{"id":15612,"date":"2022-04-19T14:03:28","date_gmt":"2022-04-19T13:03:28","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=15612"},"modified":"2024-02-11T16:04:54","modified_gmt":"2024-02-11T15:04:54","slug":"exercice-corrige-branch-and-bound","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/es\/optimizacion-combinatoria\/ejercicio-corrige-branch-and-bound\/","title":{"rendered":"1 Ejercicio corregido Branch and Bound"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"15612\" class=\"elementor elementor-15612\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9ed89d6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9ed89d6\" 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-4d5d85f\" data-id=\"4d5d85f\" 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-8ce9d09 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"8ce9d09\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/es\/optimizacion-combinatoria\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Optimizaci\u00f3n Combinatoria<\/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<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-7776d74\" data-id=\"7776d74\" 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-20411aa elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"20411aa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/es\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Pagina de inicio<\/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<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-34ce881\" data-id=\"34ce881\" 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-6bbb95b elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6bbb95b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/en.wikipedia.org\/wiki\/Branch_and_bound\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span 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-485855a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"485855a\" 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-53d917d\" data-id=\"53d917d\" 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-fbb3d7c elementor-widget elementor-widget-text-editor\" data-id=\"fbb3d7c\" 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<p>Esta p\u00e1gina presenta un ejercicio corregido detallado del problema de <a href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/\">programaci\u00f3n lineal<\/a> resuelto por el algoritmo de <a href=\"https:\/\/complex-systems-ai.com\/es\/optimizacion-combinatoria\/ramificar-y-enlazar\/\">rama y atado<\/a>.<\/p><p><img decoding=\"async\" class=\"aligncenter wp-image-11096 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/cropped-Capture.png\" alt=\"rama y atado\" width=\"97\" height=\"97\" title=\"\"><\/p>\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-e669c9f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e669c9f\" 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-e630115\" data-id=\"e630115\" 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-37ae126 elementor-widget elementor-widget-heading\" data-id=\"37ae126\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<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\/optimizacion-combinatoria\/ejercicio-corrige-branch-and-bound\/#Exercice-corrige-pas-a-pas-du-branch-and-bound\" >Ejercicio corregido paso a paso de bifurcar y acotar<\/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\/optimizacion-combinatoria\/ejercicio-corrige-branch-and-bound\/#Solution\" >Soluci\u00f3n<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/complex-systems-ai.com\/es\/optimizacion-combinatoria\/ejercicio-corrige-branch-and-bound\/#Premier-branchement\" >Primera conexi\u00f3n<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/complex-systems-ai.com\/es\/optimizacion-combinatoria\/ejercicio-corrige-branch-and-bound\/#Deuxieme-branchement\" >Segunda conexi\u00f3n<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/complex-systems-ai.com\/es\/optimizacion-combinatoria\/ejercicio-corrige-branch-and-bound\/#Troisieme-branchement\" >Tercera conexi\u00f3n<\/a><\/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\/optimizacion-combinatoria\/ejercicio-corrige-branch-and-bound\/#Recapitulatif-de-la-methode-en-anglais\" >Resumen del m\u00e9todo<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-corrige-pas-a-pas-du-branch-and-bound\"><\/span>Ejercicio corregido paso a paso de bifurcar y acotar<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-a9fbdc9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a9fbdc9\" 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-2cf986a\" data-id=\"2cf986a\" 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-dfbb9cb elementor-widget elementor-widget-text-editor\" data-id=\"dfbb9cb\" 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<p>El due\u00f1o de un taller de maquinaria planea expandirse comprando nuevas m\u00e1quinas, prensas y tornos. El propietario estim\u00f3 que cada prensa comprada aumentar\u00e1 las ganancias en 100 $ por d\u00eda y cada giro aumentar\u00e1 las ganancias en 150 $ por d\u00eda. La cantidad de m\u00e1quinas que el propietario puede comprar est\u00e1 limitada por el costo de las m\u00e1quinas y el espacio disponible en el taller. Los precios de compra de la m\u00e1quina y los requisitos de espacio son los siguientes.<\/p><p><img decoding=\"async\" class=\"alignnone wp-image-15615 size-medium\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb-300x104.png\" alt=\"separaci\u00f3n y evaluaci\u00f3n de sucursales y l\u00edmites\" width=\"300\" height=\"104\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb-300x104.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb-18x6.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb.png 481w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><p>El propietario tiene un presupuesto de 40.000 $ para la compra de maquinaria y 200 pies cuadrados de superficie disponible. El propietario quiere saber cu\u00e1ntas m\u00e1quinas de cada tipo comprar para maximizar el aumento diario de las ganancias. Resuelve este problema.