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Generating and improving orthogonal designs by using mixed integer programming

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  • Vieira Jr., Hélcio
  • Sanchez, Susan
  • Kienitz, Karl Heinz
  • Belderrain, Mischel Carmen Neyra
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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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    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711006072
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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 215 (2011)
    Issue (Month): 3 (December)
    Pages: 629-638

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    Handle: RePEc:eee:ejores:v:215:y:2011:i:3:p:629-638

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Orthogonal design creation Design of experiments Statistics;

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    Cited by:
    1. Mandal, B.N. & Koukouvinos, C., 2014. "Optimal multi-level supersaturated designs through integer programming," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 183-191.
    2. Besseris, George J., 2012. "Profiling effects in industrial data mining by non-parametric DOE methods: An application on screening checkweighing systems in packaging operations," European Journal of Operational Research, Elsevier, vol. 220(1), pages 147-161.

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