{"id":10814,"date":"2020-11-10T22:42:09","date_gmt":"2020-11-10T21:42:09","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=10814"},"modified":"2022-12-03T23:05:35","modified_gmt":"2022-12-03T22:05:35","slug":"corrected-exercises-transportation-problems","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/planning-problem\/corrected-exercises-transportation-problems\/","title":{"rendered":"Corrected Exercises: Transportation problems"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"10814\" class=\"elementor elementor-10814\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b798679 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b798679\" 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 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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-65befba\" data-id=\"65befba\" 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-11737ba elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"11737ba\" 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-adab4b0\" data-id=\"adab4b0\" 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-838542b elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"838542b\" 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-c6fb685 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c6fb685\" 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-da2cf98\" data-id=\"da2cf98\" 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-5b6c37d elementor-widget elementor-widget-heading\" data-id=\"5b6c37d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">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\/planning-problem\/corrected-exercises-transportation-problems\/#Corrected-exercises-about-transportation-problems\" >Corrected exercises about transportation 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\/planning-problem\/corrected-exercises-transportation-problems\/#Exercise-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\/planning-problem\/corrected-exercises-transportation-problems\/#Exercise-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\/planning-problem\/corrected-exercises-transportation-problems\/#Exercise-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\/planning-problem\/corrected-exercises-transportation-problems\/#Exercise-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\/planning-problem\/corrected-exercises-transportation-problems\/#Exercise-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\/planning-problem\/corrected-exercises-transportation-problems\/#Exercise-6\" >Exercise 6<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Corrected-exercises-about-transportation-problems\"><\/span>Corrected exercises about transportation 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-6acbcce elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6acbcce\" 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-0186d49\" data-id=\"0186d49\" 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-234dcad elementor-widget elementor-widget-text-editor\" data-id=\"234dcad\" 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>This page presents several corrected exercises about automated planning and scheduling problems, more especially about transportation problems and the related algorithms: the <a href=\"https:\/\/complex-systems-ai.com\/en\/planning-problem\/stepping-stone\/\">stepping stone<\/a>.<\/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-8f35466 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8f35466\" 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-df8c4f2\" data-id=\"df8c4f2\" 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-9c493cc elementor-widget elementor-widget-text-editor\" data-id=\"9c493cc\" 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<h2><span class=\"ez-toc-section\" id=\"Exercise-1\"><\/span><strong><b>Exercise 1<\/b><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><p>A company has to transport supplies from plants to the construction sites. The three plants have 300, 300, 100 supply capacity respectively. And the three construction sites demand 200, 200, 300 respectively.<\/p><p>The transporting costs are shown in the following graph:<\/p><p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter wp-image-10820 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image23.png\" alt=\"corrected exercises automated planning and scheduling problems transportation problems\" width=\"415\" height=\"243\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image23.png 415w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image23-300x176.png 300w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><\/p><p>Find how to allocate the supplies.<\/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-26500a3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"26500a3\" 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-e8ad2d4\" data-id=\"e8ad2d4\" 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-56a29bc elementor-widget elementor-widget-toggle\" data-id=\"56a29bc\" 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-9081\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-9081\" 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-9081\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-9081\"><p><img decoding=\"async\" class=\"aligncenter wp-image-10821 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image24.png\" alt=\"corrected exercises automated planning and scheduling problems transportation problems\" width=\"562\" height=\"201\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image24.png 562w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image24-300x107.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/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-e360ae9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e360ae9\" 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-b800c25\" data-id=\"b800c25\" 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-286ff4c elementor-widget elementor-widget-text-editor\" data-id=\"286ff4c\" 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<h2><span class=\"ez-toc-section\" id=\"Exercise-2\"><\/span><strong><b>Exercise 2<\/b><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><p>Wheat is harvested in the Midwest and stored in grain elevators in three different cities \u2014 Kansas City, Omaha, and Des Moines. These grain elevators supply three flour mills, located in Chicago, St. Louis, and Cincinnati. Grain is shipped to the mills in railroad cars, each car capable of holding one ton of wheat. Each grain elevator is able to supply the following number of tons (ie, railroad cars) of wheat to the mills on a monthly basis.<\/p><p><img decoding=\"async\" class=\"aligncenter wp-image-10822 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image25.png\" alt=\"corrected exercises automated planning and scheduling problems transportation problems\" width=\"222\" height=\"85\" title=\"\"><\/p><p>Each mill demands the following number of tons of wheat per month.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10823 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image26.png\" alt=\"corrected exercises automated planning and scheduling problems transportation problems\" width=\"227\" height=\"90\" title=\"\"><\/p><p>The cost of transporting one ton of wheat from each grain elevator (source) to each mill (destination) differs according to the distance and rail system. These costs are shown in the following table. For example, the cost of shipping one ton of wheat from the grain elevator at Omaha to the mill at Chicago is $7.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10824 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image27.png\" alt=\"corrected exercises automated planning and scheduling problems transportation problems\" width=\"611\" height=\"130\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image27.png 611w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image27-300x64.png 300w\" sizes=\"(max-width: 611px) 100vw, 611px\" \/><\/p><p>The problem is to determine how many tons of wheat to transport from each grain elevator to each mill on a monthly basis in order to minimize the total cost of transportation. Is there any alternative solution? If yes, which one?<\/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-3e89b71 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3e89b71\" 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-258fff4\" data-id=\"258fff4\" 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-75f7b60 elementor-widget elementor-widget-toggle\" data-id=\"75f7b60\" 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-1231\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1231\" 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-1231\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1231\"><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10825 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image28.png\" alt=\"corrected exercises automated planning and scheduling problems transportation problems\" width=\"415\" height=\"248\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image28.png 415w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image28-300x179.png 300w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><\/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-435b2ba elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"435b2ba\" 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-13ed79c\" data-id=\"13ed79c\" 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-e2046d9 elementor-widget elementor-widget-text-editor\" data-id=\"e2046d9\" 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<h2><span class=\"ez-toc-section\" id=\"Exercise-3\"><\/span><strong><b>Exercise 3<\/b><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><p>From the linear program below, formulate the transportation problem and solve it.