TY - JOUR

T1 - The Connected Facility Location Polytope

AU - Leitner, M.

AU - Ljubic, Ivana

AU - Salazar-González, Juan-José

AU - Sinnl, Markus

PY - 2018

Y1 - 2018

N2 - We analyze the polytope associated with a combinatorial problem that combines the Steiner tree problem and the uncapacitated facility location problem. The problem, called connected facility location problem, is motivated by a real-world application in the design of a telecommunication network, and concerns with deciding the facilities to open, the assignment of customers to open facilities, and the connection of the open facilities through a Steiner tree. Several solution approaches are proposed in the literature, and the contribution of our work is a polyhedral analysis for the problem. We compute the dimension of the polytope, present valid inequalities, and analyze conditions for these inequalities to be facet defining. Some inequalities are taken from the Steiner tree polytope and the uncapacitated facility location polytope. Other inequalities are new.

AB - We analyze the polytope associated with a combinatorial problem that combines the Steiner tree problem and the uncapacitated facility location problem. The problem, called connected facility location problem, is motivated by a real-world application in the design of a telecommunication network, and concerns with deciding the facilities to open, the assignment of customers to open facilities, and the connection of the open facilities through a Steiner tree. Several solution approaches are proposed in the literature, and the contribution of our work is a polyhedral analysis for the problem. We compute the dimension of the polytope, present valid inequalities, and analyze conditions for these inequalities to be facet defining. Some inequalities are taken from the Steiner tree polytope and the uncapacitated facility location polytope. Other inequalities are new.

KW - Facets

KW - Facility location

KW - Steiner trees

KW - Valid inequalities

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U2 - 10.1016/j.dam.2016.08.010

DO - 10.1016/j.dam.2016.08.010

M3 - Article

VL - 234

SP - 151

EP - 167

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -