{"id":15110,"date":"2022-04-17T07:59:22","date_gmt":"2022-04-17T06:59:22","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=15110"},"modified":"2024-02-11T19:24:40","modified_gmt":"2024-02-11T18:24:40","slug":"problemes-daffectation","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/graph-theory-2\/corrected-exercises-on-assignment-problems\/","title":{"rendered":"8 Corrected exercises on assignment problems"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"15110\" class=\"elementor elementor-15110\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e1bea84 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e1bea84\" 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-161d8ee\" data-id=\"161d8ee\" 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-1585829 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"1585829\" 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\/en\/planning-problem\/\">\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\">Planning problem<\/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-e83f3a3\" data-id=\"e83f3a3\" 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-c53695a elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"c53695a\" 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\/en\/\">\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\">Home page<\/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-7179171\" data-id=\"7179171\" 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-12e3596 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"12e3596\" 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\/Automated_planning_and_scheduling\" 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-4f1c87f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4f1c87f\" 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-0ecab41\" data-id=\"0ecab41\" 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-9737cc2 elementor-widget elementor-widget-heading\" data-id=\"9737cc2\" 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_85 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\">Contents<\/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=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/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\/en\/graph-theory-2\/corrected-exercises-on-assignment-problems\/#Exercices-corriges-sur-les-problemes-daffectation\" >Corrected exercises on assignment problems<\/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\/en\/graph-theory-2\/corrected-exercises-on-assignment-problems\/#Exercice-1\" >Exercise 1<\/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\/en\/graph-theory-2\/corrected-exercises-on-assignment-problems\/#Exercice-2\" >Exercise 2<\/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\/en\/graph-theory-2\/corrected-exercises-on-assignment-problems\/#Exercice-3\" >Exercise 3<\/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\/en\/graph-theory-2\/corrected-exercises-on-assignment-problems\/#Exercice-4\" >Exercise 4<\/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\/en\/graph-theory-2\/corrected-exercises-on-assignment-problems\/#Exercice-5\" >Exercise 5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/complex-systems-ai.com\/en\/graph-theory-2\/corrected-exercises-on-assignment-problems\/#Exercice-6\" >Exercise 6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/complex-systems-ai.com\/en\/graph-theory-2\/corrected-exercises-on-assignment-problems\/#Exercice-7\" >Exercise 7<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/complex-systems-ai.com\/en\/graph-theory-2\/corrected-exercises-on-assignment-problems\/#Exercice-8\" >Exercise 8<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercices-corriges-sur-les-problemes-daffectation\"><\/span>Corrected exercises on assignment problems<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-a0bf4e8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a0bf4e8\" 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-1f06199\" data-id=\"1f06199\" 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-fb9063c elementor-widget elementor-widget-text-editor\" data-id=\"fb9063c\" 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>The page presents several corrected exercises on automated planning and scheduling problems, in particular on assignment problems.<\/p><p><img decoding=\"async\" class=\"aligncenter wp-image-11096 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/cropped-Capture.png\" alt=\"assignment problems\" 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-d29a3fb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d29a3fb\" 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-c7f8344\" data-id=\"c7f8344\" 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-f52feef elementor-widget elementor-widget-heading\" data-id=\"f52feef\" 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=\"Exercice-1\"><\/span>Exercise 1<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-8d539a6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8d539a6\" 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-7036b96\" data-id=\"7036b96\" 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-d6068c8 elementor-widget elementor-widget-text-editor\" data-id=\"d6068c8\" 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>The Atlantic Coast network serves four cities. The management wants to allocate four factories to the cities. The price to send energy from a factory to each city is described below:<\/p><table><tbody><tr><td width=\"122\">\u00a0<\/td><td width=\"122\"><p>Raleigh<\/p><\/td><td width=\"122\"><p>Atlanta<\/p><\/td><td width=\"122\"><p>Durham<\/p><\/td><td width=\"122\"><p>Clemson<\/p><\/td><\/tr><tr><td width=\"122\"><p>Plant A<\/p><\/td><td width=\"122\"><p>210<\/p><\/td><td width=\"122\"><p>90<\/p><\/td><td width=\"122\"><p>180<\/p><\/td><td width=\"122\"><p>160<\/p><\/td><\/tr><tr><td width=\"122\"><p>Plant B<\/p><\/td><td width=\"122\"><p>100<\/p><\/td><td width=\"122\"><p>70<\/p><\/td><td width=\"122\"><p>130<\/p><\/td><td width=\"122\"><p>200<\/p><\/td><\/tr><tr><td width=\"122\"><p>Plant C<\/p><\/td><td width=\"122\"><p>175<\/p><\/td><td width=\"122\"><p>105<\/p><\/td><td width=\"122\"><p>140<\/p><\/td><td width=\"122\"><p>170<\/p><\/td><\/tr><tr><td width=\"122\"><p>Plant D<\/p><\/td><td width=\"122\"><p>80<\/p><\/td><td width=\"122\"><p>65<\/p><\/td><td width=\"122\"><p>105<\/p><\/td><td width=\"122\"><p>120<\/p><\/td><\/tr><\/tbody><\/table><p>A factory can only earn one city, and a city can only draw energies from one factory. Find the best mission at the lowest cost.<\/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-4e6e40b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4e6e40b\" 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-9da21e2\" data-id=\"9da21e2\" 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-b907c04 elementor-widget elementor-widget-toggle\" data-id=\"b907c04\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1941\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1941\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1941\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1941\"><p>After the first reduction:<\/p><table><tbody><tr><td width=\"122\">\u00a0<\/td><td width=\"122\"><p>R<\/p><\/td><td width=\"122\"><p>TO<\/p><\/td><td width=\"122\"><p>D<\/p><\/td><td width=\"122\"><p>VS<\/p><\/td><\/tr><tr><td width=\"122\"><p>TO<\/p><\/td><td width=\"122\"><p>105<\/p><\/td><td width=\"122\"><p>0<\/p><\/td><td width=\"122\"><p>55<\/p><\/td><td width=\"122\"><p>15<\/p><\/td><\/tr><tr><td width=\"122\"><p>B<\/p><\/td><td width=\"122\"><p>15<\/p><\/td><td width=\"122\"><p>0<\/p><\/td><td width=\"122\"><p>25<\/p><\/td><td width=\"122\"><p>75<\/p><\/td><\/tr><tr><td width=\"122\"><p>VS<\/p><\/td><td width=\"122\"><p>35<\/p><\/td><td width=\"122\"><p>0<\/p><\/td><td width=\"122\"><p>0<\/p><\/td><td width=\"122\"><p>10<\/p><\/td><\/tr><tr><td width=\"122\"><p>D<\/p><\/td><td width=\"122\"><p>0<\/p><\/td><td width=\"122\"><p>0<\/p><\/td><td width=\"122\"><p>5<\/p><\/td><td width=\"122\"><p>0<\/p><\/td><\/tr><\/tbody><\/table><p>Then :<\/p><table><tbody><tr><td width=\"122\">\u00a0<\/td><td width=\"122\"><p>R<\/p><\/td><td width=\"122\"><p>TO<\/p><\/td><td width=\"122\"><p>D<\/p><\/td><td width=\"122\"><p>VS<\/p><\/td><\/tr><tr><td width=\"122\"><p>TO<\/p><\/td><td width=\"122\"><p>90<\/p><\/td><td width=\"122\"><p>0<\/p><\/td><td width=\"122\"><p>40<\/p><\/td><td width=\"122\"><p>0<\/p><\/td><\/tr><tr><td width=\"122\"><p>B<\/p><\/td><td width=\"122\"><p>0<\/p><\/td><td width=\"122\"><p>0<\/p><\/td><td width=\"122\"><p>10<\/p><\/td><td width=\"122\"><p>60<\/p><\/td><\/tr><tr><td width=\"122\"><p>VS<\/p><\/td><td width=\"122\"><p>55<\/p><\/td><td width=\"122\"><p>15<\/p><\/td><td width=\"122\"><p>0<\/p><\/td><td width=\"122\"><p>10<\/p><\/td><\/tr><tr><td width=\"122\"><p>D<\/p><\/td><td width=\"122\"><p>0<\/p><\/td><td width=\"122\"><p>15<\/p><\/td><td width=\"122\"><p>5<\/p><\/td><td width=\"122\"><p>0<\/p><\/td><\/tr><\/tbody><\/table><p>Solution: 90+100+140+120=450.