Generating and improving orthogonal designs by using mixed integer programming
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Authors
Vieira, Hélcio Jr.
Sanchez, Susan
Kienitz, Karl Heinz
Belderrain, Mischel Carmen Neyra
Subjects
Orthogonal design creation
Design of experiments
Statistics
Design of experiments
Statistics
Advisors
Date of Issue
2010
Date
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Abstract
Analysts faced with conducting experiments involving quantitative factors have a variety of potential
designs in their portfolio. However, in many experimental settings involving discrete-valued factors (particularly
if the factors do not all have the same number of levels), none of these designs are suitable.
In this paper, we present a mixed integer programming (MIP) method that is suitable for constructing
orthogonal designs, or improving existing orthogonal arrays, for experiments involving quantitative factors
with limited numbers of levels of interest. Our formulation makes use of a novel linearization of the
correlation calculation.
The orthogonal designs we construct do not satisfy the definition of an orthogonal array, so we do not
advocate their use for qualitative factors. However, they do allow analysts to study, without sacrificing
balance or orthogonality, a greater number of quantitative factors than it is possible to do with orthogonal
arrays which have the same number of runs.
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Article
Description
The article of record as published may be located at http://dx.doi.org/10.1016/j.ejor.2011.07.005
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Citation
European Journal of Operational Research, Volume 215, 2011, pp. 629–638
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.