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Combining Minsum And Minmax: A Goal Programming Approach

Author

Listed:
  • Emilio Carrizosa

    (Facultad de Matemáticas, Universidad de Sevilla, C/ Tarfia s/n, 41012 Sevilla, Spain)

  • Dolores Romero-Morales

    (Decision and Information Sciences Department, Rotterdam School of Management, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands, and Facultad de Matemáticas, Universidad de Sevilla, C/ Tarfia s/n, 41012 Sevilla, Spain)

Abstract

A number of methods for multiple-objective optimization problems (MOP) give as solution to MOP the set of optimal solutions for some single-objective optimization problems associated with it. Well-known examples of these single-objective optimization problems are the minsum and the minmax. In this note, we propose a new parametric single-objective optimization problem associated with MOP by means of Goal Programming ideas. We show that the minsum and minmax are particular instances, so we are somehow combining minsum and minmax by means of a parameter. Moreover, such parameter has a clear meaning in the value space. Applications of this parametric problem to classical models in Locational Analysis are discussed.

Suggested Citation

  • Emilio Carrizosa & Dolores Romero-Morales, 2001. "Combining Minsum And Minmax: A Goal Programming Approach," Operations Research, INFORMS, vol. 49(1), pages 169-174, February.
    • Handle: RePEc:inm:oropre:v:49:y:2001:i:1:p:169-174
    DOI: 10.1287/opre.49.1.169.11190
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    References listed on IDEAS

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    1. Erkut, Erhan & Neuman, Susan, 1989. "Analytical models for locating undesirable facilities," European Journal of Operational Research, Elsevier, vol. 40(3), pages 275-291, June.
    2. Tamiz, Mehrdad & Jones, Dylan & Romero, Carlos, 1998. "Goal programming for decision making: An overview of the current state-of-the-art," European Journal of Operational Research, Elsevier, vol. 111(3), pages 569-581, December.
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    Cited by:

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    2. Rafael Blanquero & Emilio Carrizosa & Pepa Ramírez-Cobo & M. Remedios Sillero-Denamiel, 2021. "A cost-sensitive constrained Lasso," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(1), pages 121-158, March.
    3. V M Miori, 2011. "A multiple objective goal programming approach to the truckload routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(8), pages 1524-1532, August.

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