Abstract
The Big Triangle Small Triangle method has shown to be a powerful global optimization procedure to address continuous location problems. In the paper published in J. Global Optim. (37:305–319, 2007), Drezner proposes a rather general and effective approach for constructing the bounds needed. Such bounds are obtained by using the fact that the objective functions in continuous location models can usually be expressed as a difference of convex functions. In this note we show that, exploiting further the rich structure of such objective functions, alternative bounds can be derived, yielding a significant improvement in computing times, as reported in our numerical experience.
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Blanquero R., Carrizosa E., Conde E.: Finding GM-estimators with global optimization techniques. J. Global Optim. 21, 223–237 (2001)
Drezner Z.: A general global optimization approach for solving location problems in the plane. J. Global Optim. 37, 305–319 (2007)
Drezner T., Drezner Z.: Finding the optimal solution to the Huff competitive location model. Comput. Manag. Sci. 1, 193–208 (2004)
Drezner T., Drezner Z.: Equity models in planar location. Comput. Manag. Sci. 4, 1–16 (2007)
Drezner Z., Suzuki A.: The Big Triangle Small Triangle method for the solution of nonconvex facility location problems. Oper. Res. 52, 128–135 (2004)
Drezner Z., Wesolowsky G.O., Drezner T.: The gradual covering problem. Naval Res. Logist. 51, 841–855 (2004)
Hansen P., Peeters D., Richard D., Thisse J.-F.: The minisum and minimax location problems revisited. Oper. Res. 33, 1251–1265 (1985)
Plastria F.: GBSSS, the generalized big square small square method for planar single facility location. Eur. J. Oper. Res. 62, 163–174 (1992)
Plastria F.: Continuous location problems. In: Drezner, Z. (eds) Facility location, pp. 225–262. Springer Verlag, Berlin (1995)
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Blanquero, R., Carrizosa, E. Continuous location problems and Big Triangle Small Triangle: constructing better bounds. J Glob Optim 45, 389–402 (2009). https://doi.org/10.1007/s10898-008-9381-z
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DOI: https://doi.org/10.1007/s10898-008-9381-z