<\/p>\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-a6c583a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a6c583a\" 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-1b768d1\" data-id=\"1b768d1\" 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-f02b5c9 elementor-widget elementor-widget-heading\" data-id=\"f02b5c9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Solution\"><\/span>Soluci\u00f3n<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-c4ccedb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c4ccedb\" 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-5e5de4e\" data-id=\"5e5de4e\" 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-adefda6 elementor-widget elementor-widget-text-editor\" data-id=\"adefda6\" 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<p>El primer paso es modelar el problema, este es un <a href=\"https:\/\/complex-systems-ai.com\/es\/ayuda-con-la-decision\/modelado-lineal\/\">problema lineal<\/a> como un n\u00famero entero (por lo que el <a href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/metodo-simplex\/\">s\u00edmplex<\/a> no puede aplicar).<\/p><p><img decoding=\"async\" class=\"alignnone wp-image-15616 size-medium\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb2-300x155.png\" alt=\"separaci\u00f3n y evaluaci\u00f3n de sucursales y l\u00edmites\" width=\"300\" height=\"155\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb2-300x155.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb2-18x9.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb2.png 365w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><p>Siendo x_1 el n\u00famero de pulsaciones y x_2 el n\u00famero de vueltas.<\/p>\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-e77b352 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e77b352\" 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-9da86e1\" data-id=\"9da86e1\" 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-f6894b1 elementor-widget elementor-widget-text-editor\" data-id=\"f6894b1\" 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<p>Comenzamos el m\u00e9todo de bifurcaci\u00f3n y acotaci\u00f3n resolviendo primero el problema como un modelo de programaci\u00f3n lineal regular sin restricciones sobre los n\u00fameros enteros (es decir, las restricciones sobre los n\u00fameros enteros se relajan o se relajan). El modelo de programaci\u00f3n lineal para el problema y la soluci\u00f3n relajada \u00f3ptima es<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15617 size-medium\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb3-300x166.png\" alt=\"separaci\u00f3n y evaluaci\u00f3n de sucursales y l\u00edmites\" width=\"300\" height=\"166\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb3-300x166.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb3-18x10.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb3.png 334w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><p>La soluci\u00f3n \u00f3ptima relajada es x_1=2.22 y x_2=5.56 con Z=1055.56.<\/p><p>El m\u00e9todo de bifurcaci\u00f3n y vinculaci\u00f3n utiliza un diagrama que consiste en nodos y bifurcaciones como marco para el proceso de soluci\u00f3n. El primer nodo en el diagrama de rama y v\u00ednculo, que se muestra en la Figura C-1, contiene la soluci\u00f3n de programaci\u00f3n lineal relajada que se mostr\u00f3 anteriormente y la soluci\u00f3n redondeada.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15618 size-medium\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb4-300x163.png\" alt=\"separaci\u00f3n y evaluaci\u00f3n de sucursales y l\u00edmites\" width=\"300\" height=\"163\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb4-300x163.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb4-18x10.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb4.png 330w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><p>Denotamos l\u00edmite superior el resultado de la soluci\u00f3n \u00f3ptima relajada y l\u00edmite inferior el resultado de la soluci\u00f3n \u00f3ptima como un n\u00famero entero (redondeado hacia abajo).<\/p>\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-1929da9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1929da9\" 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-fc69b69\" data-id=\"fc69b69\" 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-d47b106 elementor-widget elementor-widget-heading\" data-id=\"d47b106\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Premier-branchement\"><\/span>Primera conexi\u00f3n<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-d71dd6a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d71dd6a\" 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-3b81937\" data-id=\"3b81937\" 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-b3a1a4b elementor-widget elementor-widget-text-editor\" data-id=\"b3a1a4b\" 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<p>Cree dos restricciones (o subconjuntos) para eliminar la parte fraccionaria del valor de la soluci\u00f3n y ver cu\u00e1l est\u00e1 m\u00e1s lejos del valor entero redondeado (es decir, qu\u00e9 variable tiene la parte fraccionaria m\u00e1s grande en valor absoluto). La parte 0,56 de 5,56 es la parte fraccionaria m\u00e1s grande; por lo tanto, x_2 ser\u00e1 la variable a la que vamos a &quot;conectar&quot;.<\/p><p>Es decir, crearemos dos programas lineales alternativos teniendo en cuenta respectivamente que x_2 debe ser menor o igual a 5 por un lado; y x_2 debe ser mayor o igual a 6 por otro lado.<\/p><p>Entonces tenemos la siguiente conexi\u00f3n:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15628 size-medium\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb5-300x218.png\" alt=\"separaci\u00f3n y evaluaci\u00f3n de sucursales y l\u00edmites\" width=\"300\" height=\"218\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb5-300x218.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb5-18x12.