TL;DR

This paper introduces constraint programming models for the parallel drone scheduling vehicle routing problem, addressing both theoretical and practical variants, and demonstrates their effectiveness through experiments on benchmark instances.

Contribution

It presents new constraint programming models for the problem, covering both time minimization and cost minimization variants, with validation on existing benchmark instances.

Findings

Models can solve problems to optimality

Models provide effective heuristics and bounds

Experimental results validate the models' effectiveness

Abstract

Drones are currently seen as a viable way for improving the distribution of parcels in urban and rural environments, while working in coordination with traditional vehicles like trucks. In this paper we consider the parallel drone scheduling vehicle routing problem, where the service of a set of customers requiring a delivery is split between a fleet of trucks and a fleet of drones. We consider two variations of the problem. In the first one the problem is more theoretical, and the target is the minimization of the time required to complete the service and have all the vehicles back to the depot. In the second variant more realistic constraints involving operating costs, capacity limitation and workload balance, are considered, and the target is to minimize the total operational costs. We propose several constraint programming models to deal with the two problems. An experimental champaign on the instances previously adopted in the literature is presented to validate the new solving methods. The results show that on top of being a viable way to solve problems to optimality, the models can also be used to derive effective heuristic solutions and high-quality lower bounds for the optimal cost, if the execution is interrupted after its natural end.