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\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-ca16741 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ca16741\" 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-8a178e0\" data-id=\"8a178e0\" 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-ccc3590 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"ccc3590\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\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-92d09e9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"92d09e9\" 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-2c48cd5\" data-id=\"2c48cd5\" 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-6090063 elementor-widget elementor-widget-heading\" data-id=\"6090063\" 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=\"Exercice-2\"><\/span>Exercise 2<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-085f0df elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"085f0df\" 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-f52808d\" data-id=\"f52808d\" 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-156af74 elementor-widget elementor-widget-text-editor\" data-id=\"156af74\" 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\tSwap the columns of a square matrix so as to minimize the sum of the elements on the main diagonal.\n<table>\n<tbody>\n<tr>\n<td width=\"122\">8<\/td>\n<td width=\"122\">16<\/td>\n<td width=\"122\">15<\/td>\n<td width=\"122\">91<\/td>\n<td width=\"122\">64<\/td>\n<\/tr>\n<tr>\n<td width=\"122\">83<\/td>\n<td width=\"122\">42<\/td>\n<td width=\"122\">93<\/td>\n<td width=\"122\">75<\/td>\n<td width=\"122\">27<\/td>\n<\/tr>\n<tr>\n<td width=\"122\">76<\/td>\n<td width=\"122\">95<\/td>\n<td width=\"122\">75<\/td>\n<td width=\"122\">81<\/td>\n<td width=\"122\">50<\/td>\n<\/tr>\n<tr>\n<td width=\"122\">20<\/td>\n<td width=\"122\">42<\/td>\n<td width=\"122\">96<\/td>\n<td width=\"122\">90<\/td>\n<td width=\"122\">24<\/td>\n<\/tr>\n<tr>\n<td width=\"122\">38<\/td>\n<td width=\"122\">28<\/td>\n<td width=\"122\">2<\/td>\n<td width=\"122\">15<\/td>\n<td width=\"122\">81<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-1810ec2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1810ec2\" 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-b6ba176\" data-id=\"b6ba176\" 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-bc3436d elementor-widget elementor-widget-toggle\" data-id=\"bc3436d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1971\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1971\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1971\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1971\"><p>Find an assignment solution to this matrix. Rearrange the columns so that the solution forms a diagonal.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\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-f5bb734 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f5bb734\" 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-0279b0c\" data-id=\"0279b0c\" 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-95b09ef elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"95b09ef\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\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-2205dbb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2205dbb\" 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-64fd0c5\" data-id=\"64fd0c5\" 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-4ab98f4 elementor-widget elementor-widget-heading\" data-id=\"4ab98f4\" 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=\"Exercice-3\"><\/span>Exercise 3<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-fdd5255 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fdd5255\" 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-eaef437\" data-id=\"eaef437\" 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-e5e156c elementor-widget elementor-widget-text-editor\" data-id=\"e5e156c\" 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>Three robots {a,b,c} must complete three tasks {t1, t2, t3} in the following grid. It takes a day for a robot to move from one cell to one of its neighbours.<\/p><p><img decoding=\"async\" class=\"alignnone wp-image-10943 size-full\" title=\"Corrected Exercises: Assignment Problem 1\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image30-1.png\" alt=\"assignment problem corrected exercises hungarian algorithm kuhn algorithm\" width=\"205\" height=\"202\" data-recalc-dims=\"1\" \/><\/p><p>In the following table, we list the days when each robot can complete each task on its own. Tasks should be completed as soon as possible.<\/p><p><img decoding=\"async\" class=\"alignnone wp-image-10944 size-full\" title=\"Corrected Exercises: Assignment Problem 2\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image31-1.png\" alt=\"assignment problem corrected exercises hungarian algorithm kuhn algorithm\" width=\"151\" height=\"96\" data-recalc-dims=\"1\" \/><\/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-63bcec6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"63bcec6\" 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-bb640ad\" data-id=\"bb640ad\" 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-02c2b58 elementor-widget elementor-widget-toggle\" data-id=\"02c2b58\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2891\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2891\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2891\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2891\"><p>Add the distance from Manhattan in days to the last table. Solve the assignment problem.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\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-0202636 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0202636\" 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-f6c9c05\" data-id=\"f6c9c05\" 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-44e9427 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"44e9427\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\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-a353c85 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a353c85\" 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-2741b49\" data-id=\"2741b49\" 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-4bedc94 elementor-widget elementor-widget-heading\" data-id=\"4bedc94\" 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=\"Exercice-4\"><\/span>Exercise 4<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-812248e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"812248e\" 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-3ad6ae0\" data-id=\"3ad6ae0\" 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-88272f4 elementor-widget elementor-widget-text-editor\" data-id=\"88272f4\" 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>Braneast Airlines is to staff the failed flights between New York and Chicago listed in the table below. Each of the Braneast crew lives in either New York or Chicago. Each day, a crew must fly one NY-Chicago flight and one Chicago-NY flight with at least one hour of downtime between flights.<\/p><p>Braneast wants to schedule crews to minimize total downtime. Develop an assignment problem that can be used to achieve this goal. Of course, some assignments are not possible. Find flight assignments that minimize total downtime. How many crews should be based in each city? Suppose that at the end of the day, each crew must be in their home town.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-10945 size-large\" title=\"Corrected Exercises: Assignment Problem 3\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image32-1-1024x547.png\" alt=\"assignment problem corrected exercises hungarian algorithm kuhn algorithm\" width=\"1024\" height=\"547\" data-recalc-dims=\"1\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image32-1-1024x547.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image32-1-300x160.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image32-1-768x410.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image32-1-1000x534.png 1000w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image32-1.png 1098w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/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-ef7f1c6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ef7f1c6\" 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-4edd57e\" data-id=\"4edd57e\" 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-15874eb elementor-widget elementor-widget-toggle\" data-id=\"15874eb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2251\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2251\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2251\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2251\"><p>The assignment table is constructed as follows: for the first flight departing from Chicago, given the time of arrival in NY, how long the crew must wait at the airport. For example for the first flight from Chicago, it arrives at 10am:<\/p><table><tbody><tr><td width=\"83\"><p>Flight<\/p><\/td><td width=\"76\"><p>1<\/p><\/td><td width=\"76\"><p>2<\/p><\/td><td width=\"76\"><p>3<\/p><\/td><td width=\"76\"><p>4<\/p><\/td><td width=\"76\"><p>5<\/p><\/td><td width=\"76\"><p>6<\/p><\/td><td width=\"75\"><p>7<\/p><\/td><\/tr><tr><td width=\"83\"><p>Leave New York<\/p><\/td><td width=\"76\"><p>7<\/p><\/td><td width=\"76\"><p>8<\/p><\/td><td width=\"76\"><p>10<\/p><\/td><td width=\"76\"><p>12<\/p><\/td><td width=\"76\"><p>14<\/p><\/td><td width=\"76\"><p>16<\/p><\/td><td