{"id":1392,"date":"2016-02-04T16:12:57","date_gmt":"2016-02-04T15:12:57","guid":{"rendered":"http:\/\/smart--grid.net\/?page_id=1392"},"modified":"2022-12-03T22:58:51","modified_gmt":"2022-12-03T21:58:51","slug":"stepping-stone","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/es\/problema-de-planificacion\/escalon\/","title":{"rendered":"Escal\u00f3n"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"1392\" class=\"elementor elementor-1392\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9f582aa elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9f582aa\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-16d7596\" 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class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-523203c4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"523203c4\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a148bb2\" data-id=\"a148bb2\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-19969ff7 elementor-widget elementor-widget-text-editor\" data-id=\"19969ff7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contenido<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Tabla de contenido alternativo\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Palanca<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/es\/problema-de-planificacion\/escalon\/#Stepping-Stone\" >Escal\u00f3n<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/complex-systems-ai.com\/es\/problema-de-planificacion\/escalon\/#Stepping-stone-%E2%80%93-Etape-1-obtention-dune-solution-de-base\" >Trampol\u00edn - Paso 1: obtenci\u00f3n de una soluci\u00f3n base<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/complex-systems-ai.com\/es\/problema-de-planificacion\/escalon\/#Par-coin-Nord-Ouest\" >Por la esquina noroeste<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/complex-systems-ai.com\/es\/problema-de-planificacion\/escalon\/#Par-la-methode-des-minimums\" >Por el m\u00e9todo m\u00ednimo<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/complex-systems-ai.com\/es\/problema-de-planificacion\/escalon\/#Par-la-methode-de-Vogel-ou-Balas-Hammer\" >Por el m\u00e9todo Vogel (o Balas-Hammer)<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/complex-systems-ai.com\/es\/problema-de-planificacion\/escalon\/#Stepping-stone-%E2%80%93-Etape-2-calcul-des-potentiels\" >Trampol\u00edn - Paso 2: calcular los potenciales<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/complex-systems-ai.com\/es\/problema-de-planificacion\/escalon\/#Stepping-stone-%E2%80%93-Etape-3-calcul-de-la-variation-de-cout-unitaire\" >Trampol\u00edn - Paso 3: c\u00e1lculo de la variaci\u00f3n del costo unitario<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/complex-systems-ai.com\/es\/problema-de-planificacion\/escalon\/#Stepping-stone-%E2%80%93-Etape-4-calcul-de-la-quantite-maximale-du-flot\" >Trampol\u00edn - Paso 4: c\u00e1lculo de la cantidad m\u00e1xima de flujo<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/complex-systems-ai.com\/es\/problema-de-planificacion\/escalon\/#Stepping-stone-%E2%80%93-Etape-5-mise-a-jour-du-tableau\" >Stepping Stone - Paso 5: actualice la tabla<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/complex-systems-ai.com\/es\/problema-de-planificacion\/escalon\/#Aparte\" >Aparte<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Stepping-Stone\"><\/span>Escal\u00f3n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>El problema resuelto por el algoritmo Stepping Stone es el siguiente:<\/p>\n\n<div style=\"padding: 5px; background-color: #d5edff; border: 2px solid #3c95e8; -moz-border-radius: 9px; -khtml-border-radius: 9px; -webkit-border-radius: 9px; border-radius: 9px;\">Son de diferentes or\u00edgenes, proponiendo una determinada oferta cuantificable; y destinos que requieran una determinada cantidad; se asigna un costo de transporte para cada combinaci\u00f3n de origen y destino; \u00bfC\u00f3mo satisfacer mejor la demanda al menor costo?<\/div>\n\n<p>Tomemos un ejemplo para mostrar c\u00f3mo funciona el algoritmo. Considere cuatro or\u00edgenes y cinco solicitantes con costos y cantidad de acuerdo con la tabla:<\/p>\n\n<div class=\"standard\" style=\"text-align: justify;\">\n<table>\n<tbody>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">vs<sub>ij<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>1<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>2<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>3<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>4<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>5<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">oferta<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>1<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">7<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">12<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">1<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">5<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">6<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">12<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>2<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">15<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">3<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">12<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">6<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">14<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">11<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>3<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">8<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">16<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">10<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">12<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">7<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">14<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>4<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">18<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">8<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">17<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">11<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">16<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">8<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">demanda<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">10<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">11<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">15<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">5<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">4<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<div style=\"padding: 5px; background-color: #d5edff; border: 2px solid #3c95e8; -moz-border-radius: 9px; -khtml-border-radius: 9px; -webkit-border-radius: 9px; border-radius: 9px;\">\u00a0La idea de trampol\u00edn es partir de un <a href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/metodo-simplex\/\">soluci\u00f3n b\u00e1sica<\/a> factible (no \u00f3ptimo) para mejorarlo iterativamente hasta obtener una soluci\u00f3n no optimizable. No hay mejor soluci\u00f3n, por lo que es \u00f3ptima. Es importante comprobar que la oferta y la demanda son iguales, si no es as\u00ed hay que a\u00f1adir una demanda ficticia de coste significativo para cada oferta.<\/div>\n\n<p>Es posible realizar el algoritmo usando dos tablas (una para los costos, otra para los flujos). Tambi\u00e9n es posible mostrar los dos valores en el mismo cuadro, ya que solo variar\u00e1 el flujo.<\/p>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Stepping-stone-%E2%80%93-Etape-1-obtention-dune-solution-de-base\"><\/span>Trampol\u00edn - Paso 1: obtenci\u00f3n de una soluci\u00f3n base<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Par-coin-Nord-Ouest\"><\/span>Por la esquina noroeste<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n<p>El principio es simple:<\/p>\n\n<div style=\"padding: 3px; border: 2px dotted #a5a5a5; background-color: #f6f9fa;\">1. Seleccione la celda de la esquina noroeste y asigne tantas unidades como sea posible (requisitos m\u00ednimos) disponibles para la oferta y la demanda.<br \/>2. Ajustar los valores de oferta y demanda en la asignaci\u00f3n de las respectivas filas y columnas.<br \/>3. Si se agota el suministro de la primera fila, baje a la primera celda de la siguiente fila.<br \/>4. Si se satisface la demanda de la primera celda, mu\u00e9vase horizontalmente a la siguiente celda.<br \/>5. Si para una celda la oferta es igual a la demanda, la siguiente asignaci\u00f3n se puede realizar en la celda de la siguiente fila o columna.<br \/>6. Contin\u00fae con el procedimiento hasta que la cantidad total disponible se asigne por completo a las celdas, seg\u00fan sea necesario.<\/div>\n\n<div class=\"standard\" style=\"text-align: justify;\">\n<table>\n<tbody>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">F<sub>ij<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>1<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>2<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>3<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>4<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>5<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">oferta<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>1<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">10<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">2<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">12<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>2<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">9<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">2<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">11<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>3<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">13<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">1<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">14<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>4<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">4<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">4<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">8<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">demanda<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">10<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">11<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">15<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">5<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">4<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>El costo total de la soluci\u00f3n b\u00e1sica es: 10 * 7 + 2 * 12 + 9 * 3 + 2 * 12 + 13 * 10 + 12 + 4 * 11 + 4 * 16 = 395.<\/p>\n\n<p>En muchos casos no es posible satisfacer la demanda, este m\u00e9todo, aunque r\u00e1pido, solo brinda una soluci\u00f3n factible poco realista. Aqu\u00ed no representamos los costos sino los flujos f<sub>ij<\/sub> de la oferta <strong>I<\/strong> a la solicitud <strong>j<\/strong>.