Helena Gaspars-Wieloch

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The beginning of the article is devoted to a review of different location problems discussed in the literature. In the main part of this contribution the author presents and compares three discrete optimization models that may be useful for decision-makers considering the construction and activation of a chain of homogeneous facilities belonging to one proprietor. The models goal is to maximize his or her total profit and not the gain of each facility separately. The author shows the connection of the first model with the resources allocation problem. The influence of the distance between facilities on their territory served is emphasized particularly in the second and thirdapproach. The last model is partially based on Lösch’s and Voronoi’s principles.


Location problem, Discrete optimization models, Profit maximization, Homogeneous facilities, Territory served (range of coverage, influence area), Voronoi diagram (Dirichlet tessellation), Resources allocation problem, Local extrema method, Marginal profits method


[1] Brandeau M.L., Chiu S.S., [1994], Location of competing facilities in useroptimizing environment with market externalities, TS, 28 (2), 125-140.

[2] Brimberg J., Korach E., Eden-Chaim M., Mehrez A., [2001], The capacited p-facility locationproblem on the real line, „International Transactions of Operational Research”, 8, 727-738.

[3] Brimberg J., Love R.F., [1998], Solving a class of two-dimensional uncapacited location-allocation problems by dynamic programming, „Operations Research”, 46, 702-709.

[4] Dasci A., Laporte G., [2004], Location and pricing decisions of a multistore monopoly in a spatial market, „Journal of Regional Science”, 44, 489-515.

[5] Hotelling H., [1929], Stability in competition, „Economic Journal”, 39, 41-57.

[6] Lösch A., [1940], Die räumliche Ordnung der Wirtschaft, Jena.

[7] Mendes A.B., Themido I.H., [2004], Multi-outlet retail site location assessment, „International Transactions in Operational Research”, 11, 1-18.

[8] Palander T., [1935], Beiträge zur Standorttheorie, Almqvist & Wiksell, Uppsala.

[9] Ponsard C., [1979], Economie urbaine et espaces métriques, „Sistemi Urbani”, 1, 123-135.

[10] Sadahiro Y., [2005], Spatiotemporal analysis of the distribution of urban facilities in terms ofaccessibility, „Papers in Regional Science”, 84 (1), 61-84.

[11] Samuelson W.F., Marks S.G., [2002], Managerial Economics, Wiley Publishing CO, New York.

[12] Steinhaus H., [1956], Kalejdoskop Matematyczny, PWN, Warszawa.

[13] Stevens B.H., [1961], An application of game theory to a problem in location strategy, „Papers and Proceedings in Regional Science Association”, 7.

[14] Thünen J.H., [1826], Der isolierte Staat In Beziehung auf Landwirtschaft und Nationalökonomie, Hamburg.

[15] Voronoi G.F., [1908], Nouvelles applications des parametres continus a la théorie des formes quadratiques. Deuxieme mémoire. Recherche sur les paralléloedres primitifs, „Journal für Reineund Angewandte Mathematik”, 134, 198-287.

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