width=\"75\"><p>18<\/p><\/td><\/tr><tr><td width=\"83\"><p>Waiting time<\/p><\/td><td width=\"76\"><p>impossible<\/p><\/td><td width=\"76\"><p>impossible<\/p><\/td><td width=\"76\"><p>impossible<\/p><\/td><td width=\"76\"><p>2<\/p><\/td><td width=\"76\"><p>4<\/p><\/td><td width=\"76\"><p>6<\/p><\/td><td width=\"75\"><p>8<\/p><\/td><\/tr><\/tbody><\/table><p>We note that flights 4, 5, 6, 7 from Chicago cannot be the point of departure, so we calculate the wait time from the flight from New York. Note that flight 7 from NY cannot be a departure point, so we are calculating the wait time from the flight from Chicago. From each of the elements in the table, we retain the lowest calculated value (for flights from Chicago and NY).<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-10946 size-large\" title=\"Corrected Exercises: Assignment Problem 4\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image33-1-1024x316.png\" alt=\"assignment problem corrected exercises hungarian algorithm kuhn algorithm\" width=\"1024\" height=\"316\" data-recalc-dims=\"1\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image33-1-1024x316.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image33-1-300x93.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image33-1-768x237.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image33-1-1000x309.png 1000w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image33-1.png 1120w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p><p>Solution :<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-10947 size-full\" title=\"Corrected Exercises: Assignment Problem 5\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image34-1.png\" alt=\"assignment problem corrected exercises hungarian algorithm kuhn algorithm\" width=\"989\" height=\"333\" data-recalc-dims=\"1\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image34-1.png 989w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image34-1-300x101.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image34-1-768x259.png 768w\" sizes=\"(max-width: 989px) 100vw, 989px\" \/><\/p><p>Starts in New York: (1.3), (2.4), (3.5), (5.6), (6.7).<\/p><p>Starts in Chicago: (4.1), (7.2).<\/p><p>Total downtime = 25h.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-10948 size-full\" title=\"Corrected Exercises: Assignment Problem 6\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image35-1.png\" alt=\"assignment problem corrected exercises hungarian algorithm kuhn algorithm\" width=\"927\" height=\"578\" data-recalc-dims=\"1\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image35-1.png 927w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image35-1-300x187.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image35-1-768x479.png 768w\" sizes=\"(max-width: 927px) 100vw, 927px\" \/><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\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-95914da elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"95914da\" 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-0232e3f\" data-id=\"0232e3f\" 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-de326f4 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"de326f4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\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-ac0eee3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ac0eee3\" 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-85045a8\" data-id=\"85045a8\" 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-bdc7811 elementor-widget elementor-widget-heading\" data-id=\"bdc7811\" 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=\"Exercice-5\"><\/span>Exercise 5<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-7fa5b42 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7fa5b42\" 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-b6ec2a3\" data-id=\"b6ec2a3\" 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-6be7ee0 elementor-widget elementor-widget-text-editor\" data-id=\"6be7ee0\" 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>Consider the data in the table below. If a Mumbai-based crew arrives in Delhi on a given flight, they must return to Mumbai on a subsequent flight. Assume that for any given pairing, the crew will be based in the city that results in the smallest stopover.<\/p><p>The problem is to find pairings in a way that minimizes ground time away from home, subject to a minimum one-hour interval between arrival and departure. Given the flight pairs, where should the crews be based?