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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.14839 |
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Table of Contents:
- 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 \cite{bucarey2024on}, providing an algorithmic perspective on the generalized $λ$-centdian problem. In particular, we provide a mathematical formulation for $λ\geq 0$ 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 $λ\in[0,1]$, we study the implementation of a Benders decomposition method to solve it at scale.