Polyhedral Analysis for Concentrator Location Problems

Abstract

Abstract. The concentrator location problem is to choose a subset of a given terminal set to install concentrators and to assign each remaining terminal node to a concentrator to minimize the cost of installation and assignment. The concentrators may have capacity constraints. We study the polyhedral properties of concentrator location problems with different capacity structures. We develop a branch and cut algorithm and present computational results.

A computational evaluation of a general branch-and-price framework for capacitated network location problems

“…In the CCLP each location variable y j can be replaced by a corresponding assignment variable x jj . Although some authors [36] used the name "Capacitated Concentrators" to indicate the SS-CFLP, we follow [27] and [26] and we indicate as "concentrator problems" the models in which variables x jj replace variables y j to represent location decisions.…”

“…The polyhedral structure of these problems has recently been studied in detail by Labbé and Yaman [27] [26]. Problems on networks with up to 100 terminals can be solved to optimality with a branch-and-cut approach in half an hour of CPU time.…”

Solving the hub location problem in a star–star network

“…It is full dimensional, i.e., dim(P 0 ) = n(n − 1). Its polyhedral properties are studied in Labbé and Yaman [30].…”

“…Labbé and Yaman [30] prove that the nonnegativity constraints x ij ≥ 0 and inequalities (9) define facets of P 0 . Two immediate corollaries of these results and Corollary 3 are given below: Corollary 4.…”

Polyhedral Analysis for the Uncapacitated Hub Location Problem with Modular Arc Capacities

“…(See, e.g., [2], [4], and [14] for polyhedral properties of the stable set polytope and see [9] for facet defining inequalities of P ∅ .) Polytope P ∅ is interesting since P ∅ = P roj x (P A ).…”