<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-10949 size-full\" title=\"Corrected Exercises: Assignment Problem 7\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image36-1.png\" alt=\"assignment problem corrected exercises hungarian algorithm kuhn algorithm\" width=\"430\" height=\"297\" data-recalc-dims=\"1\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image36-1.png 430w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image36-1-300x207.png 300w\" sizes=\"(max-width: 430px) 100vw, 430px\" \/><\/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-9e77d8d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9e77d8d\" 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-8eaa3b1\" data-id=\"8eaa3b1\" 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-f2a7f01 elementor-widget elementor-widget-toggle\" data-id=\"f2a7f01\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2541\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2541\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2541\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2541\"><p>As in the previous exercise, first calculate the layover time matrices, one for the layover in Mumbai and the other for Delhi.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-10950 size-full\" title=\"Corrected Exercises: Assignment Problem 8\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image37-1.png\" alt=\"assignment problem corrected exercises hungarian algorithm kuhn algorithm\" width=\"510\" height=\"195\" data-recalc-dims=\"1\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image37-1.png 510w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image37-1-300x115.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p><p>We now calculate the minimum of the values for the 36 pairs and construct the table below. For example (7.2) is the minimum between (7.2) in the first matrix and (2.7) in the second.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-10951 size-full\" title=\"Corrected Exercises: Assignment Problem 9\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image38-1.png\" alt=\"assignment problem corrected exercises hungarian algorithm kuhn algorithm\" width=\"307\" height=\"163\" data-recalc-dims=\"1\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image38-1.png 307w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image38-1-300x159.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/p><p>The solution to this problem is the pairs (7,3) Mumbai, (8,4) Mumbai, (9,2) Delhi, (10,5) Mumbai, (11,6) Delhi, (12 , 1) from Delhi with total downtime = 18h.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\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-053fd12 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"053fd12\" 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-66222a6\" data-id=\"66222a6\" 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-7d50698 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"7d50698\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\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-86bfc2f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"86bfc2f\" 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-ac46095\" data-id=\"ac46095\" 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-5bfdcc3 elementor-widget elementor-widget-heading\" data-id=\"5bfdcc3\" 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=\"Exercice-6\"><\/span>Exercise 6<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-5824b72 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5824b72\" 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-d041d03\" data-id=\"d041d03\" 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-5f46f8b elementor-widget elementor-widget-text-editor\" data-id=\"5f46f8b\" 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>Solve the following problem as an assignment problem.<\/p><p>Minimize 4X<sub>11<\/sub>+ 6X<sub>12<\/sub>+ 5X<sub>13<\/sub>+ 5X<sub>14<\/sub>+ 7X<sub>21<\/sub>+ 4X<sub>22<\/sub>+ 5X<sub>23<\/sub>+ 6X<sub>24<\/sub>\u00a0\u00a0+ 4X<sub>31<\/sub>+ 7X<sub>32<\/sub>+ 6X<sub>33<\/sub>+ 4X<sub>34<\/sub>\u00a0\u00a0+ 5X<sub>41<\/sub>+ 3X<sub>42<\/sub>+ 4X<sub>43<\/sub>+ 7X<sub>44<\/sub><\/p><p>St. X<sub>11<\/sub>+ X<sub>12<\/sub>+ X<sub>13<\/sub>+ X<sub>14<\/sub>=1<\/p><p>X<sub>21<\/sub>+ X<sub>22<\/sub>+ X<sub>24<\/sub>+ X<sub>24<\/sub>=1<\/p><p>X<sub>31<\/sub>+ X<sub>32<\/sub>+ X<sub>33<\/sub>+ X<sub>34<\/sub>=1<\/p><p>X<sub>41<\/sub>+ X<sub>42<\/sub>+ X<sub>43<\/sub>+ X<sub>44<\/sub>=1<\/p><p>X<sub>11<\/sub>+ X<sub>21<\/sub>+ X<sub>31<\/sub>+ X<sub>41<\/sub>=1<\/p><p>X<sub>12<\/sub>+ X<sub>22<\/sub>+ X<sub>32<\/sub>+ X<sub>42<\/sub>=1<\/p><p>X<sub>13<\/sub>+ X<sub>23<\/sub>+ X<sub>33<\/sub>+ X<sub>43<\/sub>=1<\/p><p>X<sub>14<\/sub>+ X<sub>24<\/sub>+ X<sub>34<\/sub>+ X<sub>44<\/sub>=1<\/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-bfc446d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bfc446d\" 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-d37133c\" data-id=\"d37133c\" 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-b3224da elementor-widget elementor-widget-toggle\" data-id=\"b3224da\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1871\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1871\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1871\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1871\"><p>You need to solve the assignment problem:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-10952 size-full\" title=\"Corrected Exercises: Assignment Problem 10\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image39-1.png\" alt=\"assignment problem corrected exercises hungarian algorithm kuhn algorithm\" width=\"171\" height=\"146\" data-recalc-dims=\"1\" \/><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\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-026ed58 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"026ed58\" 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-a366db3\" data-id=\"a366db3\" 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-eb48734 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"eb48734\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\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-c87967c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c87967c\" 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-952c133\" data-id=\"952c133\" 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-f234714 elementor-widget elementor-widget-heading\" data-id=\"f234714\" 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=\"Exercice-7\"><\/span>Exercise 7<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-f9c819d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f9c819d\" 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-75da6ed\" data-id=\"75da6ed\" 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-71b7452 elementor-widget elementor-widget-text-editor\" data-id=\"71b7452\" 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>Solve the following problem as an assignment problem.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-10953 size-full\" title=\"Corrected Exercises: Assignment Problem 11\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image40-1.png\" alt=\"assignment problem corrected exercises hungarian algorithm kuhn algorithm\" width=\"330\" height=\"205\" data-recalc-dims=\"1\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image40-1.png 330w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image40-1-300x186.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><\/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-cdae784 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cdae784\" 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-764e704\" data-id=\"764e704\" 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-38bee1e elementor-widget elementor-widget-toggle\" data-id=\"38bee1e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-5951\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-5951\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-5951\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-5951\"><p>The assignment problem is described in the table below:<\/p><table><tbody><tr><td width=\"76\">\u00a0<\/td><td width=\"76\"><p>1<\/p><\/td><td width=\"76\"><p>2<\/p><\/td><td width=\"76\"><p>3<\/p><\/td><\/tr><tr><td width=\"76\"><p>1<\/p><\/td><td width=\"76\"><p>5<\/p><\/td><td width=\"76\"><p>9<\/p><\/td><td width=\"76\"><p>inf<\/p><\/td><\/tr><tr><td width=\"76\"><p>2<\/p><\/td><td width=\"76\"><p>inf<\/p><\/td><td width=\"76\"><p>2<\/p><\/td><td width=\"76\"><p>inf<\/p><\/td><\/tr><tr><td width=\"76\"><p>3<\/p><\/td><td width=\"76\"><p>inf<\/p><\/td><td width=\"76\"><p>1<\/p><\/td><td width=\"76\"><p>1<\/p><\/td><\/tr><\/tbody><\/table><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\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-0250686 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0250686\" 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-fa530a8\" data-id=\"fa530a8\" 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-7f02013 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"7f02013\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\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-338d68b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"338d68b\" 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-3919a83\" data-id=\"3919a83\" 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-0e31d9f elementor-widget