{"id":868,"date":"2016-02-01T11:06:33","date_gmt":"2016-02-01T10:06:33","guid":{"rendered":"http:\/\/smart--grid.net\/?page_id=868"},"modified":"2024-02-11T19:50:24","modified_gmt":"2024-02-11T18:50:24","slug":"probleme-de-planification","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/planning-problem\/","title":{"rendered":"Planning problem 101"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"868\" class=\"elementor elementor-868\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-17f325b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"17f325b\" 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-2769ade\" data-id=\"2769ade\" 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-10fcafb elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"10fcafb\" 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\/2020\/04\/03\/theories-and-algorithms-2\/\">\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\">Theories<\/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-d35de9b\" data-id=\"d35de9b\" 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-8bc0c5c elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"8bc0c5c\" 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-f638d6e\" data-id=\"f638d6e\" 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-98f61ca elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"98f61ca\" 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:\/\/fr.wikipedia.org\/wiki\/Planification_(intelligence_artificielle)\" 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-5cdd8c8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5cdd8c8\" 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-920d4e1\" data-id=\"920d4e1\" 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-8be7777 elementor-widget elementor-widget-toggle\" data-id=\"8be7777\" 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-1461\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1461\" 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\">I. Scheduling \/ Planning<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1461\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1461\"><ul>\n<li><a href=\"https:\/\/complex-systems-ai.com\/en\/planning-problem\/gantt-chart\/\">Gantt<\/a><\/li>\n<li><a href=\"https:\/\/complex-systems-ai.com\/en\/planning-problem\/pert-method\/\">PERT<\/a><\/li>\n<li><a href=\"https:\/\/complex-systems-ai.com\/en\/planning-problem\/mpm-method\/\">MPM<\/a><\/li>\n<\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1462\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-1462\" 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\">II. Assignment<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1462\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-1462\"><ul>\n<li><a href=\"https:\/\/complex-systems-ai.com\/en\/planning-problem\/algorithm-hungarian\/\">Hungarian algorithm<\/a><\/li>\n<li><a href=\"https:\/\/complex-systems-ai.com\/en\/planning-problem\/algorithm\/\">Edmonds algorithm<\/a><\/li>\n<\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1463\" class=\"elementor-tab-title\" data-tab=\"3\" role=\"button\" aria-controls=\"elementor-tab-content-1463\" 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\">III. Transport<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1463\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"region\" aria-labelledby=\"elementor-tab-title-1463\"><ul>\n<li><a href=\"https:\/\/complex-systems-ai.com\/en\/planning-problem\/stepping-stone\/\">Stepping stone<\/a><\/li>\n<\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1464\" class=\"elementor-tab-title\" data-tab=\"4\" role=\"button\" aria-controls=\"elementor-tab-content-1464\" 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\">IV. Solvers<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1464\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"4\" role=\"region\" aria-labelledby=\"elementor-tab-title-1464\"><ul>\n<li><a href=\"https:\/\/complex-systems-ai.com\/en\/planning-problem\/resolution-assignment-with-excel\/\">Resolution Assignment with Excel<\/a><\/li>\n<li><a href=\"https:\/\/complex-systems-ai.com\/en\/planning-problem\/transport-resolution-with-excel\/\">Transport resolution with Excel<\/a><\/li>\n<\/ul><\/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-29105b22 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"29105b22\" 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-63f08410\" data-id=\"63f08410\" 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-5ff64a9b elementor-widget elementor-widget-text-editor\" data-id=\"5ff64a9b\" 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\n<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\/#Probleme-de-planification-et-dordonnancement\" >Planning and scheduling problem<\/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\/#Introduction-aux-problemes-de-planification\" >Introduction to planning issues<\/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\/#Sous-probleme-lordonnancement\" >Sub-problem: scheduling<\/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\/#Sous-probleme-laffectation\" >Sub-problem: assignment<\/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\/#Sous-probleme-le-transport\" >Sub-problem: transport<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Probleme-de-planification-et-dordonnancement\"><\/span>Planning and scheduling problem<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Automated planning and scheduling is about carrying out strategies or sequences of actions. Modern planning, even within AI, has increasingly reflected the integration of theory and high-performance algorithmic techniques from operations research since at least the 1950s.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Introduction-aux-problemes-de-planification\"><\/span>Introduction to planning issues<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><\/p>\n<p>Planning is the organization of the achievement of objectives in a specific area, with different means, and over a period \/ hierarchy. The result of this problem is a \u201cplan\u201d answering in detail the questions of the type QQOQCC: who, what, where, when, how and how much.