首页|On λ-cent-dians and generalized-center for network design: formulations and algorithms

On λ-cent-dians and generalized-center for network design: formulations and algorithms

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  • NETL
  • NSTL
  • Springer Nature
In this paper, we study the λ-centdian problem in the domain of network design. The focus is on designing a sub-network within a given underlying network while adhering to a budget constraint. This sub-network is intended to efficiently serve a collection of origin/destination demand pairs. We extend the work presented in Bucarey et al. (On λ-cent-dians and generalized-center for network design: definitions and properties, 2024), providing an algorithmic perspective on the generalized λ-centdian problem. In particular, we provide a mathematical formulation for λ ≥ 0 and discuss the bilevel structure of this problem for λ ≥ 1. Furthermore, we describe a procedure to obtain a complete parametrization of the Pareto-optimality set based on solving two mixed integer linear formulations by introducing the concept of maximum λ-cent-dian. We evaluate the quality of the different solution concepts using some inequality measures. Finally, for X e [0, 1], we study the implementation of a Benders decomposition method to solve it at scale.

λ-Cent-dian problemGeneralized-center problemNetwork designBenders decompositionPareto-optimality

Victor Bucarey、Natividad Gonzalez-Bianco、Martine Labbe、Juan A. Mesa

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Universidad de O'Higgins, Institute of Engineering Sciences, Rancagua, Chile||Institute Sistemas Complejos de Ingenieria (ISCI), Santiago Centro, Chile

Universidad Loyola Andaluca, Departamento de Metodos Cuantitativos, Dos Hermanas, Spain

Universite Libre de Bruxelles, Departement d'Informatique, Brassels, Belgium||Inria Lille-Nord Europe, Villeneuve d'Ascq, France

Universidad de Sevilla, Departamento de Matematica Aplicada Ⅱ, Sevilla, Spain||Universidad de Sevilla, Instituto de Matem&ticas de la Sevilla, Sevilla, Spain

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2025

10.1007/s10479-025-06583-y

Annals of operations research

Annals of operations research

ISSN：0254-5330
年,卷(期)：2025.349(3)
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