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb5.png 431w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><p>Resolvamos el problema de la izquierda:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15629 size-medium\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb6-300x189.png\" alt=\"separaci\u00f3n y evaluaci\u00f3n de sucursales y l\u00edmites\" width=\"300\" height=\"189\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb6-300x189.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb6-18x12.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb6.png 336w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><p>Esto da la soluci\u00f3n x_1=2.5, x_2=5 y Z=1000.<\/p><p>Resolvamos el sistema de la derecha:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15630 size-medium\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb7-300x179.png\" alt=\"separaci\u00f3n y evaluaci\u00f3n de sucursales y l\u00edmites\" width=\"300\" height=\"179\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb7-300x179.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb7-18x12.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb7.png 340w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><p>Este sistema tiene por soluci\u00f3n x_1=1.33 y x_2=6, Z=1033.33<\/p><p>Desde un punto de vista pr\u00e1ctico, cortamos el <a href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/lp-soluciones-y-dominio-realizable\/\">campo de definici\u00f3n<\/a> con la restricci\u00f3n x_2=6 y se han resuelto a ambos lados de la restricci\u00f3n que libera el sistema lineal.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15631 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb8.png\" alt=\"separaci\u00f3n y evaluaci\u00f3n de sucursales y l\u00edmites\" width=\"754\" height=\"418\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb8.png 754w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb8-300x166.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb8-18x10.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb8-600x333.png 600w\" sizes=\"(max-width: 754px) 100vw, 754px\" \/><\/p><p>Actualicemos nuestro <a href=\"https:\/\/complex-systems-ai.com\/es\/teoria-de-grafos\/\">grafico<\/a> con los nuevos UB y LB de cada sistema obtenidos.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15632 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb9.png\" alt=\"separaci\u00f3n y evaluaci\u00f3n de sucursales y l\u00edmites\" width=\"656\" height=\"310\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb9.png 656w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb9-300x142.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb9-18x9.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb9-600x284.png 600w\" sizes=\"(max-width: 656px) 100vw, 656px\" \/><\/p><p>Dado que a\u00fan no tenemos una soluci\u00f3n entera \u00f3ptima y factible, debemos continuar ramificando (es decir, dividiendo) el modelo, ya sea desde el nodo 2 o desde el nodo 3. Una mirada a la Figura revela que si ramificamos desde el nodo 2, el el valor m\u00e1ximo que posiblemente se puede alcanzar es 1000 $ (el l\u00edmite superior).<\/p><p>Sin embargo, si comenzamos desde el nodo 3, es posible un valor m\u00e1ximo m\u00e1s alto de 1033 $. Por lo tanto, nos bifurcaremos desde el nodo 3. En general, siempre bifurquemos desde el nodo con el l\u00edmite superior m\u00e1ximo.<\/p>\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-168372d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"168372d\" 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-5de9616\" data-id=\"5de9616\" 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-397392e elementor-widget elementor-widget-heading\" data-id=\"397392e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Deuxieme-branchement\"><\/span>Segunda conexi\u00f3n<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-abd8d9e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"abd8d9e\" 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-30b767f\" data-id=\"30b767f\" 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-004e493 elementor-widget elementor-widget-text-editor\" data-id=\"004e493\" 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<p>Ahora los pasos de bifurcaci\u00f3n seguidos previamente en el nodo 1 se repiten en el nodo 3. Primero, se selecciona la variable que tiene el valor con la parte fraccionaria m\u00e1s grande. Como x_2 tiene un valor entero, x_1, con una parte fraccionaria de 0.33, es la \u00fanica variable que podemos seleccionar. Por tanto, se desarrollan dos nuevas restricciones a partir de x_1.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15633 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb10.png\" alt=\"separaci\u00f3n y evaluaci\u00f3n de sucursales y l\u00edmites\" width=\"701\" height=\"462\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb10.png 701w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb10-300x198.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb10-18x12.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb10-600x395.png 600w\" sizes=\"(max-width: 701px) 100vw, 701px\" \/><\/p><p>Tomando el nodo 4, tenemos el siguiente programa lineal:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15634 size-medium\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb11-300x214.png\" alt=\"separaci\u00f3n y evaluaci\u00f3n de sucursales y l\u00edmites\" width=\"300\" height=\"214\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb11-300x214.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb11-18x12.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb11-120x85.png 120w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb11.png 334w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><p>La soluci\u00f3n al problema es x_1=1 y x_2=6.17 con Z=1025.<\/p><p>El segundo problema es:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15635 size-medium\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb12-300x225.png\" alt=\"separaci\u00f3n y evaluaci\u00f3n de sucursales y l\u00edmites\" width=\"300\" height=\"225\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb12-300x225.