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New models for locating a moving service facility

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  • Justo Puerto
  • Antonio Rodríguez-Chía

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. Copyright Springer-Verlag 2006

Suggested Citation

  • Justo Puerto & Antonio Rodríguez-Chía, 2006. "New models for locating a moving service facility," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 31-51, February.
    • Handle: RePEc:spr:mathme:v:63:y:2006:i:1:p:31-51
    DOI: 10.1007/s00186-005-0011-y
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    References listed on IDEAS

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    1. Jack Brimberg & Robert F. Love, 1993. "Global Convergence of a Generalized Iterative Procedure for the Minisum Location Problem with lp Distances," Operations Research, INFORMS, vol. 41(6), pages 1153-1163, December.
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    Cited by:

    1. Victor Blanco & Justo Puerto & Safae El Haj Ben Ali, 2014. "Revisiting several problems and algorithms in continuous location with $$\ell _\tau $$ ℓ τ norms," Computational Optimization and Applications, Springer, vol. 58(3), pages 563-595, July.
    2. C. Valero Franco & A. Rodríguez-Chía & I. Espejo Miranda, 2008. "The single facility location problem with average-distances," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 164-194, July.

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