The Connected Facility Location Polytope

M. Leitner, Ivana Ljubic, Juan-José Salazar-González, Markus Sinnl

Research output: Contribution to JournalArticleAcademicpeer-review


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.
Original languageEnglish
Pages (from-to)151-167
Number of pages17
JournalDiscrete Applied Mathematics
Publication statusPublished - 2018


This work is supported by the Vienna Science and Technology Fund (WWTF) through project ICT15-014. M. Leitner, I. Ljubić, and M. Sinnl are supported by the Austrian Research Fund (FWF) under grants I892-N23 and P26755-N19 . J.J. Salazar-González is supported by the Spanish Government through the project MTM2015-63680-R (MINECO/FEDER, UE).

FundersFunder number
Austrian Research Fund
Spanish GovernmentMTM2015-63680-R
Vienna Science and Technology FundICT15-014
Austrian Science FundP26755-N19, I892-N23


    • Facets
    • Facility location
    • Steiner trees
    • Valid inequalities


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