{"id":78,"date":"2019-09-18T14:47:14","date_gmt":"2019-09-18T14:47:14","guid":{"rendered":"https:\/\/www.penalara.com\/blog\/?p=78"},"modified":"2019-09-18T14:48:08","modified_gmt":"2019-09-18T14:48:08","slug":"sera-possivel-ter-o-horario-perfeito","status":"publish","type":"post","link":"https:\/\/www.penalara.com\/blog\/index.php\/pt\/2019\/09\/18\/sera-possivel-ter-o-horario-perfeito\/","title":{"rendered":"Ser\u00e1 poss\u00edvel ter o hor\u00e1rio perfeito?"},"content":{"rendered":"\n<p><strong>Encaixar os hor\u00e1rios semanais <\/strong>de um centro de ensino moderadamente grande ou complexo <strong>n\u00e3o \u00e9 uma tarefa f\u00e1cil<\/strong>. Este facto \u00e9 bem conhecido por quem j\u00e1 teve em m\u00e3os este problema nalgum momento e, nomeadamente, de quem tem a responsabilidade de o fazer todos os anos; h\u00e1 que solucionar um verdadeiro puzzle. De facto, se j\u00e1 \u00e9 dif\u00edcil encontrar uma solu\u00e7\u00e3o que satisfa\u00e7a os requisitos m\u00ednimos, encontrar a melhor solu\u00e7\u00e3o aparenta ser uma tarefa imposs\u00edvel. Esta \u00e9 precisamente a pergunta que colocamos:<strong> Ser\u00e1 poss\u00edvel fazer hor\u00e1rios perfeitos?<\/strong><\/p>\n\n\n\n<p>Na realidade, e infelizmente, devemos dizer que o hor\u00e1rio perfeito \u00e9 imposs\u00edvel de obter e existem v\u00e1rias raz\u00f5es para o afirmar. A primeira e mais obvia \u00e9 que qualquer modelo para representar algo que se procura ter\u00e1 imperfei\u00e7\u00f5es. Efetivamente, o modelo matem\u00e1tico atrav\u00e9s do qual se calcula uma fun\u00e7\u00e3o de peso que permita obter o hor\u00e1rio \u00f3timo e a sua aplica\u00e7\u00e3o aos diversos elementos que o comp\u00f5em: alunos, professores, aulas, etc\u2026, ser\u00e1 sempre uma aproxima\u00e7\u00e3o \u00e0 realidade que, no melhor dos casos, se estimar\u00e1 de forma precisa correspondendo-se com o que se procura.<\/p>\n\n\n\n<p>A segunda raz\u00e3o, que j\u00e1 n\u00e3o \u00e9 t\u00e3o obvia, \u00e9 que o conjunto de solu\u00e7\u00f5es \u00e9  t\u00e3o elevado que a procura exaustiva \u00e9 imposs\u00edvel, mesmo para o mais  r\u00e1pido computador do mundo. <\/p>\n\n\n\n<p>Lembra-se do paradoxo da lenda do inventor do xadrez?<\/p>\n\n\n\n<p><em>Segundo a Lenda, um Rei Persa que gostava do jogo do xadrez, mandou chamar o seu inventor para o recompensar pelo seu invento. De forma imprudente o Rei disse-lhe que pedisse o que quisesse e ao que o inventor respondeu: basta-me 1 gr\u00e3o de trigo pela primeira casa do tabuleiro, 2 pela segunda, 4 pela terceira, 8 pela quarta e assim por diante at\u00e9 \u00e0 casa 64 do tabuleiro. Ou seja, a soma da s\u00e9rie 1+2+4+8+\u2026. at\u00e9 completar os 64 termos da progress\u00e3o geom\u00e9trica. O Rei pensou que o que lhe estava a ser pedido era uma pechincha e mandou preparar o pr\u00e9mio solicitado. No entanto, ao fazerem os c\u00e1lculos deram-se conta que era imposs\u00edvel cumprir com a ordem j\u00e1 que a soma das quantidades dos gr\u00e3os das 64 casas do tabuleiro era nada mais, nada menos que 36.893.488.147.419.103.231 gr\u00e3os. Ora, se em cada quilograma de trigo cabem aproximadamente 25.000 gr\u00e3os, ent\u00e3o o resultado seria de cerca de 1.475.739.525.896 toneladas. Se o maior cargueiro pode transportar at\u00e9 186.000 toneladas l\u00edquidas, seriam necess\u00e1rios 8 milh\u00f5es de enormes cargueiros para transportar todo o trigo. Mais de 1000 vezes a produ\u00e7\u00e3o anual mundial de trigo.