The truck traveling salesman problem with drone and boat for humanitarian relief distribution in flood disaster: Mathematical model and solution methods

This paper presents an optimization model to distribute logistical items from a warehouse to shelters in the case of humanitarian flood disaster relief. The model utilizes three transportation modes, namely, a truck, a drone, and an inflatable boat. We refer to this problem as the Traveling Salesman Problem with Drone and Boat (TSP-DB). The truck acts as a mothership vehicle, carrying a drone and a boat. Shelters in the dry area can be served by truck and drone, while those in the flooded area can be accessed by boat and drone. The drone and boat are deployed from the truck to deliver items to shelters. Due to the limited capacity and the high relative demand at a shelter, the drone can only make one visit at a time before returning to the truck, while the boat can perform multiple visits in a single trip. The objective is to minimize the completion time. The proposed problem is first modeled using mixed integer linear programming. As the problem is hard to solve exactly, especially for relatively larger instances, an effective matheuristic that combines an exact method and the metaheuristic record-to-record travel algorithm is then proposed. The performance of the proposed approach is assessed using generated and benchmark instances. The results reveal that our method is robust and competitive when compared against existing state-of-the-art methods on related traveling salesman problems with drones. The proposed method is also applied to a real case study in Jakarta, Indonesia, where interesting and valuable managerial insights are discussed and analyzed.