{"id":41309,"date":"2024-04-22T09:00:58","date_gmt":"2024-04-22T07:00:58","guid":{"rendered":"https:\/\/www.hiberus.com\/crecemos-contigo\/?p=41309"},"modified":"2024-04-22T09:56:19","modified_gmt":"2024-04-22T07:56:19","slug":"investigacion-operativa","status":"publish","type":"post","link":"https:\/\/www.hiberus.com\/crecemos-contigo\/investigacion-operativa\/","title":{"rendered":"Investigaci\u00f3n operativa: C\u00f3mo aplicar matem\u00e1ticas para mejorar procesos"},"content":{"rendered":"<p><span data-contrast=\"none\">En el mundo tecnol\u00f3gico actual, donde la eficiencia y la precisi\u00f3n son cada vez m\u00e1s esenciales, las <\/span><b><span data-contrast=\"none\">matem\u00e1ticas <\/span><\/b><span data-contrast=\"none\">emergen como una herramienta para la optimizaci\u00f3n de proyectos. Por tanto, desde el departamento de IA y data de hiberus buscamos c\u00f3mo implementar t\u00e9cnicas matem\u00e1ticas para encontrar <\/span><b><span data-contrast=\"none\">soluciones \u00f3ptimas a desaf\u00edos complejos.<\/span><\/b><span data-contrast=\"none\"> En este art\u00edculo, nos centraremos en particular, en una rama de la matem\u00e1tica aplicada, la <\/span><b><span data-contrast=\"none\">investigaci\u00f3n operativa y los problemas de optimizaci\u00f3n<\/span><\/b><span data-contrast=\"none\">.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<h2><b><span data-contrast=\"none\">\u00bfQu\u00e9 es la investigaci\u00f3n operativa?<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/h2>\n<p><span data-contrast=\"none\">La investigaci\u00f3n operativa es una rama de la matem\u00e1tica aplicada centrada en el estudio de m\u00e9todos matem\u00e1ticos que permiten ayudar en la <\/span><b><span data-contrast=\"none\">resoluci\u00f3n de problemas y la toma de decisiones<\/span><\/b><span data-contrast=\"none\"> a trav\u00e9s del an\u00e1lisis de los datos disponibles de un problema.\u00a0<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><span data-contrast=\"none\">Dentro de la investigaci\u00f3n operativa existen tres principales vertientes: simulaci\u00f3n, optimizaci\u00f3n y probabilidad y estad\u00edstica.\u00a0<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"none\">La <\/span><b><span data-contrast=\"none\">simulaci\u00f3n <\/span><\/b><span data-contrast=\"none\">se centra en la construcci\u00f3n de modelos que permiten replicar o simular posibles escenarios. As\u00ed, se puede determinar cu\u00e1l es la mejor opci\u00f3n sin necesidad de implementar todas. Por ejemplo, la simulaci\u00f3n de tratamientos m\u00e9dicos para determinar cu\u00e1l puede ser el m\u00e1s eficaz seg\u00fan el historial del paciente.\u00a0<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/li>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"none\">La <\/span><b><span data-contrast=\"none\">probabilidad y la estad\u00edstica<\/span><\/b><span data-contrast=\"none\"> permiten, a partir de unos datos, sacar relaciones entre ellos para realizar inferencias y predicciones. Por ejemplo, para predecir tendencias o sacar correlaciones en los datos.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/li>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"none\">Finalmente, la <\/span><b><span data-contrast=\"none\">optimizaci\u00f3n <\/span><\/b><span data-contrast=\"none\">se centra en la b\u00fasqueda de la mejor soluci\u00f3n dados un objetivo y unas restricciones. <\/span><span data-contrast=\"none\">Este enfoque abarca una variedad de aplicaciones, desde la planificaci\u00f3n de rutas hasta la asignaci\u00f3n eficiente de recursos.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:720,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259,&quot;335559991&quot;:360}\">\u00a0<\/span><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-41311 size-full\" src=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img221.jpg\" alt=\"Principales vertientes de la investigaci\u00f3n operativa: simulaci\u00f3n, optimizaci\u00f3n y probabilidad y estad\u00edstica.\" width=\"712\" height=\"241\" srcset=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img221.jpg 712w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img221-300x102.jpg 300w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img221-360x122.jpg 360w\" sizes=\"auto, (max-width: 712px) 100vw, 712px\" \/><\/p>\n<p><span data-contrast=\"none\">Estos modelos permiten una resoluci\u00f3n eficaz, r\u00e1pida y objetiva de problemas con una funci\u00f3n objetivo concreta.