<\/p>\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Par-la-methode-des-minimums\"><\/span>Por el m\u00e9todo m\u00ednimo<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n<div style=\"padding: 3px; border: 2px dotted #a5a5a5; background-color: #f6f9fa;\">1. Identifique la caja con el costo unitario m\u00ednimo de transporte c<sub>ij<\/sub>.<br \/>2. Si el costo m\u00ednimo no es \u00fanico, puede elegir cualquier celda.<br \/>3. Elija el valor de x tanto como sea posible<sub>ij<\/sub> correspondiente, dependiendo de las limitaciones de capacidad y requisitos.<br \/>4. Repita los pasos 1 a 3 hasta que se cumplan todas las restricciones.<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-6333 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/04\/transport3.png\" alt=\"algoritmo de trampol\u00edn problema de planificaci\u00f3n balas-hammer vogel\" width=\"583\" height=\"181\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/04\/transport3.png 583w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/04\/transport3-300x93.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/figure>\n<\/div>\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Par-la-methode-de-Vogel-ou-Balas-Hammer\"><\/span>Por el m\u00e9todo Vogel (o Balas-Hammer)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n<p>Este m\u00e9todo utiliza la diferencia de transporte entre las dos mejores opciones para la oferta y la demanda. La soluci\u00f3n b\u00e1sica suele estar muy cerca de la soluci\u00f3n \u00f3ptima.<\/p>\n\n<div style=\"padding: 3px; border: 2px dotted #a5a5a5; background-color: #f6f9fa;\">\n<p>1. Determine un costo de penalizaci\u00f3n para cada fila (columna) restando el costo de celda unitario m\u00e1s bajo en la fila (columna) del costo de celda unitario m\u00e1s bajo en la misma fila (columna).<\/p>\n<div>2. Identifique la fila o columna con el mayor costo de penalizaci\u00f3n. Romper los empates arbitrariamente (si los hay). Asigne tanto como sea posible a la variable con el costo unitario m\u00e1s bajo en la fila o columna seleccionada. Ajuste la oferta y la demanda y tache la fila o columna que ya est\u00e1 satisfecha. Si una fila y una columna se satisfacen simult\u00e1neamente, tache solo una de las dos y asigne una oferta o demanda de cero a la restante.<\/div>\n<div>\u00a0<\/div>\n<p>3.<\/p>\n<ul>\n<li>Si queda exactamente una fila o columna con oferta o demanda cero, det\u00e9ngase.<\/li>\n<li>Si queda una fila (columna) con una oferta (demanda) positiva, determine las variables b\u00e1sicas en la fila (columna) utilizando el m\u00e9todo de m\u00ednimos. Parada.<\/li>\n<li>Si todas las filas y columnas que no han sido tachadas tienen una oferta o demanda (restante) de cero, use el m\u00e9todo m\u00ednimo. Parada.<\/li>\n<\/ul>\n<p>En todos los dem\u00e1s casos, vaya al paso 1.<\/p>\n<\/div>\n\n<p>La primera iteraci\u00f3n del m\u00e9todo da: D<sub>O1<\/sub> = 4, D<sub>O2<\/sub> = 3, D<sub>O3<\/sub> = 1, D<sub>O4<\/sub> = 3, D<sub>D1<\/sub> = 1, D<sub>D2<\/sub> = 5, D<sub>D3<\/sub> = 9, D<sub>D4<\/sub> = 1, D<sub>D5<\/sub> = 2. Columna D<sub>3<\/sub> tiene la diferencia de costo m\u00e1s grande, el costo m\u00e1s peque\u00f1o es 1, por lo que saturamos la intersecci\u00f3n O<sub>1<\/sub> con<sub>3<\/sub> con el flujo m\u00ednimo (12, 15). La oferta de O<sub>1<\/sub> por lo tanto, est\u00e1 saturado.<\/p>\n\n<div class=\"standard\" style=\"text-align: justify;\">\n<table>\n<tbody>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">F<sub>ij<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>1<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>2<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>3<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>4<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>5<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">oferta<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>1<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">X<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">X<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">12<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">X<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">X<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">12<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>2<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">11<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>3<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">14<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>4<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">8<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">demanda<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">10<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">11<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">15<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">5<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">4<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Para el nuevo c\u00e1lculo de la diferencia de costo, ya no tendremos en cuenta los valores de la fila O<sub>1<\/sub>. Obtenemos despu\u00e9s de 5 iteraciones a la siguiente configuraci\u00f3n:<\/p>\n\n<div class=\"standard\" style=\"text-align: justify;\">\n<table>\n<tbody>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">F<sub>ij<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>1<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>2<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>3<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>4<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>5<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">oferta<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>1<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">12<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">12<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>2<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">11<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">11<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>3<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">10<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">4<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">14<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>4<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">3<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">5<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">8<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">demanda<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">10<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">11<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">15<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">5<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">4<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Stepping-stone-%E2%80%93-Etape-2-calcul-des-potentiels\"><\/span>Trampol\u00edn - Paso 2: calcular los potenciales<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p>Una vez que tenga una soluci\u00f3n b\u00e1sica, la idea es modificar la soluci\u00f3n para mejorarla. Es decir, es necesario modificar los flujos. Para esto, elegiremos un flujo que reduzca al m\u00e1ximo el costo total de transporte. El primer paso para determinar este flujo es calcular los potenciales. Los potenciales se calculan \u00daNICAMENTE en las celdas con un flujo distinto de cero.<\/p>\n\n<div style=\"padding: 3px; border: 2px dotted #a5a5a5; background-color: #f6f9fa;\">Establezcamos un potencial de 0 en la l\u00ednea con la celda con el flujo de mayor costo. Aqu\u00ed tomaremos la soluci\u00f3n b\u00e1sica proporcionada por el m\u00e9todo de la esquina noroeste: p<sub>O1<\/sub> = 0.<\/div>\n\n<p>Luego podemos calcular otros potenciales. Los potenciales se calculan paso a paso. En nuestro caso, hemos calculado el potencial de la fila 1 a partir de c<sub>12<\/sub>, por lo tanto, es posible calcular el potencial de la columna 1 o la columna 2.<\/p>\n\n<div style=\"padding: 3px; border: 2px dotted #a5a5a5; background-color: #f6f9fa;\">\u00a0Para calcular los potenciales aplicamos la siguiente regla: p<sub>D<\/sub> + p<sub>O<\/sub> = c<sub>ij\u00a0<\/sub>lo que da N ecuaciones con N inc\u00f3gnitas.<\/div>\n\n<p>Tomemos el ejemplo nuevamente: para la columna 1, p<sub>D1<\/sub> = c<sub>11<\/sub> + P<sub>O1<\/sub> = 7. Para la fila 2, p<sub>D2<\/sub> = c<sub>12<\/sub> + P<sub>O1<\/sub> = 12. Lo mismo para las otras filas y columnas: p<sub>O2<\/sub>\u00a0 = p<sub>D2<\/sub> - vs<sub>22<\/sub> = 12 -3 = 9; pag<sub>D3<\/sub> = 21; pag<sub>03<\/sub> = 11; PAG<sub>D4<\/sub> = 23: P<sub>O4<\/sub> = 12; PAG<sub>D5<\/sub> = 28.<\/p>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Stepping-stone-%E2%80%93-Etape-3-calcul-de-la-variation-de-cout-unitaire\"><\/span>Trampol\u00edn - Paso 3: c\u00e1lculo de la variaci\u00f3n del costo unitario<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<div style=\"padding: 3px; border: 2px dotted #a5a5a5; background-color: #f6f9fa;\">Para cada celda con flujo cero, calculamos v<sub>ij<\/sub> sumando el potencial del origen asociado al costo unitario de la caja y restando el potencial del destino correspondiente: v<sub>ij<\/sub> = c<sub>ij<\/sub> - pag<sub>Oi<\/sub> - pag<sub>DJ<\/sub>.<\/div>\n\n<p>Obtenemos la siguiente tabla:<\/p>\n\n<div class=\"standard\" style=\"text-align: justify;\">\n<table>\n<tbody>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">v<sub>ij<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>1<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>2<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>3<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>4<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>5<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">pag<sub>O<\/sub><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>1<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">-20<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">-18<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">-19<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">0<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>2<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">17<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">-8<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">-5<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">9<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>3<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">12<\/td>\n<td