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

Víctor Bucarey (), Natividad González-Blanco (), Martine Labbé () and Juan A. Mesa ()
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Víctor Bucarey: Institute of Engineering Sciences
Natividad González-Blanco: Departamento de Métodos Cuantitativos
Martine Labbé: Département d’Informatique
Juan A. Mesa: Departamento de Matemática Aplicada II

Annals of Operations Research, 2025, vol. 349, issue 3, No 3, 1553-1573

Abstract: Abstract In this paper, we study the $$\lambda $$ 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 $$\lambda $$ λ -cent-dians and generalized-center for network design: definitions and properties, 2024), providing an algorithmic perspective on the generalized $$\lambda $$ λ -centdian problem. In particular, we provide a mathematical formulation for $$\lambda \ge 0$$ λ ≥ 0 and discuss the bilevel structure of this problem for $$\lambda >1$$ 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 $$\lambda $$ λ -cent-dian. We evaluate the quality of the different solution concepts using some inequality measures. Finally, for $$\lambda \in [0,1]$$ λ ∈ [ 0 , 1 ] , we study the implementation of a Benders decomposition method to solve it at scale.

Keywords: $$\lambda $$ λ -Cent-dian problem; Generalized-center problem; Network design; Benders decomposition; Pareto-optimality (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10479-025-06583-y

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