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<h2><b><span data-contrast=\"none\">Aplicaciones de la Investigaci\u00f3n operativa: Optimizaci\u00f3n matem\u00e1tica<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/h2>\n<p><span data-contrast=\"none\">En este art\u00edculo nos vamos a centrar en esta \u00faltima vertiente, donde hiberus ya ha participado en varias soluciones. En primer lugar, expondremos brevemente algunos casos de \u00e9xito. <\/span><\/p>\n<h3><b><span data-contrast=\"none\">Asignaci\u00f3n de horarios<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/h3>\n<p><span data-contrast=\"none\">La primera aplicaci\u00f3n de modelos de optimizaci\u00f3n fue para elaborar un calendario laboral, determinando los d\u00edas de trabajo y descanso de los empleados. <\/span><span data-contrast=\"none\">Esta aplicaci\u00f3n ha reducido significativamente la carga de trabajo asociada con la generaci\u00f3n de estos calendarios, ya que implica asegurar el cumplimiento de ciertas condiciones espec\u00edficas.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<h3><b><span data-contrast=\"none\">Asignaci\u00f3n de quir\u00f3fanos<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/h3>\n<p><span data-contrast=\"none\">Otro caso de \u00e9xito ha sido la aplicaci\u00f3n de modelos de optimizaci\u00f3n en el sector m\u00e9dico. En este caso, el objetivo del modelo era reducir el tiempo de espera medio en la lista de espera. As\u00ed, en un primer lugar el modelo determinaba cu\u00e1ntas horas asignar a cada especialidad m\u00e9dica y, a continuaci\u00f3n, distribu\u00eda las operaciones correspondientes en esos rangos de tiempo.\u00a0<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<h3><b><span data-contrast=\"none\">Planificaci\u00f3n de campa\u00f1as de plantaci\u00f3n<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/h3>\n<p><span data-contrast=\"none\">Por \u00faltimo, se aplic\u00f3 un modelo de optimizaci\u00f3n para la planificaci\u00f3n de campa\u00f1as de plantaci\u00f3n. En este caso, a partir de unos modelos de <em>Machine Learning<\/em> previamente entrenados, el objetivo consist\u00eda en <\/span><span data-contrast=\"none\">establecer la cantidad \u00f3ptima a plantar semanalmente para asegurar el cumplimiento de la demanda de la campa\u00f1a y minimizar las p\u00e9rdidas de plantas.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<h2><b><span data-contrast=\"none\">Etapas de un modelo de investigaci\u00f3n operativa<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/h2>\n<p><span data-contrast=\"none\">Pero \u00bfqu\u00e9 proceso debemos seguir para llegar a elaborar e implementar un modelo?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<ol>\n<li><span data-contrast=\"none\">En primer lugar, es importante realizar un buen <\/span><b><span data-contrast=\"none\">an\u00e1lisis del problema<\/span><\/b><span data-contrast=\"none\">, es decir, identificar y definir los objetivos, variables y restricciones del problema.\u00a0<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:0,&quot;335559739&quot;:390,&quot;335559740&quot;:259}\">\u00a0<\/span><\/li>\n<li data-leveltext=\"%1.\" data-font=\"Aptos\" data-listid=\"6\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769242&quot;:[65533,0],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"none\">Una vez se ha formulado el problema, hay que <\/span><b><span data-contrast=\"none\">definir un modelo matem\u00e1tico<\/span><\/b><span data-contrast=\"none\"> que lo represente y permita su resoluci\u00f3n.\u00a0<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:0,&quot;335559739&quot;:390,&quot;335559740&quot;:259}\">\u00a0<\/span><\/li>\n<li data-leveltext=\"%1.\" data-font=\"Aptos\" data-listid=\"6\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769242&quot;:[65533,0],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"none\">Despu\u00e9s, teniendo en cuenta el modelo matem\u00e1tico, se debe decidir qu\u00e9 <\/span><b><span data-contrast=\"none\">m\u00e9todo de resoluci\u00f3n<\/span><\/b><span data-contrast=\"none\"> es el m\u00e1s apropiado para resolver el problema.\u00a0<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:0,&quot;335559739&quot;:390,&quot;335559740&quot;:259}\">\u00a0<\/span><\/li>\n<li data-leveltext=\"%1.