Approximation of discrete spatial data for continuous facility location design

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.

[1]  Steven Fortune,et al.  A sweepline algorithm for Voronoi diagrams , 1986, SCG '86.

[2]  Mauricio G. C. Resende,et al.  A fast swap-based local search procedure for location problems , 2007, Ann. Oper. Res..

[3]  George S. Lueker,et al.  A data structure for orthogonal range queries , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[4]  Polly Bart,et al.  Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph , 1968, Oper. Res..

[5]  R. A. Whitaker,et al.  A Fast Algorithm For The Greedy Interchange For Large-Scale Clustering And Median Location Problems , 1983 .

[6]  Hojjat Adeli,et al.  Wavelets in Intelligent Transportation Systems , 2005 .

[7]  Yanfeng Ouyang,et al.  Integrated Planning of Supply Chain Networks and Multimodal Transportation Infrastructure Expansion: Model Development and Application to the Biofuel Industry , 2013, Comput. Aided Civ. Infrastructure Eng..

[8]  P. Hansen,et al.  Variable neighborhood search for the p-median , 1997 .

[9]  Albert,et al.  Food , 1917, Nature.

[10]  Mark S. Daskin,et al.  Network and Discrete Location: Models, Algorithms and Applications , 1995 .

[11]  M. Rosenblatt.  Remarks on Some Nonparametric Estimates of a Density Function , 1956 .

[12]  Yanfeng Ouyang,et al.  Reliable Facility Location Design Under the Risk of Disruptions , 2010, Oper. Res..

[13]  G. F. Newell,et al.  Configuration of physical distribution networks , 1986, Networks.

[14]  G. F. Newell.  Dispatching Policies for a Transportation Route , 1971 .

[15]  Yanfeng Ouyang,et al.  Discretization and Validation of the Continuum Approximation Scheme for Terminal System Design , 2003, Transp. Sci..

[16]  Xiaopeng Li,et al.  Effects of Disruption Risks on Biorefinery Location Design: Discrete and Continuous Models , 2015 .

[17]  Yanfeng Ouyang,et al.  A continuum approximation approach to reliable facility location design under correlated probabilistic disruptions , 2010 .

[18]  Mark de Berg,et al.  Computational geometry: algorithms and applications, 3rd Edition , 1997 .

[19]  Yanfeng Ouyang,et al.  A Continuum Approximation Approach to Competitive Facility Location Design Under Facility Disruption Risks , 2013 .

[20]  Yanfeng Ouyang,et al.  Dynamic Planning of Facility Locations with Benefits from Multitype Facility Colocation , 2013, Comput. Aided Civ. Infrastructure Eng..

[21]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .