<?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>0121-750X</journal-id>
<journal-title><![CDATA[Ingeniería]]></journal-title>
<abbrev-journal-title><![CDATA[ing.]]></abbrev-journal-title>
<issn>0121-750X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Distrital Francisco José de Caldas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0121-750X2022000100205</article-id>
<article-id pub-id-type="doi">10.14483/23448393.18468</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[A P-Robustness Approach for the Stochastic Inventory Routing Problem]]></article-title>
<article-title xml:lang="es"><![CDATA[Una aproximación a través del modelo p-robusto para el problema estocástico de ruteo e inventario]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Franco]]></surname>
<given-names><![CDATA[Carlos]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Figueroa-García]]></surname>
<given-names><![CDATA[Juan Carlos]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Tenjo-García]]></surname>
<given-names><![CDATA[Jhoan Sebastián]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad del Rosario  ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Distrital Francisco José de Caldas  ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Nacional de Colombia  ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>04</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>04</month>
<year>2022</year>
</pub-date>
<volume>27</volume>
<numero>1</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0121-750X2022000100205&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0121-750X2022000100205&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0121-750X2022000100205&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract  Context:  Approaches to logistics solutions through mathematical optimization are widely studied in the literature given their importance for business operations and their computational complexity. In this way, studying the uncertainty associated to operations is a key factor in modeling and decision-making.  Method:  A stochastic mathematical model is proposed for the Inventory Routing Problem (IRP), considering scenarios with variation in the demands. To obtain a suitable approach, a p-robustness approach and the reformulation of the classical IRP are presented.  Results:  The performed experiments show the benefits of including uncertainty through a p-robust approach when they are analyzed within an instance of the IRP. Moreover, given the selected modeling, the benefits of combining the approaches can be analyzed.  Conclusions:  The development of stochastic approaches for decision-making applied to the IRP allow analysts to handle uncertainty and also reduce the complexity of decision when combining different types of problems (Routing + Inventory) in the same model.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen  Contexto:  Las aproximaciones de soluciones logísticas a través de la optimización matemática son altamente estudiadas en la literatura debido a su importancia en las operaciones de las compañías y su complejidad computacional. En este sentido, el estudio de la incertidumbre asociada a la operación es un factor fundamental del modelamiento y la toma de decisiones.  Método:  Un modelo matemático estocástico es propuesto para el problema combinado de ruteo e inventario (IRP), considerando escenarios de variaciones en la demanda. Para obtener un enfoque adecuado, se presenta una aproximación de p-robusto y la reformulación del problema clásico de aplicación.  Resultados:  Los experimentos realizados muestran los beneficios de incluir la incertidumbre a través de la aproximación de p-robusto cuando se analizan en el marco de una instancia del IRP. También, dado el tipo de modelado seleccionado, se pueden analizar los beneficios de combinar las aproximaciones.  Conclusiones:  El desarrollo de aproximaciones estocásticas de toma de decisiones aplicadas al problema IRP permite a los analistas gestionar la incertidumbre y reducir la complejidad de las decisiones cuando se combinan diferentes tipos de problemas (Ruteo + Inventario) en un mismo modelo.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[inventory routing problem]]></kwd>
<kwd lng="en"><![CDATA[p-robustness]]></kwd>
<kwd lng="en"><![CDATA[uncertainty.]]></kwd>
<kwd lng="es"><![CDATA[problema de ruteo e inventarios]]></kwd>
<kwd lng="es"><![CDATA[p-robusto]]></kwd>
<kwd lng="es"><![CDATA[incertidumbre.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>[1]</label><nlm-citation citation-type="journal">
<collab>Cordeau, and G. Laporte</collab>
<article-title xml:lang=""><![CDATA[Consistency in multi-vehicle inventory-routing,&#8221; Transp. Res. Part C (1) C. Franco-Franco and J. C. Figueroa-García, &#8220;A column generation-based algorithm for solving combined inventory and routing problems]]></article-title>
<source><![CDATA[Ingeniare]]></source>
<year>2016</year>
<volume>24</volume>
<numero>2</numero>
<issue>2</issue>
</nlm-citation>
</ref>
<ref id="B2">
<label>[2]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Aghezzaf]]></surname>
<given-names><![CDATA[E.-H.]]></given-names>
</name>
<name>