\" data-font=\"Aptos\" data-listid=\"6\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769242&quot;:[65533,0],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"none\">Tras la resoluci\u00f3n del problema se debe<\/span><b><span data-contrast=\"none\"> validar el modelo<\/span><\/b><span data-contrast=\"none\">, es decir, que la soluci\u00f3n devuelta sea factible y, por tanto, el modelo funciona correctamente.\u00a0<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:0,&quot;335559739&quot;:390,&quot;335559740&quot;:259}\">\u00a0<\/span><\/li>\n<li data-leveltext=\"%1.\" data-font=\"Aptos\" data-listid=\"6\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769242&quot;:[65533,0],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"none\">Finalmente, una vez se ha obtenido un modelo efectivo, es posible <\/span><b><span data-contrast=\"none\">implementar la soluci\u00f3n<\/span><\/b><span data-contrast=\"none\"> en el mercado.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:0,&quot;335559739&quot;:390,&quot;335559740&quot;:259}\">\u00a0<\/span><\/li>\n<\/ol>\n<h3><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-41312 size-full\" src=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img271.jpg\" alt=\"Etapas de un modelo de investigaci\u00f3n operativa\u00a0\" width=\"733\" height=\"303\" srcset=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img271.jpg 733w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img271-300x124.jpg 300w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img271-360x149.jpg 360w\" sizes=\"auto, (max-width: 733px) 100vw, 733px\" \/><\/h3>\n<h2><b><span data-contrast=\"none\">Tipos de problemas<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> de <\/span><b><span data-contrast=\"none\">investigaci\u00f3n operativa<\/span><\/b><\/h2>\n<p><span data-contrast=\"none\">Los modelos se clasifican seg\u00fan el<\/span><b><span data-contrast=\"none\"> tipo de variable<\/span><\/b><span data-contrast=\"none\"> y seg\u00fan la <\/span><b><span data-contrast=\"none\">naturaleza de la funci\u00f3n objetivo y las restricciones<\/span><\/b><span data-contrast=\"none\">.\u00a0<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><span data-contrast=\"none\">Seg\u00fan el tipo de variable distinguimos entre:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"11\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"none\">Problemas <\/span><b><span data-contrast=\"none\">enteros<\/span><\/b><span data-contrast=\"none\">: con todas las variables binarias o enteras, como podr\u00eda ser el n\u00famero de productos a fabricar.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/li>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"11\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"none\">Problemas <\/span><b><span data-contrast=\"none\">continuos<\/span><\/b><span data-contrast=\"none\">: donde todas las variables son continuas. Por ejemplo, el coste de fabricaci\u00f3n de un producto.\u00a0\u00a0<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/li>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"11\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"none\">Problemas <\/span><b><span data-contrast=\"none\">mixtos<\/span><\/b><span data-contrast=\"none\">: aquellos que poseen tanto variables continuas como enteras. <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/li>\n<\/ul>\n<p><span data-contrast=\"none\">Por otro lado, seg\u00fan la naturaleza de la funci\u00f3n objetivo y de las restricciones se clasifica en:\u00a0<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"12\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"none\">Problemas <\/span><b><span data-contrast=\"none\">lineales<\/span><\/b><span data-contrast=\"none\">: todas las funciones objetivo y restricciones son lineales<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/li>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"12\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"none\">Problemas <\/span><b><span data-contrast=\"none\">no lineales<\/span><\/b><span data-contrast=\"none\">: en otro caso<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:720,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259,&quot;335559991&quot;:360}\">\u00a0<\/span><\/li>\n<\/ul>\n<h3><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-41313\" src=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img301.jpg\" alt=\"investigaci\u00f3n operativa: Tipos de problemas seg\u00fan variables, restricciones y funci\u00f3n objetivo\" width=\"600\" height=\"277\" srcset=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img301.jpg 956w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img301-300x138.jpg 300w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img301-768x354.jpg 768w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img301-360x166.jpg 360w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/h3>\n<h2><b><span data-contrast=\"none\">M\u00e9todos de resoluci\u00f3n<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/h2>\n<p><span data-contrast=\"none\">Para finalizar, hablaremos sobre los distintos m\u00e9todos de resoluci\u00f3n de un problema de optimizaci\u00f3n. Estos m\u00e9todos se dividen en dos categor\u00edas: exactos y aproximados.