On the Min-cost Traveling Salesman Problem with Drone

TL;DR

This paper introduces a new variant of the traveling salesman problem involving drones, proposing heuristics to minimize total transportation costs in last-mile delivery scenarios with experimental validation.

Contribution

It formulates the TSP with drone (TSP-D) focusing on cost minimization and develops two heuristics, DFTS and TFDS, for effective route planning.

Findings

DFTS outperforms TFDS in certain scenarios

Heuristics significantly reduce total transportation costs

Numerical experiments validate effectiveness across various instances

Abstract

Once known to be used exclusively in military domain, unmanned aerial vehicles (drones) have stepped up to become a part of new logistic method in commercial sector called "last-mile delivery". In this novel approach, small unmanned aerial vehicles (UAV), also known as drones, are deployed alongside with trucks to deliver goods to customers in order to improve the service quality or reduce the transportation cost. It gives rise to a new variant of the traveling salesman problem (TSP), of which we call TSP with drone (TSP-D). In this article, we consider a variant of TSP-D where the main objective is to minimize the total transportation cost. We also propose two heuristics: "Drone First, Truck Second" (DFTS) and "Truck First, Drone Second" (TFDS), to effectively solve the problem. The former constructs route for drone first while the latter constructs route for truck first. We solve a TSP to generate route for truck and propose a mixed integer programming (MIP) formulation with different profit functions to build route for drone. Numerical results obtained on many instances with different sizes and characteristics are presented. Recommendations on promising algorithm choices are also provided.