Capacitated Vehicle Routing Problem with Heterogeneous Fixed Proprietary Fleet and Outsourcing Delivery—A Clustering-Based Approach

  • Ricardo Bertoluci
  • António G. RamosEmail author
  • Manuel Lopes
  • João Bastos
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 278)


This paper describes a solution method that was created with the objective of obtaining a more efficient finished goods distribution process for a food industry company. The finished goods distribution process involves the use of the companys own fleet to serve a specific group of customers, and the use of outsourcing transportation services that can make direct and transshipment customer deliveries. The complexity of the problem is due to the need to decide which customers should be served by each of the outsourcing transportation services, direct or transshipment, and to find cost efficient solutions for the multiple vehicle routing problems created. First, an original clustering method consisting of a logical division of the customer orders using a delivery ratio based on the transportation unit cost, distance and order weight, is used to define customer clusters by service type. Then, an exact method based on a mixed integer programming model, is used to obtain optimal vehicle routing solutions, for each cluster created. The solution method for the company real instances, proved able to reach the initial proposed objectives and obtain promising results that suggest an average reduction of 34% for the operational costs, when compared to the current distribution model of the company.


Outsourcing Heterogeneous fleet Clustering Vehicle routing problem 



We acknowledge the financial support of CIDEM, R&D unit funded by the FCT—Portuguese Foundation for the Development of Science and Technology, Ministry of Science, Technology and Higher Education, under the Project “UID/EMS/0615/2016”. This research was also financed by the ERDF—European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation—COMPETE 2020 Programme within project “POCI-01-0145-FEDER-006961”, and by National Funds through the Portuguese funding agency, FCT—Fundação para a Ciência e a Tecnologia as part of project “UID/EEA/50014/2013”.


  1. 1.
    Braekers, K., Ramaekers, K., Van Nieuwenhuyse, I.: The vehicle routing problem: state of the art classification and review. Comput. Ind. Eng. 99, 300–313 (2016)CrossRefGoogle Scholar
  2. 2.
    Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manag. Sci. 6(1), 80–91 (1959)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Lahyani, R., Khemakhem, M., Semet, F.: Rich vehicle routing problems: from a taxonomy to a definition. Eur. J. Oper. Res. 241(1), 1–14 (2015)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Laporte, G., Gendreau, M., Potvin, J.-Y., Semet, F.: Classical and modern heuristics for the vehicle routing problem. Int. Trans. Oper. Res. 7(4–5), 285–300 (2000)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Miller, C.E., Tucker, A.W., Zemlin, R.A.: Integer programming formulation of traveling salesman problems. J. ACM (JACM) 7(4), 326–329 (1960)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Montoya-Torres, J.R., Franco, J.L., Isaza, S.N., Jiménez, H.F., Herazo-Padilla, N.: A literature review on the vehicle routing problem with multiple depots. Comput. Ind. Eng. 79, 115–129 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ricardo Bertoluci
    • 1
  • António G. Ramos
    • 2
    Email author
  • Manuel Lopes
    • 3
  • João Bastos
    • 4
  1. 1.School of EngineeringPolytechnic of PortoPortoPortugal
  2. 2.INESC TEC and CIDEM, School of EngineeringPolytechnic of PortoPortoPortugal
  3. 3.CIDEM, School of EngineeringPolytechnic of PortoPortoPortugal
  4. 4.INESC TEC and School of EngineeringPolytechnic of PortoPortoPortugal

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