\u00a0<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><span data-contrast=\"none\">Los <\/span><b><span data-contrast=\"none\">m\u00e9todos exactos<\/span><\/b><span data-contrast=\"none\"> son aquellos que siempre devuelven la soluci\u00f3n \u00f3ptima al problema. Por tanto, un modelo de optimizaci\u00f3n se resolver\u00e1 idealmente con m\u00e9todos exactos. Sin embargo, esto no siempre es posible. Ya sea porque la dimensi\u00f3n del problema es demasiado grande, lo que incurre en un tiempo de resoluci\u00f3n alto; o porque las restricciones complican excesivamente el problema, y el m\u00e9todo exacto ni siquiera es capaz de resolverlo. <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><span data-contrast=\"none\">Ser\u00e1 en estos casos cuando se apliquen <\/span><b><span data-contrast=\"none\">m\u00e9todos aproximados<\/span><\/b><span data-contrast=\"none\">. El enfoque m\u00e1s com\u00fan es el empleo de <\/span><b><span data-contrast=\"none\">metaheur\u00edsticas<\/span><\/b><span data-contrast=\"none\">, modelos que, a partir de una soluci\u00f3n inicial y otros algoritmos ya definidos, como el gen\u00e9tico, van aproxim\u00e1ndose hacia la soluci\u00f3n \u00f3ptima hasta que se cumpla un criterio de terminaci\u00f3n.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><span data-contrast=\"none\">Algunos ejemplos de algoritmos exactos que se pueden emplear son el <\/span><b><span data-contrast=\"none\">algoritmo simplex<\/span><\/b><span data-contrast=\"none\"> para modelos continuos y el <\/span><b><span data-contrast=\"none\">algoritmo de ramificaci\u00f3n y acotaci\u00f3n<\/span><\/b><span data-contrast=\"none\"> para modelos enteros o mixtos.\u00a0<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-41314\" src=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img311.jpg\" alt=\"Investigaci\u00f3n operativa: Tipos de m\u00e9todos de resoluci\u00f3n: exactos y aproximados\" width=\"600\" height=\"192\" srcset=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img311.jpg 977w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img311-300x96.jpg 300w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img311-768x245.jpg 768w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img311-360x115.jpg 360w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/span><\/p>\n<h2><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:0,&quot;335559739&quot;:390,&quot;335559740&quot;:259}\">\u00a0<\/span><b><span data-contrast=\"none\">Ejemplo pr\u00e1ctico de investigaci\u00f3n operativa<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:0,&quot;335559739&quot;:390,&quot;335559740&quot;:259}\">\u00a0<\/span><\/h2>\n<p><span data-contrast=\"none\">Para terminar, explicaremos como resolver un problema sencillo de asignaci\u00f3n de recursos con la librer\u00eda de optimizaci\u00f3n de <\/span><b><span data-contrast=\"none\">Google OR Tools<\/span><\/b><span data-contrast=\"none\">. Comenzamos instalando la librer\u00eda e importando el modelo que vamos a emplear para resolver el problema<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-41315 size-full\" src=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img431.jpg\" alt=\"investigaci\u00f3n operativa: Problema matem\u00e1tico en Google OR Tools\" width=\"591\" height=\"246\" srcset=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img431.jpg 591w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img431-300x125.jpg 300w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img431-360x150.jpg 360w\" sizes=\"auto, (max-width: 591px) 100vw, 591px\" \/><\/span><\/p>\n<p><span data-contrast=\"none\">Supongamos que queremos modelar y plantear el siguiente problema:\u00a0<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><i><span data-contrast=\"none\">Una compa\u00f1\u00eda produce escritorios, mesas y sillas. La fabricaci\u00f3n de cada unidad de uno de estos muebles precisa madera y dos tipos de mano de obra: acabado y carpinter\u00eda. La cantidad de cada recurso necesaria para fabricar una unidad y el beneficio son los siguientes:<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<table data-tablestyle=\"MsoTableGrid\" data-tablelook=\"1696\" aria-rowcount=\"5\">\n<tbody>\n<tr aria-rowindex=\"1\">\n<td data-celllook=\"4369\"><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">Escritorio<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">Mesas<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">Sillas<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">Disponibilidad<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<\/tr>\n<tr aria-rowindex=\"2\">\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">Madera (unidades)<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">8<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">6<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">1<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">48<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<\/tr>\n<tr aria-rowindex=\"3\">\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">Acabado (horas)<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">4<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">2<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">1,5<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">20<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<\/tr>\n<tr aria-rowindex=\"4\">\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">Carpinter\u00eda (horas)<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">2<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">1,5<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">0,5<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">8<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<\/tr>\n<tr aria-rowindex=\"5\">\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">Beneficio (euros)<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">60<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">30<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\"><i><span data-contrast=\"none\">20<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/td>\n<td data-celllook=\"4369\">\n<p style=\"text-align: center;\"><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><i><span data-contrast=\"none\">\u00bfC\u00f3mo debe organizar la compa\u00f1\u00eda la producci\u00f3n para maximizar los beneficios?<\/span><\/i><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><span data-contrast=\"none\">En primer lugar, definimos las variables. En este caso, <\/span><span data-contrast=\"none\">ser\u00e1n la cantidad de escritorios, mesas y sillas a producir respectivamente. Por tanto, ser\u00e1n variables enteras.\u00a0<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-41316 size-full\" src=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img441.jpg\" alt=\"Definici\u00f3n de variables en Google OR Tools\" width=\"402\" height=\"140\" srcset=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img441.jpg 402w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img441-300x104.jpg 300w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img441-360x125.jpg 360w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/span><\/p>\n<p><span data-contrast=\"none\">As\u00ed, una vez hemos definido las variables, podemos formular la funci\u00f3n objetivo y las restricciones. Como el objetivo del problema es maximizar los beneficios, la funci\u00f3n objetivo es: <\/span><span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;block&quot;&gt;&lt;mn&gt;60&lt;\/mn&gt;&lt;mi&gt;x&lt;\/mi&gt;&lt;mo&gt;+&lt;\/mo&gt;&lt;mn&gt;30&lt;\/mn&gt;&lt;mi&gt;y&lt;\/mi&gt;&lt;mo&gt;+&lt;\/mo&gt;&lt;mn&gt;20&lt;\/mn&gt;&lt;mi&gt;z&lt;\/mi&gt;&lt;mo&gt;&amp;#xA0;&lt;\/mo&gt;&lt;\/math&gt;\">60<em>x<\/em>+30<em>y<\/em>+20<em>z<\/em>\u00a0<\/span><\/p>\n<p><span data-contrast=\"none\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-41317 size-full\" src=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img451.jpg\" alt=\"Funci\u00f3n objetivo en Google OR Tools\" width=\"284\" height=\"60\" \/><\/span><\/p>\n<p><span data-contrast=\"none\">Por otro lado, las restricciones considerar\u00e1n que no se excedan las unidades u horas disponibles para la fabricaci\u00f3n de los productos. Por tanto, las restricciones ser\u00e1n las