align=\"center\" valign=\"top\">15<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">-10<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">11<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>4<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">23<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">8<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">8<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">12<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">pag<sub>D<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">7<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">12<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">21<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">23<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">28<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Stepping-stone-%E2%80%93-Etape-4-calcul-de-la-quantite-maximale-du-flot\"><\/span>Trampol\u00edn - Paso 4: c\u00e1lculo de la cantidad m\u00e1xima de flujo<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<div style=\"padding: 3px; border: 2px dotted #a5a5a5; background-color: #f6f9fa;\">Ahora conocemos la variaci\u00f3n en el costo de una unidad seg\u00fan el origen y el destino en comparaci\u00f3n con la soluci\u00f3n inicial. Ahora debemos determinar los circuitos de flujo que permitan reducir el costo total. Este c\u00e1lculo se realiza solo para el v<sub>ij<\/sub> negativo.<\/div>\n\n<div style=\"padding: 3px; border: 2px dotted #a5a5a5; background-color: #f6f9fa;\">\u00a0Para llenar una celda vac\u00eda, debe vaciar una celda llena. Al buscar un circuito (un &quot;bucle&quot;), debemos asegurarnos de que una celda con un flujo siempre sucede a la \u00faltima celda elegida en el circuito. As\u00ed, el circuito se compone de una caja vac\u00eda y cajas llenas. El flujo m\u00e1ximo que se puede mover para llenar la celda vac\u00eda es el m\u00ednimo de los flujos de las celdas distintas de cero.<\/div>\n\n<p>Por ejemplo para la casilla 0<sub>1<\/sub>-D<sub>3<\/sub>, tomamos el siguiente circuito f<sub>13<\/sub> -&gt; f<sub>12<\/sub> -&gt; f<sub>22<\/sub> -&gt; f<sub>23<\/sub> -&gt; f<sub>13<\/sub> con el caudal m\u00ednimo de 2. Obtenemos la siguiente tabla:<\/p>\n\n<div class=\"standard\" style=\"text-align: justify;\">\n<table>\n<tbody>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">F<sub>ij<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>1<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>2<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>3<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>4<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>5<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">pag<sub>O<\/sub><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>1<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">2<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">1<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">1<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">0<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>2<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">1<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">1<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">9<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>3<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">1<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">11<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>4<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">12<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">pag<sub>D<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">7<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">12<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">21<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">23<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">28<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Multiplicando f<sub>ij<\/sub>* v<sub>ij<\/sub>, conocemos la variaci\u00f3n del costo total por la modificaci\u00f3n por el flujo f<sub>ij<\/sub>. Elegimos la caja con la mayor f<sub>ij<\/sub>* v<sub>ij<\/sub>, aqui la caja O<sub>1<\/sub>-D<sub>3<\/sub><\/p>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Stepping-stone-%E2%80%93-Etape-5-mise-a-jour-du-tableau\"><\/span>Stepping Stone - Paso 5: actualice la tabla<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p>El c\u00e1lculo de la actualizaci\u00f3n del flujo se realiza mediante la regla \u201c+ -\u201d sin contar el retorno a la caja original. Entonces en el circuito: f<sub>13<\/sub> + = 2, f<sub>12<\/sub> - = 2, f<sub>22<\/sub> + = 2 y f<sub>23<\/sub> - = 2. La tabla es la siguiente:<\/p>\n\n<div class=\"standard\" style=\"text-align: justify;\">\n<table>\n<tbody>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">F<sub>ij<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>1<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>2<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>3<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>4<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>5<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">oferta<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>1<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">10<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">2-2 = \u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">0+2 = 2<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">12<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>2<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">9+2 = 11<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">2-2 = \u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">11<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>3<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">13<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">1<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">14<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>4<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">4<\/td>\n<td