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Pareto optimality and robustness in bi-blending problems

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  • Juan Herrera
  • Leocadio Casado
  • Eligius Hendrix
  • Inmaculada García

Abstract

The mixture design problem for two products concerns finding simultaneously two recipes of a blending problem with linear, quadratic and semi-continuity constraints. A solution of the blending problem minimizes a linear cost objective and an integer valued objective that keeps track of the number of raw materials that are used by the two recipes, i.e. this is a bi-objective problem. Additionally, the solution must be robust. We focus on possible solution approaches that provide a guarantee to solve bi-blending problems with a certain accuracy, where two products are using (partly) the same scarce raw materials. The bi-blending problem is described, and a search strategy based on Branch-and-Bound is analysed. Specific tests are developed for the bi-blending aspect of the problem. The whole is illustrated numerically. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • Juan Herrera & Leocadio Casado & Eligius Hendrix & Inmaculada García, 2014. "Pareto optimality and robustness in bi-blending problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 254-273, April.
    • Handle: RePEc:spr:topjnl:v:22:y:2014:i:1:p:254-273
    DOI: 10.1007/s11750-012-0253-9
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    References listed on IDEAS

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