Affiliations: [a] Operations Research Department, CSX Transportation, Jacksonville, FL, USA | [b] Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA
Correspondence:
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Corresponding author: Yanfeng Ouyang, Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 North Mathews Avenue, Urbana, IL, USA. Tel.: +1 217 333 9858; Fax: +1 217 333 1924; E-mail: yfouyang@illinois.edu.
Abstract: The paper proposes methodologies to adaptively convert discrete spatial data into continuous functions in a metric space so that the continuum approximation (CA) optimization framework can be applied to a general class of discrete facility location problems. We implement a Voronoi diagram based interpolation method to estimate the optimal system cost and the optimal number of facilities, and then develop an enhanced disk model to compute near-optimum facility location design, both based on discrete input data. The results from the proposed CA method can be further improved by neighborhood search algorithms. Numerical experiments show that the proposed CA framework effectively finds near-optimum solutions to very large problem instances within a short time.
Keywords: Continuum approximation, discrete, facility location, Voronoi diagram, disk model, fast interchange
