Abstract
Our research sets in the field of k-facilities location-allocation problems. More precisely, we developed an approach, that aims to assess the sensitivity of centers to different metrics used to locate them, according to various spatial distributions of demands. We start by a concise state of the art. Then, we justify our approach with several examples on real or simulated data. Two mathematical formalisms of the 1–facility problem and the sensitivity estimation are provided. We finally propose different ways to assess the influence of points of demand on the centers, including exploratory spatial data analysis and random simulations on consequent samples.
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References
Haggett, P.: L’analyse spatiale en géographie humaine. Collection U. Armand Colin (1973)
Brunet, R., Ferras, R., Thery, H.: Les mots de la géographie, dictionnaire critique. Dynamiques du territoire. Montpellier: GIP RECLUS. la Documentation française, Paris (1993)
Hakimi, S.: Optimum locations of switching center and the absolute center and medians of a graph. Operations Research 12, 450–459 (1964)
Hansen, P., Labbé, M., Peeters, D., Thisse, J.F., Vernon Henderson, J.: Systems of cities and facility locations. In: Fundamentals of pure and applied economics, Harwood academic publisher, London (1987)
Shan, Y.: Location Transport and Landuse, Modelling Spatial-Temporal Information. Springer, Heidelberg (2005)
Drezner, Z., Hamacher, H.W.e.: Facility locations. Application and theories. Springer, Heidelberg (2004)
Griffith, D.A., Amrhein, C.G., Huriot, J.M.e.: Econometric advances in spatial modelling and methodology. Essays in honour of Jean Paelinck. Advanced studies in theoretical and applied econometrics, vol. 35 (1998)
Nickel, S., Puerto, J.: Location theory. A unified approach. Springer, Heidelberg (2005)
Thomas, I.: Transportation Networks and the Optimal Location of Human Activities, a numerical geography approach. Transports economics, management and policy. Edward Elgar, Northampton, Massachusetts (2002)
Brandeau, M.L., Saintfort, F., Pierskalla, W.P.: Operations research and health care, A handbook of methods and applications. Kluwer, Dordrecht (2004)
Buttazzo, G., Pratelli, A., Solimini, S., Stepanov, E.: Optimal urban networks via mass transportation. Lecture Notes in Mathematics, vol. 1961. Springer, Berlin (2009)
Fekete, S.P., Mitchell, J.S.B., Beurer, K.: On the continuous Fermat-Weber problem. Oper. Res. 53(1), 61–76 (2005)
Gugat, M., Pfeiffer, B.: Weber problems with mixed distances and regional demand. Math. Methods Oper. Res. 66(3), 419–449 (2007)
McAsey, M., Mou, L.: Existence and characterization of optimal locations. J. Global Optim. 15(1), 85–104 (1999)
Tierney, L.: Lisp-Stat, an object oriented environment for statistical computing and dynamic graphics. Wiley-Interscience Publication, John Wiley and Sons, New York (1990)
Cook, R.D., Weisberg, S.: Applied Regression Including Computing and Graphics. Wiley, Chichester (1999)
Young, F.W., Valero-Mora, P.M., Friendly, M.: Visual statistics. Wiley Series in Probability and Statistics, Seeing data with dynamic interactive graphics. Wiley-Interscience (John Wiley & Sons), Hoboken (2006)
Josselin, D.: Interactive geographical information system using lispstat: prototypes and applications. Journal of Statistical Software 13(6) (2005)
Josselin, D., Ladiray, D.: Combining l 1 and l 2 norms, for a more robust spatial analysis: the “meadian attitude”. Cybergeo 222 (2002)
Drezner, Z.: Sensitivity analysis of the optimal location of a facility. Naval Res. Logist. Quart. 32(2), 209–224 (1985)
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Ciligot-Travain, M., Josselin, D. (2009). Impact of the Norm on Optimal Locations. In: Gervasi, O., Taniar, D., Murgante, B., Laganà, A., Mun, Y., Gavrilova, M.L. (eds) Computational Science and Its Applications – ICCSA 2009. ICCSA 2009. Lecture Notes in Computer Science, vol 5592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02454-2_30
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DOI: https://doi.org/10.1007/978-3-642-02454-2_30
Publisher Name: Springer, Berlin, Heidelberg
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