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An Exact Solution Method for the TSP with Drone Based on Decomposition

Sebastián A. Vásquez(savasquez***at***uc.cl)
Gustavo Angulo(gangulo***at***ing.puc.cl)
Mathias A. Klapp(maklapp***at***ing.puc.cl)

Abstract: The Traveling Salesperson Problem with Drone (TSP--D) is a routing model in which a given set of customer locations must be visited in the least amount of time, either by a truck route starting and ending at a depot or by a drone dispatched from the truck en route. We study the TSP--D model and propose a mixed--integer programming formulation which exploits the model's structure and decomposes it into two natural decision stages: (1) selecting and sequencing a subset of customers served by the truck and (2) planning where to execute drone direct dispatches from the truck to each of the remaining customer locations. We design a Benders--type decomposition algorithm, strengthened by valid inequalities arising from structural properties of optimal solutions, and improved optimality cuts stemming from the notions of t-shortcut and t-reduction, which might be of independent interest. Finally, our solution approach is empirically tested over an extensive family of computationally simulated instances, which show its effectiveness.

Keywords: traveling salesman problem, vehicle routing, drones, Benders' decomposition

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Category 2: Applications -- OR and Management Sciences (Production and Logistics )

Citation: School of Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile

Download: [PDF]

Entry Submitted: 04/02/2020
Entry Accepted: 04/03/2020
Entry Last Modified: 04/02/2020

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