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Programación semidefinida aplicada a problemas de cantidad económica de pedido

  • Jenny Carolina Saldaña Cortés

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    Desde hace muchos años los modelos (S, s) han sido una herramienta importante de la teoría económica aplicada. Estos son modelos de propósito general de toma de decisiones económicas en situaciones donde se tienen dos características definidas: una variable de estado que afecta los pagos de flujo y los costos fijos que ejercen control sobre la variable de estado. El origen de este tipo de problemas son los modelos de control de inventario los cuales tienen como principal objetivo encontrar la mejor manera de equilibrar los costos de explotación del inventario, los costos asociados con el funcionamiento de inventario, y los costos asociados con la recepción y el procesamiento de órdenes. La solución computacional de este tipo problemas aumenta su nivel de complejidad si se le incluyen variables binarias con la finalidad de simular economías de escala.Tradicionalmente la optimización ha sido un fundamento básico de los economistasquienes necesariamente tienen que recurrir a modelos matemáticos para representar sistemas técnico-económicos que se comporten bajo teorías de racionalidad económica (maximizar beneficios socio-económicos), ya sea a nivel microeconómico o a nivel macroeconómico. En la medida que los algoritmos matemáticos de optimización se han vuelto más poderosos los modelos económicos reflejan más apropiadamente los sistemas técnico-económicos. Sin embargo, los problemas binarios siguen siendo un tema de investigación debido a los recursos computacionales que requieren para su solución. Este no es un problema superado.Este trabajo es un aporte de investigación en dirección a encontrar nuevos caminospara resolver problemas básicos tipo (S, s), como lo es de la cantidad económica depedido (EOQ)1 de una manera eficaz. Para tal fin se proponen métodos alternativos de relajación semidefinida de programas dinámicos con variables binarias. Con el objeto de ofrecer, una aproximación cuantitativa, como caso ilustrativo, los modelos desarrollados se aplican a datos procedentes de una firma representativa del sector cerámico colombiano.

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    File URL: http://economia.uniandes.edu.co/publicaciones/dcede2011-10.pdf
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    Paper provided by UNIVERSIDAD DE LOS ANDES-CEDE in its series DOCUMENTOS CEDE with number 008735.

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    Length: 43
    Date of creation: 20 Mar 2011
    Date of revision:
    Handle: RePEc:col:000089:008735
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    1. Andrew Caplin & John Leahy, 2010. "Economic Theory and the World of Practice: A Celebration of the ( S, s ) Model," Journal of Economic Perspectives, American Economic Association, vol. 24(1), pages 183-202, Winter.
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    9. Gaetan Belvaux & Laurence A. Wolsey, 2001. "Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs," Management Science, INFORMS, vol. 47(7), pages 993-1007, July.
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    12. Stadtler, Hartmut, 1996. "Mixed integer programming model formulations for dynamic multi-item multi-level capacitated lotsizing," European Journal of Operational Research, Elsevier, vol. 94(3), pages 561-581, November.
    13. Suerie, Christopher & Stadtler, Hartmut, 2003. "The Capacitated lot-sizing problem with linked lot sizes," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 20206, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
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