The Design of the Physical Distribution System with the Application of the Multiple Objective Mathematical Programming. Case Study

  • Maciej Hapke
  • Andrzej Jaszkiewicz
  • Jacek Żak
Part of the Advances in Soft Computing book series (AINSC, volume 12)


The paper presents the multiobjective optimization of the all-Polish physical distribution system of cosmetics, detergents and washing articles. The research report refers to a real life case. The optimization process is focused on minimization of both total distribution cost and the delivery time within the distribution system. The primary concern of the project is to define the number and the location of the warehouses in the distribution network. The optimization process leads to the redesign of the existing distribution system. The problem is formulated in terms of bi-criteria mathematical mixed-integer programming. It has been solved with the application of an extended version of MS Excel Solver — Premium Solver Plus. A set of Pareto-optimal distribution systems has been generated. The number of Regional Distribution Centers (RDC-s) ranges from 7 to 23 in Pareto-optimal solutions. The results of the experiment are promising.


Distribution System Delivery Time Potential Location Single Objective Optimization Total Annual Cost 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Arthur Andersen and Co. (1992). Facing the forces of change 2000: The new realities in wholesale Distribution, Washington DC, Distribution Research and Education Foundation.Google Scholar
  2. [2]
    Bodin L., Golden B., Assad A., Ball M. (1981). The state of the art in the routing and scheduling of vehicles and crews, Final Report, Univ. Research for U.S. Dept. of Transportation, National Technical Information Service, Springfield.Google Scholar
  3. [3]
    Fowler R.J., Paterson M S, Tanimoto S.L., Optimal packing and covering in the plane are NP-hard. Information Processing Letters, 12, 133–137, 1987.CrossRefGoogle Scholar
  4. [4]
    Gopal Ch., Gypress H. (1993). Integrated distribution management,Business One Inwin.Google Scholar
  5. [5]
    McKinnon A. (1989). Physical distribution systems, Routledge, New York.Google Scholar
  6. [6]
    Ross D. (1996). Distribution. Planning and Control, Kluwer Academic Publishers, Boston-Dordrecht, London.Google Scholar
  7. [7]
    Solomon M. (1997). Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research, 55.Google Scholar
  8. [8]
    Sousa J. (1991). A computer based interactive approach to crew scheduling, EJOR, 55 /3, 233–258.CrossRefGoogle Scholar
  9. [9]
    Steuer R.E. (1986). Multiple criteria optimization - theory, computation and application, Wiley, New York.Google Scholar
  10. [10]
    Tzeng G.-H., Tu S.-W. (1992). Multiobjective and fuzzy time-window heuristic method in vehicle routing problems, Proceedings of the Tenth International Conference on Multiple Criteria Decision Making, Taipei 19–24.07.93, vol. 4, 217–227.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Maciej Hapke
    • 1
  • Andrzej Jaszkiewicz
    • 1
  • Jacek Żak
    • 2
  1. 1.Institute of Computing SciencePoznań University of TechnologyPoznańPoland
  2. 2.Institute of Working Machines & VehiclesPoznań University of TechnologyPoznańPoland

Personalised recommendations