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Linearisierungsverfahren für Standortplanungsprobleme mit nichtlinearen Transportkosten


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  • Stolletz, Raik
  • Stolletz, Lars
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    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.

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    Bibliographic Info

    Paper provided by Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät in its series Hannover Economic Papers (HEP) with number dp-388.

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    Length: 20 pages
    Date of creation: Feb 2008
    Date of revision:
    Handle: RePEc:han:dpaper:dp-388

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

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    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. Fleischmann, Bernhard, 1993. "Designing distribution systems with transport economies of scale," European Journal of Operational Research, Elsevier, vol. 70(1), pages 31-42, October.
    3. HANSEN, Pierre & PEETERS, Dominique & RICHARD, Denis & THISSE, Jacques-François, . "The minisum and minimax location problems revisited," CORE Discussion Papers RP -683, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. 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).
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