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Towards the Solution of the (Generalised) Multi-Weber Problem

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  • K E Rosing

    (Economisch-Googrofisch Instituut, Erasmus Universiteit Rotterdam, Postbus 1738, 3000 Dr Rotterdam, The Netherlands; and Department of Geography, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2)

Abstract

Despite the long history of the multi-Weber problem and the generalised multi-Weber problem, there is no general optimal method for its solution. This paper has two aims. The first aim is a study of the shape of the objective function of the single and multi-Weber problem. The form of the objective function and the relation of a heuristic to it are critical to the decision to use a heuristic or to seek an optimal solution. The objective function of the multi-Weber problem is shown to be extremely steep in the neighbourhood of the optimal solution, indicating the importance of an optimal rather than heuristic solution. The second aim is a description of a two-step algorithm which, although it cannot guarantee optimality, will frequently terminate optimally and thus appears to be superior to other available heuristics.

Suggested Citation

  • K E Rosing, 1991. "Towards the Solution of the (Generalised) Multi-Weber Problem," Environment and Planning B, , vol. 18(3), pages 347-360, September.
    • Handle: RePEc:sae:envirb:v:18:y:1991:i:3:p:347-360
    DOI: 10.1068/b180347
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    References listed on IDEAS

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    1. S. L. Hakimi, 1965. "Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems," Operations Research, INFORMS, vol. 13(3), pages 462-475, June.
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    2. Alan Murray, 1998. "Assessing clustering methods for exploratory spatial data analysis," ERSA conference papers ersa98p346, European Regional Science Association.

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