siguientes:\u00a0<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<ul>\n<li><span data-contrast=\"none\">Madera: <\/span>8<em>x<\/em>+6<em>y<\/em>+<em>z<\/em> \u2264 48<\/li>\n<li><span data-contrast=\"none\">Acabado: <\/span>4<em>x<\/em>+2<em>y<\/em>+1.5<em>z<\/em> \u2264 20<\/li>\n<li><span data-contrast=\"none\">Carpinter\u00eda: <\/span>2<em>x<\/em>+1.5<em>y<\/em>+0.5<em>z<\/em> \u2264 8\u00a0<span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/li>\n<\/ul>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-41318 size-full\" src=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img481.jpg\" alt=\"Restricciones en Google OR Tools\" width=\"319\" height=\"175\" srcset=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img481.jpg 319w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img481-300x165.jpg 300w\" sizes=\"auto, (max-width: 319px) 100vw, 319px\" \/><\/span><\/p>\n<p><span data-contrast=\"none\">Finalmente, una vez se ha planteado el problema, basta con llamar al solucionador para obtener la soluci\u00f3n \u00f3ptima:\u00a0<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-41319 size-full\" src=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img491.jpg\" alt=\"\u00daltimos pasos para solucionar el problema en Google OR Tools\" width=\"503\" height=\"354\" srcset=\"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img491.jpg 503w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img491-300x211.jpg 300w, https:\/\/www.hiberus.com\/crecemos-contigo\/wp-content\/uploads\/2024\/03\/img491-360x253.jpg 360w\" sizes=\"auto, (max-width: 503px) 100vw, 503px\" \/><\/p>\n<p><span data-contrast=\"auto\">Por tanto, para maximizar los beneficios, se deben fabricar<\/span><b><span data-contrast=\"auto\"> dos escritorios y ocho sillas<\/span><\/b><span data-contrast=\"auto\">, obteniendo un beneficio de <\/span><b><span data-contrast=\"auto\">280 euros.<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p>&nbsp;<\/p>\n<p>En hiberus contamos con una unidad especializada en servicios de <a href=\"https:\/\/www.hiberus.com\/data-ia\/data-insights\" target=\"_blank\" rel=\"noopener\">Data &amp; Analytics<\/a>\u00a0formada por un equipo de expertos en\u00a0<a href=\"https:\/\/www.hiberus.com\/enterprise-efficiency\" target=\"_blank\" rel=\"noopener\">Big Data<\/a>,\u00a0<a href=\"https:\/\/www.hiberus.com\/enterprise-efficiency\" target=\"_blank\" rel=\"noopener\">Machine Learning<\/a>, IA, Gobierno de Datos, <a href=\"https:\/\/www.hiberus.com\/soluciones\" target=\"_blank\" rel=\"noopener\">Business Intelligence<\/a> y Analytics, entre otras tecnolog\u00edas. \u00bfNecesitas una soluci\u00f3n basada en <strong>tecnolog\u00eda de datos<\/strong>? \u00a1Contacta con nosotros y estaremos encantados de ayudarte?<\/p>\n        <div class=\"row\">\n            <div class=\"block-cta-form\" style=\"background-color: #003664;\">\n                <div class=\"content-cta-form\">\n                    <div class=\"text-cta-form\">\n                        <p 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herramienta&#8230;<\/p>\n","protected":false},"author":365,"featured_media":41327,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_ayudawp_aiss_exclude":false,"footnotes":""},"categories":[236,7],"tags":[198],"class_list":{"0":"post-41309","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-data-ia","8":"category-next-tech","9":"tag-data"},"acf":[],"_links":{"self":[{"href":"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-json\/wp\/v2\/posts\/41309","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-json\/wp\/v2\/users\/365"}],"replies":[{"embeddable":true,"href":"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-json\/wp\/v2\/comments?post=41309"}],"version-history":[{"count":6,"href":"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-json\/wp\/v2\/posts\/41309\/revisions"}],"predecessor-version":[{"id":41397,"href":"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-json\/wp\/v2\/posts\/41309\/revisions\/41397"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-json\/wp\/v2\/media\/41327"}],"wp:attachment":[{"href":"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-json\/wp\/v2\/media?parent=41309"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-json\/wp\/v2\/categories?post=41309"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.hiberus.com\/crecemos-contigo\/wp-json\/wp\/v2\/tags?post=41309"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}