<surname><![CDATA[Raa]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Van Landeghem]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Modeling inventory routing problems in supply chains of high consumption products]]></article-title>
<source><![CDATA[Eur. J. Oper. Res]]></source>
<year>2006</year>
<volume>169</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>1048-63</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>[3]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Archetti]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Bertazzi]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Laporte]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Speranza]]></surname>
<given-names><![CDATA[M. G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A Branch-and-Cut Algorithm for a Vendor-Managed Inventory-Routing Problem]]></article-title>
<source><![CDATA[Transp. Sci]]></source>
<year>2007</year>
<volume>41</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>382-91</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>[4]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Coelho]]></surname>
<given-names><![CDATA[L. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Laporte]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The exact solution of several classes of inventory-routing problems]]></article-title>
<source><![CDATA[Comput. Oper. Res]]></source>
<year>2013</year>
<volume>40</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>558-65</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>[5]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Yadollahi]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Aghezzaf]]></surname>
<given-names><![CDATA[E. H.]]></given-names>
</name>
<name>
<surname><![CDATA[Walraevens]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Raa]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Claeys]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Evaluating approximate solution models for the stochastic periodic inventory routing problem]]></article-title>
<source><![CDATA[J. Manuf. Syst]]></source>
<year>2019</year>
<volume>50</volume>
<page-range>25-35</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>[6]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Coelho]]></surname>
<given-names><![CDATA[L. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Laporte]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The exact solution of several classes of inventory-routing problems]]></article-title>
<source><![CDATA[Comput. Oper. Res]]></source>
<year>2013</year>
<volume>40</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>558-65</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>[7]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Aghezzaf]]></surname>
<given-names><![CDATA[E. H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Robust distribution planning for supplier-managed inventory agreements when demand rates and travel times are stationary]]></article-title>
<source><![CDATA[J. Oper. Res. Soc]]></source>
<year>2008</year>
<volume>59</volume>
<numero>8</numero>
<issue>8</issue>
<page-range>1055-65</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>[8]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Coelho]]></surname>
<given-names><![CDATA[L. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Cordeau]]></surname>
<given-names><![CDATA[J. F.]]></given-names>
</name>
<name>
<surname><![CDATA[Laporte]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Heuristics for dynamic and stochastic inventory-routing]]></article-title>
<source><![CDATA[Comput. Oper. Res]]></source>
<year>2014</year>
<volume>52</volume>
<page-range>55-67</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>[9]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rahimi]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Baboli]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Rekik]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Multi-objective inventory routing problem: A stochastic model to consider profit, service level and green criteria]]></article-title>
<source><![CDATA[Transp. Res. Part E Logist. Transp. Rev]]></source>
<year>2017</year>
<volume>101</volume>
<page-range>59-83</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>[10]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Diaz]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Bailey]]></surname>
<given-names><![CDATA[M. P.]]></given-names>
</name>
<name>
<surname><![CDATA[Kumar]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Analyzing a lost-sale stochastic inventory model with Markov- modulated demands: A simulation-based optimization study]]></article-title>
<source><![CDATA[J. Manuf. Syst]]></source>
<year>2016</year>
<volume>38</volume>
<page-range>1-12</page-range></nlm-citation>
</ref>
<ref id="B11">
<label>[11]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bell]]></surname>
<given-names><![CDATA[W. J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Improving the Distribution of Industrial Gases with an On-Line Computerized Routing and Scheduling Optimizer]]></article-title>
<source><![CDATA[Interfaces (Providence)]]></source>
<year>1983</year>