<\/em><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"512\" height=\"303\" src=\"https:\/\/www.penalara.com\/blog\/wp-content\/uploads\/2019\/09\/imagen.png\" alt=\"\" class=\"wp-image-79\" srcset=\"https:\/\/www.penalara.com\/blog\/wp-content\/uploads\/2019\/09\/imagen.png 512w, https:\/\/www.penalara.com\/blog\/wp-content\/uploads\/2019\/09\/imagen-300x178.png 300w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><figcaption>Cavaleiros Templ\u00e1rios jogando xadrez  <\/figcaption><\/figure>\n\n\n\n<p>Este paradoxo tamb\u00e9m ocorre no problema da gera\u00e7\u00e3o de hor\u00e1rios escolares; aparentemente seria relativamente f\u00e1cil testar todas as combina\u00e7\u00f5es poss\u00edveis com um computador mas, em boa verdade, \u00e9 imposs\u00edvel. A quest\u00e3o \u00e9 que o n\u00famero de combina\u00e7\u00f5es cresce exponencialmente e levar-se-iam anos com c\u00e1lculos, mesmo utilizando o computador mais potente, para as percorrer a todas. Os processos que solucionam este puzzle estudam-se atrav\u00e9s de uma disciplina matem\u00e1tica e computacional que tenta dar a melhor solu\u00e7\u00e3o poss\u00edvel, dentro de um intervalo de tempo razo\u00e1vel, a problemas excessivamente complexos.<\/p>\n\n\n\n<p>O Gerador de Hor\u00e1rios para\nCentros de Ensino <strong>GHC<\/strong> da Pe\u00f1alara\ntem por base um software de hor\u00e1rios <strong>capaz\nde encontrar solu\u00e7\u00f5es e de as otimizar<\/strong> de uma forma extraordinariamente\neficaz, em intervalos de tempo suficientemente curtos, mesmo perante os\ncen\u00e1rios mais complicados. A boa not\u00edcia \u00e9 que este tipo de problemas de\ndif\u00edcil solu\u00e7\u00e3o conseguem ser solucionados em grande medida via processos de\nprocura exaustiva <strong>utilizando algoritmos\ninteligentes<\/strong>. Por fim, podemos afirmar com grande satisfa\u00e7\u00e3o e al\u00edvio, para\nquem tem a responsabilidade de fazer hor\u00e1rios letivos, que os <strong>hor\u00e1rios \u201cperfeitos\u201d<\/strong>, na pr\u00e1tica, <strong>s\u00e3o poss\u00edveis<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Encaixar os hor\u00e1rios semanais de um centro de ensino moderadamente grande ou complexo n\u00e3o \u00e9 uma tarefa f\u00e1cil. Este facto \u00e9 bem conhecido por quem j\u00e1 teve em m\u00e3os este problema nalgum momento e, nomeadamente, de quem tem a responsabilidade de o fazer todos os anos; h\u00e1 que solucionar um verdadeiro puzzle. De facto, se &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/www.penalara.com\/blog\/index.php\/pt\/2019\/09\/18\/sera-possivel-ter-o-horario-perfeito\/\" class=\"more-link\">Continuar leyendo<span class=\"screen-reader-text\"> \u00abSer\u00e1 poss\u00edvel ter o hor\u00e1rio perfeito?\u00bb<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[20],"tags":[35,41,39,37],"class_list":["post-78","post","type-post","status-publish","format-standard","hentry","category-uncategorized-pt","tag-algoritmos-pt","tag-historia-pt","tag-horarios","tag-xadrez"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Ser\u00e1 poss\u00edvel ter o hor\u00e1rio perfeito? - Blog de organizaci\u00f3n y optimizaci\u00f3n de horarios<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.penalara.com\/blog\/index.php\/pt\/2019\/09\/18\/sera-possivel-ter-o-horario-perfeito\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ser\u00e1 poss\u00edvel ter o hor\u00e1rio perfeito? - Blog de organizaci\u00f3n y optimizaci\u00f3n de horarios\" \/>\n<meta property=\"og:description\" content=\"Encaixar os hor\u00e1rios semanais de um centro de ensino moderadamente grande ou complexo n\u00e3o \u00e9 uma tarefa f\u00e1cil. Este facto \u00e9 bem conhecido por quem j\u00e1 teve em m\u00e3os este problema nalgum momento e, nomeadamente, de quem tem a responsabilidade de o fazer todos os anos; h\u00e1 que solucionar um verdadeiro puzzle. 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