Abstract
We propose a general approach for constructing bounds required for the “Big Triangle Small Triangle” (BTST) method for the solution of planar location problems. Optimization problems, which constitute a sum of individual functions, each a function of the Euclidean distance to a demand point, are analyzed and solved. These bounds are based on expressing each of the individual functions in the sum as a difference between two convex functions of the distance, which is not the same as convex functions of the location. Computational experiments with nine different location problems demonstrated the effectiveness of the proposed procedure.
Similar content being viewed by others
References
Berman O., Wang J., Drezner Z., Wesolowsky G.O. (2003) A probabilistic minimax location problem on the plane. Ann. Oper. Res. 122, 59–70
Drezner T., Drezner Z. (2004) Finding the optimal Solution to the Huff competitive location model. Comput. Manage. Sci. 1, 193–208
Drezner T., Drezner Z.: Equity models in planar location. Comput. Manage. Sci. (2006a) (accepted for publication)
Drezner T., Drezner Z.: Lost demand in a competitive environment. in review (2006b)
Drezner Z., Drezner T., Wesolowsky G.O.: Location with acceleration-deceleration distance. in review (2006)
Drezner Z., Scott C.H.: Locating a service facility with some unserviced demand. IMA J Manage Math. in press (2006)
Drezner Z., Scott C.H., Song J.S. (2003) The central warehouse location problem revisited. IMA J Manage Math 14, 321–336
Drezner Z., Suzuki A. (2004) The big triangle small triangle method for the solution of non-convex facility location problems. Oper Res. 52, 128–135
Drezner Z., Wesolowsky G.O. (1991) The Weber problem on the plane with some negative weights. Inf. Syst. Oper. Res. 29, 87–99
Drezner Z., Wesolowsk G.O., Drezner T. (2004) The Gradual covering problem. Nav. Res Logist. 51, 841–855
Hansen P., Peeters D., Thisse J. (1981) On the location of an obnoxious facility. Sistemi Urbani 3, 299–317
Krarup J. (1998) On a complementary problem of Courant and Robbins. Location Sci. 6, 337–354
Maranas C.D., Floudas C.A. (1994) A global optimization method for Weber’s problem with attraction and repulsion. In Hager W.W., Hearn D.W., Pardalos P.M. (eds) Large Scale Optimization: State of the Art. Kluwer, Dordrecht, The Netherlands
Ohya T., Iri M., Murota K. (1984) Improvements of the incremental method of the Voronoi diagram with computational comparison of various algorithms. J. Oper. Res. Soc. Jpn 27, 306–337
Plastria F. (1992) GBSSS, the generalized big square small square method for planar single facility location. Euro. J. Oper. Res. 62, 163–174
Sugihara K., Iri M.(1994) A robust topology-oriented incremental algorithm for Voronoi diagram. Int. J. Comput Geome. Appli. 4, 179–228
Tellier L.N., Polanski B. (1989) The Weber problem: frequency and different solution types and extension to repulsive forces and dynamic processes. J. Reg. Sci. 29, 387–405
Tuy H. (1998) Convex Analysis and Global Optimization. Kluwer Academic Publishers, Dordrecht
Tuy H., Al-Khayyal F., Zhou F. (1995) A DC optimization method for single facility location problems. J. Global Optim. 7, 209-227
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Drezner, Z. A General Global Optimization Approach for Solving Location Problems in the Plane. J Glob Optim 37, 305–319 (2007). https://doi.org/10.1007/s10898-006-9051-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-006-9051-y