A Mathematical Model to Optimize Transport Cost and Inventory Level in a Single Level Logistic Network

  • Laila KechmaneEmail author
  • Benayad Nsiri
  • Azeddine Baalal
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 343)


This paper proposes a mathematical model that minimizes transportation costs and optimizes distribution organization in a single level logistic network. The objective is to allocate customers to distribution centers and vehicles to travels in order to cut down the traveled distances, while observing the storage capacities of vehicles and distribution centers and covering the customers’ needs. We propose a mixed integer programming formula that can be solved using Lingo 14.0. A digital example will be given in the end to illustrate the practicability of the model.


Distribution organization Mixed integer programming Single level logistic network Transportation costs 


  1. 1.
    Davendra, D.: Traveling Salesman Problem, Theory and Applications. InTech, Hyderabad (2010)zbMATHCrossRefGoogle Scholar
  2. 2.
    Exnar, F., Machac, O.: The travelling salesman problem and its application in logistic practice. WSEAS Trans. Bus. Econ. 8(4), 163–173 (2011)Google Scholar
  3. 3.
    Fahimnia, B., Luong, L., Marian, R.: Optimisation/simulation modeling of the integrated production-distribution plan: an innovative survey. WSEAS Trans. Bus. Econ. 5(3), 44–57 (2008)Google Scholar
  4. 4.
    Chopra, S.: Designing the distribution network in a supply chain. Transp. Res. Part E Logist. Transp. Rev. 39, 123–140 (2003)CrossRefGoogle Scholar
  5. 5.
    Guerra, L., Murino, E., Romano, E.: The location-routing problem: an innovative approach. In: 6th WSEAS Transactions on System Science and Simulation in Engineering, Venice, Italy, 21–23 November 2007Google Scholar
  6. 6.
    Laporte, G.: The traveling salesman problem: an overview of exact and approximate algorithms. Eur. J. Oper. Res. 59, 231–247 (1992)zbMATHCrossRefGoogle Scholar
  7. 7.
    Dantzig, G.B., Fulkerson, D.R., Johnson, S.M.: The solution of a large-scale traveling salesman problem. Oper. Res. 2, 393–410 (1954)MathSciNetGoogle Scholar
  8. 8.
    Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manag. Sci. 6, 80–91 (1959)zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Laporte, G.: The vehicle routing problem: an overview of exact and approximate algorithms. Eur. J. Oper. Res. 59, 345–358 (1992)zbMATHCrossRefGoogle Scholar
  10. 10.
    Toth, P., Vigo, D.: The Vehicle Routing Problem. SIAM Monographs on Discrete Mathematics and Applications. Society for Industrial and Applied Mathematics, Philadelphia (2001)Google Scholar
  11. 11.
    Solomon, M.: Algorithms for the vehicle routing problem with time windows. Transp. Sci. 29(2), 156–166 (1995)CrossRefGoogle Scholar
  12. 12.
    Parragh, S.N., Doerner, K.F., Hartl, R.F.: A survey on pickup and delivery problems, part I: transportation between customers and depot. J. Betriebswirt. 58, 21–51 (2008)CrossRefGoogle Scholar
  13. 13.
    Ralphs, T.K., Kopman, L., Pulleyblank, W.R., Trotter Jr., L.E.: On the capacitated vehicle routing problem. Math. Program. 94(2–3), 343–359 (2003)zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Toth, P., Vigo, D.: An exact algorithm for the vehicle routing problem with backhauls. Transp. Sci. 31(4), 372–385 (1997)zbMATHCrossRefGoogle Scholar
  15. 15.
    Clarke, G., Wright, J.W.: Scheduling of vehicles from a central depot to a number of delivery points. Oper. Res. 12, 568–581 (1964)CrossRefGoogle Scholar
  16. 16.
    Laporte, G.: What you should know about the vehicle routing problem. Nav. Res. Logist. 54(8), 811–819 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    LINGO: The Modeling Language and Optimizer. LINDO Systems Inc., Chicago (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Laila Kechmane
    • 1
    Email author
  • Benayad Nsiri
    • 1
  • Azeddine Baalal
    • 1
  1. 1.Faculty of Sciences Casablanca, MACS Laboratory, Department of Mathematics and ComputingUniversity Hassan IIMaarifMorocco

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