Carrizosa Priego, Emilio JoséMuñoz Márquez, ManuelPuerto Albandoz, Justo2021-04-262021-04-261998-01-01Carrizosa Priego, E.J., Muñoz Márquez, M. y Puerto Albandoz, J. (1998). Location and shape of a rectangular facility in ℝn. Convexity properties. Convexity properties. Mathematical Programming, 83 (2), 277-290.0025-56101436-4646https://hdl.handle.net/11441/107727In this paper we address a generalization of the Weber problem, in which we seek for the center and the shape of a rectangle (the facility) minimizing the average distance to a given set (the demand-set) which is not assumed to be finite. Some theoretical properties of the average distance are studied, and an expression for its gradient, involving solely expected distances to rectangles, is obtained. This enables the resolution of the problem by standard optimization techniques.application/pdf13 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Regional locationFacilitiesAverage distanceinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1007/BF02680563