On {\lambda}-Cent-Dians and Generalized-Center for Network Design: Definitions and Properties

Abstract

In this paper, we extend the notions of $\lambda$-cent-dian and generalized-center from Facility Location Theory to the more intricate domain of Network Design. Our focus is on the task of 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 pairs of demand. The $\lambda$-cent-dian problem studies the balance between efficiency and equity. We investigate the properties of the $\lambda$-cent-dian and generalized-center solution networks under the lens of equity, efficiency, and Pareto-optimality. We finally prove that the problems solved here are NP-hard.