A new mathematical modeling and a genetic algorithm search for milk run problem (an auto industry supply chain case study)

  • S. J. Sadjadi
  • M. Jafari
  • T. Amini


The idea of Milk Run has been used in the context of logistic and supply chain problems in order to manage the transportation of materials. In this paper, we propose a new Milk Run method, as a mixed integer approach, to manage supply chain problems. Since the resulted problem formulation is NP-Hard, we use some meta-heuristic and compare the results with the optimal solutions of the proposed Milk Run method. The mathematical modeling of this paper is purposely customized for a special case of an auto industry. We implement the mathematical formulation and the meta-heuristic using some actual data and compare the results with the current strategy. The preliminary results indicate that the proposed method could provide a practical tool to significantly reduce the cost of logistic.


Logistic Milk run system Vehicle Routing Problem (VRP) 


  1. 1.
    Doerner KF, Gronalt M, Hartl RF, Kiechle G, Reimann M (2008) Exact and heuristic algorithms for the vehicle routing problem with multiple interdependent time windows. Comput Oper Res 35:3034–3048 doi: 10.1016/j.cor.2007.02.012 MATHCrossRefGoogle Scholar
  2. 2.
    Jozefowiez N, Semet F, Talbi E (2008) Multi-objective vehicle routing problems. Eur J Oper Res 189:293–309 doi: 10.1016/j.ejor.2007.05.055 MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Kallehauge B (2008) Formulations and exact algorithms for the vehicle routing problem with time windows. Comput Oper Res 35:2307–2330 doi: 10.1016/j.cor.2006.11.006 MATHCrossRefGoogle Scholar
  4. 4.
    Dantzig GB, Ramser JH (1959) The truck dispatching problem. Manage Sci 6:80–91MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Toth P, Vigo D (2002) Branch-and-bound algorithms for the capacitated VRP. In: Toth P, Vigo D (eds) The vehicle routing problem SIAM monographs on discrete mathematics and applications. SIAM, Philadalphia, pp 29–51Google Scholar
  6. 6.
    Christofides N, Mingozzi A, Toth P (1981) Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations. Math Program 20:255–282 doi: 10.1007/BF01589353 MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Alexandre LB, Teodor GC (2005) A cooperative parallel meta-heuristic for the vehicle routing problem with time windows. Comput Oper Res 32:1685–1708 doi: 10.1016/j.cor.2003.11.023 MATHCrossRefGoogle Scholar
  8. 8.
    Reimann M, Doerner K, Hartl RF (2004) D-Ants: Savings based Ants divide and conquer the vehicle routing problem. Comput Oper Res 31:563–591 doi: 10.1016/S0305-0548(03)00014-5 MATHCrossRefGoogle Scholar
  9. 9.
    Jeon G, Leep HR, Shim JY (2007) A vehicle routing problem solved by using a hybrid genetic algorithm. Comput Ind Eng 53:680–692 doi: 10.1016/j.cie.2007.06.031 CrossRefGoogle Scholar
  10. 10.
    Alvarenga GB, Mateus GR, de Tomi G (2007) A genetic and set partitioning two-phase approach for the vehicle routing problem with time windows. Comput Oper Res 34:1561–1584 doi: 10.1016/j.cor.2005.07.025 MATHCrossRefGoogle Scholar
  11. 11.
    Lacomme P, Prins C, Sevaux M (2006) A genetic algorithm for a bi-objective capacitated arc routing problem. Comput Oper Res 33:3473–3493 doi: 10.1016/j.cor.2005.02.017 MATHCrossRefGoogle Scholar
  12. 12.
    Berger J, Barkaoui M (2004) A parallel hybrid genetic algorithm for the vehicle routing problem with time windows. Comput Oper Res 31:2037–2053 doi: 10.1016/S0305-0548(03)00163-1 MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Du T, Wang FK, Lu P (2007) A real-time vehicle-dispatching system for consolidating milk runs. Transp Res Part E 43:565–577 doi: 10.1016/j.tre.2006.03.001 CrossRefGoogle Scholar
  14. 14.
    Christopher M (1998) Logistics and supply chain management-strategies for reducing cost and improving service, 2nd ed. Prentice Hall, LondonGoogle Scholar
  15. 15.
    Laporte G, Osman IH (1995) Routing problems: a bibliography. Ann Oper Res 61:227–262 doi: 10.1007/BF02098290 MATHCrossRefGoogle Scholar
  16. 16.
    Safaei N, Sadjadi SJ, Babakhani M (2006) An efficient genetic algorithm for determining the optimal price discrimination. Appl Math Comput 181:1693–1702 doi: 10.1016/j.amc.2006.03.022 MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2008

Authors and Affiliations

  1. 1.Department of Industrial EngineeringIran University of Science and TechnologyTehranIran

Personalised recommendations