New models for locating a moving service facility |
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Authors: | Justo Puerto Antonio M Rodríguez-Chía |
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Institution: | (1) Facultad de Matemáticas, Universidad de Sevilla, C/Tarfia s/n, 41012 Sevilla, Spain;(2) Facultad de Ciencias del Mar, Universidad de Cádiz, Pol. Río San Pedro, Puerto Real, Cádiz, Spain |
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Abstract: | In this paper we analyze a new location problem which is a generalization of the well-known single facility location model.
This extension consists of introducing a general objective function and replacing fixed locations by trajectories. We prove
that the problem is well-stated and solvable. A Weiszfeld type algorithm is proposed to solve this generalized dynamic single
facility location problem on L
p
spaces of functions, with p ∈(1,2]. We prove global convergence of our algorithm once we have assumed that the set of demand functions and the initial
step function belong to a subspace of L
p
called Sobolev space. Finally, examples are included illustrating the application of the model to generalized regression
analysis and the convergence of the proposed algorithm. The examples also show that the pointwise extension of the algorithm
does not have to converge to an optimal solution of the considered problem while the proposed algorithm does. |
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Keywords: | Location Weber Problem Hyperbolic approximation |
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