align=\"center\" valign=\"top\">4<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">8<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">demanda<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">10<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">11<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">15<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">5<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">4<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>El costo total de la soluci\u00f3n b\u00e1sica es: 10 * 7 + 2 * 12 + 9 * 3 + 2 * 12 + 13 * 10 + 12 + 4 * 11 + 4 * 16 = 395. El costo de esta soluci\u00f3n es: 10 * 7 + 11 * 3 + 2 * 1 + 13 * 10 + 12 + 4 * 11 + 4 * 16 = 355. Sea la soluci\u00f3n b\u00e1sica menos f<sub>13<\/sub>* v<sub>13<\/sub> = 2*20 = 40.<\/p>\n\n<div style=\"padding: 3px; border: 2px dotted #a5a5a5; background-color: #f6f9fa;\">Repetimos los pasos 2 a 5 hasta que no haya m\u00e1s v<sub>ij<\/sub> negativo. Sabemos entonces que no existe un circuito para reducir el costo total, por lo que tenemos una soluci\u00f3n \u00f3ptima.<\/div>\n\n<p>En nuestro ejemplo, finalmente tenemos la siguiente tabla:<\/p>\n\n<div class=\"standard\" style=\"text-align: justify;\">\n<table>\n<tbody>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">F<sub>ij<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>1<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>2<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>3<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>4<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">D<sub>5<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">oferta<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>1<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">12<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">12<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>2<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">11<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">11<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>3<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">10<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">4<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">14<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">O<sub>4<\/sub><\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">\u2013<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">3<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">5<\/td>\n<td align=\"center\" valign=\"top\">\u2013<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">8<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">demanda<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">10<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">11<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">15<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">5<\/div>\n<\/td>\n<td align=\"center\" valign=\"top\">\n<div class=\"plain_layout\">4<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Con un costo total de: 10 * 8 + 11 * 3 + 12 * 1 + 3 * 17 + 5 * 11 + 4 * 7 = 259.<\/p>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Aparte\"><\/span>Aparte<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p>Hablamos de flujo porque el problema se resuelve como un problema de flujo de costo m\u00ednimo (<a href=\"https:\/\/complex-systems-ai.com\/es\/problema-de-flujo-maximo\/\">flujo maximo<\/a> al m\u00ednimo costo) en un <a href=\"https:\/\/complex-systems-ai.com\/es\/teoria-de-grafos\/\">grafico<\/a> bipartito completo: un conjunto de fuentes conectadas a un conjunto de sumideros (de ah\u00ed la regla &quot;+ -&quot;, ya que vamos una vez en la direcci\u00f3n del flujo y luego en la direcci\u00f3n opuesta en el circuito elegido).<\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-9824 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/Stepping-Stone-Method-Flowchart72.png\" alt=\"algoritmo de trampol\u00edn problema de planificaci\u00f3n balas-hammer vogel\" width=\"850\" height=\"673\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/Stepping-Stone-Method-Flowchart72.png 850w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/Stepping-Stone-Method-Flowchart72-300x238.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/Stepping-Stone-Method-Flowchart72-768x608.png 768w\" sizes=\"(max-width: 850px) 100vw, 850px\" \/><\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Problema de planificaci\u00f3n P\u00e1gina de inicio Wiki Stepping Stone El problema que resuelve el algoritmo Stepping Stone es el siguiente: Dados diferentes or\u00edgenes, proponer un \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":868,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1392","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/1392","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/comments?post=1392"}],"version-history":[{"count":4,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/1392\/revisions"}],"predecessor-version":[{"id":17919,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/1392\/revisions\/17919"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/868"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/media?parent=1392"}],"curies":[{"name":"gracias","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}