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10826 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image29.png\" alt=\"corrected exercises automated planning and scheduling problems transportation problems\" width=\"594\" height=\"213\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image29.png 594w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image29-300x108.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p><p>Is there any alternative solution? If yes, which one?<\/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-b0d83b2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b0d83b2\" 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-8637911\" data-id=\"8637911\" 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-2e1d6f7 elementor-widget elementor-widget-toggle\" data-id=\"2e1d6f7\" 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-4831\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-4831\" 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-4831\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-4831\"><p>Same as exercise 2.<\/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-7d96668 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7d96668\" 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-dc26272\" data-id=\"dc26272\" 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-2721e94 elementor-widget elementor-widget-text-editor\" data-id=\"2721e94\" 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<h2><span class=\"ez-toc-section\" id=\"Exercise-4\"><\/span><strong><b>Exercise 4<\/b><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><p>Take the same problem as exercise 2. Change the demand at Cincinnati to 350 tons. Solve it.<\/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-bd39659 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bd39659\" 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-f7c4c88\" data-id=\"f7c4c88\" 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-6f2123c elementor-widget elementor-widget-toggle\" data-id=\"6f2123c\" 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-1161\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1161\" 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-1161\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1161\"><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10827 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image30.png\" alt=\"corrected exercises automated planning and scheduling problems transportation problems\" width=\"416\" height=\"297\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image30.png 416w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image30-300x214.png 300w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><\/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-589ce45 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"589ce45\" 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-c0d3678\" data-id=\"c0d3678\" 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-38d182a elementor-widget elementor-widget-text-editor\" data-id=\"38d182a\" 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<h2><span class=\"ez-toc-section\" id=\"Exercise-5\"><\/span><strong><b>Exercise 5<\/b><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><p>Resolve the following LP problem:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10828 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image31.png\" alt=\"corrected exercises automated planning and scheduling problems transportation problems\" width=\"633\" height=\"201\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image31.png 633w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image31-300x95.png 300w\" sizes=\"(max-width: 633px) 100vw, 633px\" \/><\/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-b4702cc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b4702cc\" 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-580a9ce\" data-id=\"580a9ce\" 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-514b69e elementor-widget elementor-widget-toggle\" data-id=\"514b69e\" 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-8521\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-8521\" 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-8521\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-8521\"><p>We introduce a dummy for j because supply (45 + 60 + 35) -demand (50 + 60) = 30:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10829 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image32.png\" alt=\"corrected exercises automated planning and scheduling problems transportation problems\" width=\"703\" height=\"209\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image32.png 703w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image32-300x89.png 300w\" sizes=\"(max-width: 703px) 100vw, 703px\" \/><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10830 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image33.png\" alt=\"corrected exercises automated planning and scheduling problems transportation problems\" width=\"379\" height=\"195\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image33.png 379w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image33-300x154.png 300w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/><\/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-894e097 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"894e097\" 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-9b05ff2\" data-id=\"9b05ff2\" 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-510f12e elementor-widget elementor-widget-text-editor\" data-id=\"510f12e\" 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<h2><span class=\"ez-toc-section\" id=\"Exercise-6\"><\/span><strong><b>Exercise 6<\/b><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><p>The Atlantic Coast Conference has four basketball games on a particular night. The conference office wants to assign four teams of officials to the four games in a way that will minimize the total distance traveled by the officials. The distances in miles for each team of officials to each game location are shown in Table below:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10831 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image34.png\" alt=\"corrected exercises automated planning and scheduling problems transportation problems\" width=\"519\" height=\"142\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image34.png 519w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image34-300x82.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/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-4b90b47 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4b90b47\" 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-5f8f445\" data-id=\"5f8f445\" 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-54ecc4f elementor-widget elementor-widget-toggle\" data-id=\"54ecc4f\" 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-8901\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-8901\" 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-8901\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-8901\"><p>Each supply and each demand are equal to 1. Solve it as a transportation 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<\/div>","protected":false},"excerpt":{"rendered":"<p>Scheduling problem Home page Wiki Corrected exercises about transportation problems This page presents several corrected exercises about automated planning and scheduling problems, more especially \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":868,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"elementor_header_footer","meta":{"footnotes":""},"class_list":["post-10814","page","type-page","status-publish","hentry"],"amp_enabled":false,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/10814","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/comments?post=10814"}],"version-history":[{"count":7,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/10814\/revisions"}],"predecessor-version":[{"id":19080,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/10814\/revisions\/19080"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/868"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/media?parent=10814"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}