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Linearisierungsverfahren für Standortplanungsprobleme mit nichtlinearen Transportkosten


  • Stolletz, Raik
  • Stolletz, Lars


This paper analyzes the Steiner-Weber-Problem with piecewise linear or piecewise constant transportation costs. These non-differentiable cost functions are analyzed using different one-step and dynamic linearization methods, which are based on approximations via average and marginal costs. An extensive numerical study compares these approaches with solutions based on linear and geometric regressions of the cost functions. In the numerical examples the dynamic linearization approaches give results near the optimal solutions. The relative deviations of the transportation costs of the approximated solutions to the minimal costs depend on the initialization of the dynamic approaches and improve as the number of demand points increases.

Suggested Citation

  • Stolletz, Raik & Stolletz, Lars, 2008. "Linearisierungsverfahren für Standortplanungsprobleme mit nichtlinearen Transportkosten," Hannover Economic Papers (HEP) dp-388, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  • Handle: RePEc:han:dpaper:dp-388

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    References listed on IDEAS

    1. Holmberg, Kaj & Ling, Jonas, 1997. "A Lagrangean heuristic for the facility location problem with staircase costs," European Journal of Operational Research, Elsevier, vol. 97(1), pages 63-74, February.
    2. repec:cor:louvrp:-683 is not listed on IDEAS
    3. Domschke, Wolfgang, 1997. "Logistik: Rundreisen und Touren. 4. Aufl," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 8162, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    4. Fleischmann, Bernhard, 1993. "Designing distribution systems with transport economies of scale," European Journal of Operational Research, Elsevier, vol. 70(1), pages 31-42, October.
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    More about this item


    Steiner-Weber-Problem; Standortplanung in der Ebene; stückweise lineare Transportkosten; Linearisierung; Dynamic Slope Scaling.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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