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A column-oriented optimization approach for the generation of correlated random vectors

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Abstract

To induce a desired correlation structure among random variables, widely popular simulation software relies upon the method of Iman and Conover (IC). The underlying premise is that the induced Spearman rank correlation is a meaningful way to approximate other correlation measures among the random variables (e.g., Pearson’s correlation). However, as expected, the desired a posteriori correlation structure often deviates from the Spearman correlation structure. Rooted in the same principle of IC, we propose an alternative distribution-free method based on mixed-integer programming to induce a Pearson correlation structure to bivariate or multivariate random vectors. We also extend our distribution-free method to other correlation measures such as Kendall’s coefficient of concordance, Phi correlation coefficient, and relative risk. We illustrate our method in four different contexts: (1) the simulation of a healthcare facility, (2) the analysis of a manufacturing tandem queue, (3) the imputation of correlated missing data in statistical analysis, and (4) the estimation of the budget overrun risk in a construction project. We also explore the limits of our algorithms by conducting extensive experiments using randomly generated data from multiple distributions.

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Acknowledgements

The authors would like to thank Professor Jim Wilson from NC State University for sharing his encouraging and valuable input at an earlier stage of this work. The authors sincerely thank Professor Douglas Montgomery at Arizona State University for his valuable comments to improve the manuscript. Also, authors thank Gurobi and FICO for providing access to their commercial optimization solvers under their academic licensing programs. The authors would like to thank the two anonymous reviewers, whose comments greatly improved the article. This material is based upon work supported by Dr. Sefair’s National Science Foundation Grant No. 1740042.

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Authors and Affiliations

  1. School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, AZ, USA

    Jorge A. Sefair

  2. Centro para la Optimización y Probabilidad Aplicada (COPA), Departamento de Ingeniería Industrial, Universidad de los Andes, Bogotá, Colombia

    Oscar Guaje & Andrés L. Medaglia

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  1. Jorge A. Sefair
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Correspondence to Jorge A. Sefair.

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Sefair, J.A., Guaje, O. & Medaglia, A.L. A column-oriented optimization approach for the generation of correlated random vectors. OR Spectrum 43, 777–808 (2021). https://doi.org/10.1007/s00291-021-00620-5

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