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