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Link-Length Minimization in Networks

Author

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  • William Miehle

    (The Institute for Cooperative Research, University of Pennsylvania, Philadelphia, Pennsylvania)

Abstract

Three general methods are described for attacking link-length minimization problems. All methods assume a system of fixed points that are to be interconnected by a network of links the sum of whose lengths is a minimum. In the mechanical and numeric-analytic methods, the interconnections are made through a specified number of junction points whose locations are to be determined although the connections thereto are specified initially. Constraints on the variable points and weighting of links are possible. In the soap-film method, network configurations are produced directly without assuming variable points or junctions.

Suggested Citation

  • William Miehle, 1958. "Link-Length Minimization in Networks," Operations Research, INFORMS, vol. 6(2), pages 232-243, April.
    • Handle: RePEc:inm:oropre:v:6:y:1958:i:2:p:232-243
    DOI: 10.1287/opre.6.2.232
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    3. ReVelle, C. S. & Eiselt, H. A., 2005. "Location analysis: A synthesis and survey," European Journal of Operational Research, Elsevier, vol. 165(1), pages 1-19, August.
    4. James F. Campbell & Morton E. O'Kelly, 2012. "Twenty-Five Years of Hub Location Research," Transportation Science, INFORMS, vol. 46(2), pages 153-169, May.
    5. Vergis, Anastasios & Steiglitz, Kenneth & Dickinson, Bradley, 1986. "The complexity of analog computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 28(2), pages 91-113.
    6. Pey-Chun Chen & Pierre Hansen & Brigitte Jaumard & Hoang Tuy, 1998. "Solution of the Multisource Weber and Conditional Weber Problems by D.-C. Programming," Operations Research, INFORMS, vol. 46(4), pages 548-562, August.
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    8. Drexl, Andreas & Klose, Andreas, 2001. "Facility location models for distribution system design," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 546, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    9. Jing Yao & Alan T. Murray, 2014. "Serving regional demand in facility location," Papers in Regional Science, Wiley Blackwell, vol. 93(3), pages 643-662, August.
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    14. D. H. Aneesh & A. Mohanapriya & P. Renjith & N. Sadagopan, 2022. "Steiner tree in k-star caterpillar convex bipartite graphs: a dichotomy," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1221-1247, September.
    15. Klose, Andreas & Drexl, Andreas, 2005. "Facility location models for distribution system design," European Journal of Operational Research, Elsevier, vol. 162(1), pages 4-29, April.
    16. Simeon Reich & Truong Minh Tuyen, 2023. "The Generalized Fermat–Torricelli Problem in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 78-97, January.
    17. Franksen, Ole Immanuel & Grattan-Guinness, Ivor, 1989. "The earliest contribution to location theory? Spatio-economic equilibrium with Lamé and Clapeyron, 1829," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 31(3), pages 195-220.
    18. Fadda, Edoardo & Manerba, Daniele & Cabodi, Gianpiero & Camurati, Paolo Enrico & Tadei, Roberto, 2021. "Comparative analysis of models and performance indicators for optimal service facility location," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).

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