<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0034-7426</journal-id>
<journal-title><![CDATA[Revista Colombiana de Matemáticas]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.colomb.mat.]]></abbrev-journal-title>
<issn>0034-7426</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0034-74262007000300006</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Control of inventories under non-convex polynomial cost functions]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[HERNÁNDEZ FLÓREZ]]></surname>
<given-names><![CDATA[MÓNICA]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad de los Andes Departamento de Matemáticas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
</aff>
<pub-date pub-type="pub">
<day>29</day>
<month>10</month>
<year>2007</year>
</pub-date>
<pub-date pub-type="epub">
<day>29</day>
<month>10</month>
<year>2007</year>
</pub-date>
<volume>41</volume>
<fpage>221</fpage>
<lpage>246</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262007000300006&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262007000300006&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262007000300006&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[I propose an alternative method for computing effectively the solution of the control inventory problem under non-convex polynomial cost functions. I apply the method of moments in global optimization to transform the corresponding, non-convex dynamic programming problem into an equivalent optimal control problem with linear and convex structure. I device computational tools based on convex optimization, to solve the convex formulation of the original problem.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Propongo un método alternativo para calcular de manera efectiva la solución del problema de control de inventarios bajo funciones de costo polinomiales no convexas. Aplico el método de momentos en optimización global para transformar el correspondiente problema de programación dinámica no convexo en un problema de control óptimo equivalente con estructura lineal y convexa. Diseño herramientas computacionales basada en optimización convexa para resolver la formulación convexa del problema original.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Method of moments]]></kwd>
<kwd lng="en"><![CDATA[control of inventories]]></kwd>
<kwd lng="en"><![CDATA[non-convex polynomial functions]]></kwd>
<kwd lng="en"><![CDATA[global optimization]]></kwd>
<kwd lng="es"><![CDATA[Método de momentos]]></kwd>
<kwd lng="es"><![CDATA[control de inventorias]]></kwd>
<kwd lng="es"><![CDATA[funciones polinomiales no convexas]]></kwd>
<kwd lng="es"><![CDATA[optimización global]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[   <font face="verdana" size="2">      <p><b><font size="4">    <center>Control of inventories under non-convex polynomial cost functions</center></font></b></p>      <center>M&Oacute;NICA HERN&Aacute;NDEZ FL&Oacute;REZ<sup>1</sup></center></p> <sup>1</sup> Departamento de Matem&aacute;ticas, Universidad de los Andes, Bogot&aacute;, Colombia. E-mail: <a href="mailto:monic-he@uniandes.edu.co">monic-he@uniandes.edu.co </a>  <hr size=1>      <p><b>    <center>Abstract</center></b></p>      <p align="justify"> I propose an alternative method for computing effectively the solution of the control inventory problem under non-convex polynomial cost functions. I apply the method of moments in global optimization to transform the corresponding, non-convex dynamic programming problem into an equivalent optimal control problem with linear and convex structure. I device computational tools based on convex optimization, to solve the convex formulation of the original problem. </p>      <p><b>Key words:</b> Method of moments, control of inventories, non-convex polynomial functions, global optimization. </p>  <hr size=1> <i>2000 Mathematics Subject Classification: Primary: 54H25. Secondary: 47H10</i> <hr size=1>      <p><b>    <center>Resumen</center></b></p>      ]]></body>
<body><![CDATA[<p align="justify"> Propongo un m&eacute;todo alternativo para calcular de manera efectiva la soluci&oacute;n del problema de control de inventarios bajo funciones de costo polinomiales no convexas. Aplico el m&eacute;todo de momentos en optimizaci&oacute;n global para transformar el correspondiente problema de programaci&oacute;n din&aacute;mica no convexo en un problema de control &oacute;ptimo  equivalente con estructura lineal y convexa. Diseño herramientas computacionales basada en optimizaci&oacute;n convexa para resolver la formulaci&oacute;n convexa del problema original. </p>      <p><b>Palabras clave:</b> M&eacute;todo de momentos, control de inventorias, funciones polinomiales no convexas, optimizaci&oacute;n global.</p>  <hr size=1>      <p>Texto completo disponible en <a href="pdf/rcm/v41s1/v41s1a6.pdf">PDF</a></p>  <hr size=1>      <p><b><font size="3">References</font></b></p>      <!-- ref --><p> 1 N. I. 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