elementor-widget-heading\" data-id=\"0e31d9f\" 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=\"Exercice-8\"><\/span>Exercise 8<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-e8ebbaf elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e8ebbaf\" 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-7fca9db\" data-id=\"7fca9db\" 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-c1ec3ea elementor-widget elementor-widget-text-editor\" data-id=\"c1ec3ea\" 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>The Department of Art History wishes to offer six courses per semester. There are seven professors in the department, each of whom can only teach certain courses, as shown in the table. Is it possible to assign all six courses to teachers so that no teacher teaches more than one course?<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-10954 size-full\" title=\"Corrected Exercises: Assignment Problem 12\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image41-1.png\" alt=\"assignment problem corrected exercises hungarian algorithm kuhn algorithm\" width=\"354\" height=\"174\" data-recalc-dims=\"1\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image41-1.png 354w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image41-1-300x147.png 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><\/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-c33a3bc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c33a3bc\" 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-371d6fb\" data-id=\"371d6fb\" 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-bb49969 elementor-widget elementor-widget-toggle\" data-id=\"bb49969\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1961\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1961\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1961\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1961\"><p>The assignment problem is described in the table below:<\/p><table><tbody><tr><td width=\"101\">\u00a0<\/td><td width=\"73\"><p>Ant<\/p><\/td><td width=\"73\"><p>Bat<\/p><\/td><td width=\"73\"><p>Cat<\/p><\/td><td width=\"74\"><p>Dodo<\/p><\/td><td width=\"74\"><p>Frog<\/p><\/td><td width=\"74\"><p>Gnat<\/p><\/td><td width=\"72\"><p>Hog<\/p><\/td><\/tr><tr><td width=\"101\"><p>Antique<\/p><\/td><td width=\"73\"><p>1<\/p><\/td><td width=\"73\"><p>1<\/p><\/td><td width=\"73\"><p>1<\/p><\/td><td width=\"74\"><p>1<\/p><\/td><td width=\"74\"><p>inf<\/p><\/td><td width=\"74\"><p>inf<\/p><\/td><td width=\"72\"><p>inf<\/p><\/td><\/tr><tr><td width=\"101\"><p>Renaissance<\/p><\/td><td width=\"73\"><p>1<\/p><\/td><td width=\"73\"><p>inf<\/p><\/td><td width=\"73\"><p>inf<\/p><\/td><td width=\"74\"><p>inf<\/p><\/td><td width=\"74\"><p>1<\/p><\/td><td width=\"74\"><p>1<\/p><\/td><td width=\"72\"><p>inf<\/p><\/td><\/tr><tr><td width=\"101\"><p>Baroque<\/p><\/td><td width=\"73\"><p>1<\/p><\/td><td width=\"73\"><p>inf<\/p><\/td><td width=\"73\"><p>inf<\/p><\/td><td width=\"74\"><p>inf<\/p><\/td><td width=\"74\"><p>1<\/p><\/td><td width=\"74\"><p>inf<\/p><\/td><td width=\"72\"><p>inf<\/p><\/td><\/tr><tr><td width=\"101\"><p>Impressionism<\/p><\/td><td width=\"73\"><p>inf<\/p><\/td><td width=\"73\"><p>inf<\/p><\/td><td width=\"73\"><p>inf<\/p><\/td><td width=\"74\"><p>inf<\/p><\/td><td width=\"74\"><p>1<\/p><\/td><td width=\"74\"><p>1<\/p><\/td><td width=\"72\"><p>inf<\/p><\/td><\/tr><tr><td width=\"101\"><p>Modern<\/p><\/td><td width=\"73\"><p>inf<\/p><\/td><td width=\"73\"><p>inf<\/p><\/td><td width=\"73\"><p>1<\/p><\/td><td width=\"74\"><p>inf<\/p><\/td><td width=\"74\"><p>inf<\/p><\/td><td width=\"74\"><p>1<\/p><\/td><td width=\"72\"><p>1<\/p><\/td><\/tr><tr><td width=\"101\"><p>Contemporary<\/p><\/td><td width=\"73\"><p>1<\/p><\/td><td width=\"73\"><p>inf<\/p><\/td><td width=\"73\"><p>inf<\/p><\/td><td width=\"74\"><p>inf<\/p><\/td><td width=\"74\"><p>inf<\/p><\/td><td width=\"74\"><p>1<\/p><\/td><td width=\"72\"><p>inf<\/p><\/td><\/tr><tr><td width=\"101\"><p>dummy<\/p><\/td><td width=\"73\"><p>1<\/p><\/td><td width=\"73\"><p>1<\/p><\/td><td width=\"73\"><p>1<\/p><\/td><td width=\"74\"><p>1<\/p><\/td><td width=\"74\"><p>1<\/p><\/td><td width=\"74\"><p>1<\/p><\/td><td width=\"72\"><p>1<\/p><\/td><\/tr><\/tbody><\/table><p>In order to find a mission, it is better to use the stepping stone method instead of the Hungarian method.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\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>Scheduling problem Home page Wiki Corrected exercises on assignment problems The page presents several corrected exercises on planning and scheduling problems \u2026 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