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MIP models for connected facility location: A theoretical and computational study.

Stefan Gollowitzer¹, Ivana Ljubić¹

¹Department of Statistics and Decision Support Systems, Faculty of Business, Economics, and Statistics, University of Vienna, Austria.

Computers & Operations Research

|July 11, 2014

Summary

This study introduces mixed integer programming models for the connected facility location problem (ConFL), optimizing facility opening, assignment, and Steiner tree connection costs. Researchers developed new models and algorithms, achieving near-optimal solutions for complex network design problems.

Keywords:

Facility location LP-relaxations Mixed integer programming models Steiner trees

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Area of Science:

Operations Research
Combinatorial Optimization
Network Design

Background:

The connected facility location problem (ConFL) integrates facility location with Steiner tree requirements.
Minimizing costs involves facility opening, customer assignment, and network interconnections.

Purpose of the Study:

To present the first theoretical and computational study of mixed integer programming (MIP) models for ConFL.
To develop and compare various MIP formulations and algorithms for solving ConFL.

Main Methods:

Formulation of ConFL using seven compact and three exponential-size mixed integer programming models.
Transformation of ConFL into the Steiner arborescence problem.
Development of a branch-and-cut algorithm for two exponential-size models.

Main Results:

A hierarchy of the proposed models was established.
Extensive computational studies on large-scale instances (up to 1300 nodes) were conducted.
Optimal or near-optimal solutions (gaps < 0.6%) were achieved for most instances.

Conclusions:

The study provides robust theoretical and computational foundations for ConFL.
The developed MIP models and algorithms offer effective solutions for complex network optimization problems.
This research advances the field of facility location and network design.