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb12-16x12.png 16w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb12.png 317w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><p>Este problema no admite soluci\u00f3n (se viola la primera restricci\u00f3n). Entonces tenemos el siguiente gr\u00e1fico soluci\u00f3n:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15636 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb13.png\" alt=\"separaci\u00f3n y evaluaci\u00f3n de sucursales y l\u00edmites\" width=\"705\" height=\"451\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb13.png 705w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb13-300x192.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb13-18x12.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb13-600x384.png 600w\" sizes=\"(max-width: 705px) 100vw, 705px\" \/><\/p><p>Todav\u00eda no tenemos una soluci\u00f3n entera, por lo que tenemos que continuar con el algoritmo de bifurcaci\u00f3n y l\u00edmite.<\/p>\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-b7c390e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b7c390e\" 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-9ac46f4\" data-id=\"9ac46f4\" 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-3ea6162 elementor-widget elementor-widget-heading\" data-id=\"3ea6162\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Troisieme-branchement\"><\/span>Tercera conexi\u00f3n<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-9817b4f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9817b4f\" 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-f87d1b7\" data-id=\"f87d1b7\" 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-c3af834 elementor-widget elementor-widget-text-editor\" data-id=\"c3af834\" 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<p>El nodo 4 tiene la mejor UB. Dado que x_2 es la \u00fanica variable que no es un n\u00famero entero, nos bifurcaremos a esta variable.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15637 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb14.png\" alt=\"separaci\u00f3n y evaluaci\u00f3n de sucursales y l\u00edmites\" width=\"691\" height=\"599\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb14.png 691w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb14-300x260.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb14-14x12.png 14w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb14-600x520.png 600w\" sizes=\"(max-width: 691px) 100vw, 691px\" \/><\/p><p>Despu\u00e9s de resolver los dos programas lineales en los nodos 6 y 7, obtenemos los siguientes resultados:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15638 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb15.png\" alt=\"separaci\u00f3n y evaluaci\u00f3n de sucursales y l\u00edmites\" width=\"712\" height=\"604\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb15.png 712w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb15-300x254.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb15-14x12.png 14w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb15-600x509.png 600w\" sizes=\"(max-width: 712px) 100vw, 712px\" \/><\/p><p>La soluci\u00f3n al nodo 6 corresponde a los criterios del problema original (es decir, en n\u00famero entero). Solo la rama en 3 y 4 tiene una UB superior al nodo 6, sin embargo, la rama que da a los nodos 5 y 7 no tiene soluci\u00f3n factible. Concluimos que la soluci\u00f3n \u00f3ptima se encuentra en el nodo 6.<\/p>\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-9f7bcd6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9f7bcd6\" 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-4ed004f\" data-id=\"4ed004f\" 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-2bb33df elementor-widget elementor-widget-heading\" data-id=\"2bb33df\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Recapitulatif-de-la-methode-en-anglais\"><\/span>Resumen del m\u00e9todo<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-4335172 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4335172\" 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-e14f86b\" data-id=\"e14f86b\" 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-0d4c5b5 elementor-widget elementor-widget-text-editor\" data-id=\"0d4c5b5\" 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<p>Aqu\u00ed hay un resumen en ingl\u00e9s del m\u00e9todo que acabamos de usar.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15639 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb16.png\" alt=\"separaci\u00f3n y evaluaci\u00f3n de sucursales y l\u00edmites\" width=\"855\" height=\"642\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb16.png 855w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb16-300x225.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb16-768x577.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb16-16x12.png 16w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/bnb16-600x451.png 600w\" sizes=\"(max-width: 855px) 100vw, 855px\" \/><\/p>\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>P\u00e1gina principal de Wiki de Optimizaci\u00f3n Combinatoria Esta p\u00e1gina presenta un ejercicio corregido detallado del problema de programaci\u00f3n lineal resuelto por el algoritmo de ramificaci\u00f3n y acotaci\u00f3n. Ejercicio \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":1770,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-15612","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/15612","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=15612"}],"version-history":[{"count":6,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/15612\/revisions"}],"predecessor-version":[{"id":20259,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/15612\/revisions\/20259"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/1770"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/media?parent=15612"}],"curies":[{"name":"gracias","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}