<volume>13</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>4-23</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>[12]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Yeh]]></surname>
<given-names><![CDATA[Q. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Chang]]></surname>
<given-names><![CDATA[T. P.]]></given-names>
</name>
<name>
<surname><![CDATA[Chang]]></surname>
<given-names><![CDATA[H. C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An inventory control model with Gamma distribution]]></article-title>
<source><![CDATA[Microelectron. Reliab]]></source>
<year>1997</year>
<volume>37</volume>
<numero>8</numero>
<issue>8</issue>
<page-range>1197-201</page-range></nlm-citation>
</ref>
<ref id="B13">
<label>[13]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rayat]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Musavi]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Bozorgi-Amiri]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Bi-objective reliable location-inventory-routing problem with partial backordering under disruption risks: A modified AMOSA approach]]></article-title>
<source><![CDATA[Appl. Soft Comput]]></source>
<year>2017</year>
<volume>59</volume>
<page-range>622-43</page-range></nlm-citation>
</ref>
<ref id="B14">
<label>[14]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Coelho]]></surname>
<given-names><![CDATA[L. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Cordeau]]></surname>
<given-names><![CDATA[J.-F.]]></given-names>
</name>
<name>
<surname><![CDATA[Laporte]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Consistency in multi-vehicle inventory-routing]]></article-title>
<source><![CDATA[Transp. Res. Part C Emerg. Technol]]></source>
<year>2012</year>
<volume>24</volume>
<page-range>270-87</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>[15]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Coelho]]></surname>
<given-names><![CDATA[L. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Laporte]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Optimal joint replenishment, delivery and inventory management policies for perishable products]]></article-title>
<source><![CDATA[Comput. Oper. Res]]></source>
<year>2014</year>
<volume>47</volume>
<page-range>42-52</page-range></nlm-citation>
</ref>
<ref id="B16">
<label>[16]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Snyder]]></surname>
<given-names><![CDATA[L. V.]]></given-names>
</name>
<name>
<surname><![CDATA[Daskin]]></surname>
<given-names><![CDATA[M. S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Stochastic p -robust location problems]]></article-title>
<source><![CDATA[IIE Trans]]></source>
<year>2006</year>
<volume>38</volume>
<numero>11</numero>
<issue>11</issue>
<page-range>971-85</page-range></nlm-citation>
</ref>
<ref id="B17">
<label>[17]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Franco]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Augusto]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Garaix]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Alfonso-Lizarazo]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Bourdelin]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Bontemps]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<source><![CDATA[&#8220;Strategic territorial deployment of hospital pharmacy robots using a stochastic p-robust optimization approach,&#8221; in 2018 IEEE 14th]]></source>
<year>2018</year>
<page-range>390-5</page-range><publisher-name><![CDATA[International Conference on Automation Science and Engineering (CASE)]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<label>[18]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Franco]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Guzmán Cortés]]></surname>
<given-names><![CDATA[Diana]]></given-names>
</name>
<name>
<surname><![CDATA[Figueroa García]]></surname>
<given-names><![CDATA[Juan Carlos]]></given-names>
</name>
<name>
<surname><![CDATA[Díaz Aldana]]></surname>
<given-names><![CDATA[N. L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Mathematical model for centralized supply chains with sharing resources decisions]]></article-title>
<source><![CDATA[Ingeniería]]></source>
<year>2020</year>
<volume>25</volume>
<numero>3</numero>
<issue>3</issue>
</nlm-citation>
</ref>
<ref id="B19">
<label>[19]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Franco]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Alfonso-Lizarazo]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Optimization under uncertainty of the pharmaceutical supply chain in hospitals]]></article-title>
<source><![CDATA[Comput. Chem. Eng]]></source>
<year>2020</year>
<volume>135</volume>
<page-range>106689</page-range></nlm-citation>
</ref>
<ref id="B20">
<label>[20]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Morales]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Franco]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Mendez-Giraldo]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Dynamic inventory routing problem: Policies considering network disruptions]]></article-title>
<source><![CDATA[Int. J. Ind. Eng. Comput]]></source>
<year>2018</year>
<volume>9</volume>
<numero>4</numero>
<issue>4</issue>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
