Branch-and-Cut-and-Price for Capacitated Connected Facility Location
Journal of Mathematical Modelling and Algorithms
A node splitting technique for two level network design problems with transition nodes
INOC'11 Proceedings of the 5th international conference on Network optimization
MIP modeling of incremental connected facility location
INOC'11 Proceedings of the 5th international conference on Network optimization
EUROCAST'11 Proceedings of the 13th international conference on Computer Aided Systems Theory - Volume Part I
Layered Graph Approaches to the Hop Constrained Connected Facility Location Problem
INFORMS Journal on Computing
A cutting plane algorithm for the Capacitated Connected Facility Location Problem
Computational Optimization and Applications
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This article comprises the first theoretical and computational study on mixed integer programming (MIP) models for the connected facility location problem (ConFL). ConFL combines facility location and Steiner trees: given a set of customers, a set of potential facility locations and some inter-connection nodes, ConFL searches for the minimum-cost way of assigning each customer to exactly one open facility, and connecting the open facilities via a Steiner tree. The costs needed for building the Steiner tree, facility opening costs and the assignment costs need to be minimized. We model ConFL using seven compact and three mixed integer programming formulations of exponential size. We also show how to transform ConFL into the Steiner arborescence problem. A full hierarchy between the models is provided. For two exponential size models we develop a branch-and-cut algorithm. An extensive computational study is based on two benchmark sets of randomly generated instances with up to 1300 nodes and 115,000 edges. We empirically compare the presented models with respect to the quality of obtained bounds and the corresponding running time. We report optimal values for all but 16 instances for which the obtained gaps are below 0.6%.