An Integer Programming Based Approach to Delivery Drone Routing under Load-Dependent Flight Speed

  1. Nishira, Mao 1
  2. Ito, Satoshi 1
  3. Nishikawa, Hiroki 2
  4. Kong, Xiangbo 3
  5. Tomiyama, Hiroyuki 1
  6. González Aguilera, Diego 4
  1. 1 Graduate School of Science and Engineering, Ritsumeikan University, Kusatsu 525-8577, Shiga, Japan
  2. 2 Graduate School of Information Science and Technology, Osaka University, Suita 565-0871, Osaka, Japan
  3. 3 Department of Intelligent Robotics, Faculty of Engineering, Toyama Prefectural University, Imizu 939-0398, Toyama, Japan
  4. 4 Universidad de Salamanca

    Universidad de Salamanca

    Salamanca, España



ISSN: 2504-446X

Year of publication: 2023

Volume: 7

Issue: 5

Pages: 320

Type: Article

DOI: 10.3390/DRONES7050320 GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Drones


Delivery drones have been attracting attention as a means of solving recent logistics issues, and many companies are focusing on their practical applications. Many research studies on delivery drones have been active for several decades. Among them, extended routing problems for drones have been proposed based on the Traveling Salesman Problem (TSP), which is used, for example, in truck vehicle routing problems. In parcel delivery by drones, additional constraints such as battery capacity, payload, and weather conditions need to be considered. This study addresses the routing problem for delivery drones. Most existing studies assume that the drone’s flight speed is constant regardless of the load. On the other hand, some studies assume that the flight speed varies with the load. This routing problem is called the Flight Speed-Aware Traveling Salesman Problem (FSTSP). The complexity of the drone flight speed function in this problem makes it difficult to solve the routing problem using general-purpose mathematical optimization solvers. In this study, the routing problem is reduced to an integer programming problem by using linear and quadratic approximations of the flight speed function. This enables us to solve the problem using general-purpose mathematical optimization solvers. In experiments, we compared the existing and proposed methods in terms of solving time and total flight time. The experimental results show that the proposed method with multiple threads has a shorter solving time than the state-of-the-art method when the number of customers is 17 or more. In terms of total flight time, the proposed methods deteriorate by an average of 0.4% for integer quadratic programming and an average of 1.9% for integer cubic programming compared to state-of-the-art methods. These experimental results show that the quadratic and cubic approximations of the problem have almost no degradation of the solution.

Funding information


  • JSPS Kakenhi
    • 20H04160
  • NEDO
    • JPNP22006

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