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Over the past few years, unmanned aerial vehicles (UAV), also known asdrones, have been adopted as part of a new logistic method in the commercialsector called "last-mile delivery". In this novel approach, they are deployedalongside trucks to deliver goods to customers to improve the quality ofservice and reduce the transportation cost. This approach gives rise to a newvariant of the traveling salesman problem (TSP), called TSP with drone (TSP-D).A variant of this problem that aims to minimize the time at which truck anddrone finish the service (or, in other words, to maximize the quality ofservice) was studied in the work of Murray and Chu (2015). In contrast, thispaper considers a new variant of TSP-D in which the objective is to minimizeoperational costs including total transportation cost and one created by wastetime a vehicle has to wait for the other. The problem is first formulatedmathematically. Then, two algorithms are proposed for the solution. The firstalgorithm (TSP-LS) was adapted from the approach proposed by Murray and Chu(2015), in which an optimal TSP solution is converted to a feasible TSP-Dsolution by local searches. The second algorithm, a Greedy Randomized AdaptiveSearch Procedure (GRASP), is based on a new split procedure that optimallysplits any TSP tour into a TSP-D solution. After a TSP-D solution has beengenerated, it is then improved through local search operators. Numericalresults obtained on various instances of both objective functions withdifferent sizes and characteristics are presented. The results show that GRASPoutperforms TSP-LS in terms of solution quality under an acceptable runningtime.

On the Min-cost Traveling Salesman Problem with Drone