λ-Cent-Dians and Generalized-Center for Network Design
arxiv(2024)
摘要
In this paper, we extend the notions of λ-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 λ-cent-dian problem studies the balance between efficiency and
equity. We investigate the properties of the λ-cent-dian and
generalized-center solution networks under the lens of equity, efficiency, and
Pareto-optimality. 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
λ∈[0,1], we study the implementation of a Benders decomposition
method to solve it at scale.
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