<\/p>\n<p><\/p>\n<div style=\"padding: 3px; border: 2px dotted #a5a5a5; background-color: #f6f9fa;\">\n<p style=\"text-align: justify;\">The planning problem makes it possible, depending on the conditions and the information, to answer the following questions:<\/p>\n<ul style=\"text-align: justify;\">\n<li>How to manage the logical sequence of tasks and distribute them over time?<\/li>\n<li>How to analyze the workloads requested from resources or means if they are limited?<\/li>\n<li>How to express a need for resources or means if they are not limited?<\/li>\n<li>How to take into account the constraints external to the project (customer order, supplier delivery, etc.)?<\/li>\n<li>How to analyze the consequences of a difference between actual and forecast events?<\/li>\n<li>How to identify late start or early end dates for activities?<\/li>\n<li>How to simulate optimistic, pessimistic, or most probable assumptions?<\/li>\n<li>How to analyze the impact of a hazard or risk if it turns into a problem?<\/li>\n<li>How to prioritize tasks?<\/li>\n<\/ul>\n<\/div>\n<p><\/p>\n<p>The assignment problem is linked to many other problems in operations research (reduction of problems in the 21 Karp problems for example). Here we will see two sub-problems frequently encountered in assignment problems.<\/p>\n<p><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Sous-probleme-lordonnancement\"><\/span>Sub-problem: scheduling<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><\/p>\n<p>The scheduling problem is a task scheduling problem in which it is a matter of deciding the order in which the tasks should be performed. This problem is Np-difficult taking into account the variety and the complexity of its constraints.<\/p>\n<p><\/p>\n<p>The different methods presented in this course make it possible to clearly and quickly show the data related to the realization of a plan, such as:<\/p>\n<p><\/p>\n<ul class=\"wp-block-list\">\n<li>times, deadlines<\/li>\n<li>means, or resources<\/li>\n<li>the costs.<\/li>\n<\/ul>\n<p><\/p>\n<p>The classic scheduling problem is as follows:<\/p>\n<p><\/p>\n<div style=\"padding: 5px; background-color: #d5edff; border: 2px solid #3c95e8; -moz-border-radius: 9px; -khtml-border-radius: 9px; -webkit-border-radius: 9px; border-radius: 9px;\">Let N tasks T<sub>i<\/sub> requiring a duration of<sub>i<\/sub> data and start date t<sub>i<\/sub> to be determined. The problem is subject to two types of constraints: time constraints - task duration and precedence; resource constraints - disjunctive: if tasks i and j are performed on machine k, they must be done in such and such an order; or cumulative: task i consumes a<sub>ik<\/sub> of the resource k. The resource k has a capacity A<sub>k<\/sub>. At all times, the sum of the consumptions on the machine k must be less than its capacity.<\/div>\n<p><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Sous-probleme-laffectation\"><\/span>Sub-problem: assignment<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><\/p>\n<p>This problem is to best assign tasks to agents. Each agent can perform a single task for a given cost and each task must be performed by a single agent. The assignments (that is to say the agent-task pairs) all have a defined cost, the aim being to minimize the total cost of the assignments in order to carry out all the tasks. This problem is solved in polynomial time.<\/p>\n<p><\/p>\n<div style=\"padding: 5px; background-color: #d5edff; border: 2px solid #3c95e8; -moz-border-radius: 9px; -khtml-border-radius: 9px; -webkit-border-radius: 9px; border-radius: 9px;\">Given a set of agents <strong>S<\/strong> and a set of tasks <strong>T<\/strong>, it is possible to model the problem by a <a href=\"https:\/\/complex-systems-ai.com\/en\/graph-theory-2\/\">graph<\/a> bipartisan <strong>G = ((S, T), E)<\/strong>, with a weight function <strong>vs<\/strong> on the edges. The assignment problem therefore consists in finding a perfect coupling F\u2282E minimizing the sum \u2211<sub>e\u2208F<\/sub> c (e) the weights of the edges of <strong>F<\/strong>.<\/div>\n<p><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Sous-probleme-le-transport\"><\/span>Sub-problem: transport<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><\/p>\n<p>Like the two previous problems, the transport problem is a maximization. The transport problem is one of the subclasses of linear programming problems where the objective is to transport various quantities of a single homogeneous product which are initially stored at various origins, to different destinations such that the transport total is minimal.<\/p>\n<p><\/p>\n<div style=\"padding: 5px; background-color: #d5edff; border: 2px solid #3c95e8; -moz-border-radius: 9px; -khtml-border-radius: 9px; -webkit-border-radius: 9px; border-radius: 9px;\">\n<p>Let a<sub>i<\/sub> the quantity of the commodity available at origin i; b<span style=\"font-size: 13.3333px;\">j<\/span>\u00a0or the quantity of product required for destination j; vs<sub>ij<\/sub> the cost of transporting one unit of a good from origin i to destination j; and x<sub>ij<\/sub>\u00a0is the quantity transported from origin i to destination j.<\/p>\n<p>Here is the problem :<\/p>\n<figure><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-6328 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/04\/transport.png\" alt=\"planning scheduling transportation assignment\" width=\"353\" height=\"170\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/04\/transport.png 353w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/04\/transport-300x144.png 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/figure>\n<p>\u00a0<\/p>\n<\/div>\n<p><\/p>\n<p>If the sum of the sources is equal to the sum of the demands, the problem is said to be balanced, in this case the constraints become equalities. Otherwise, we create a virtual demand point (dummy) corresponding to the excess supply and with a zero transport cost.<\/p>\n<p><\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" class=\"alignnone wp-image-6329 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/04\/transport2.png\" alt=\"planning scheduling transportation assignment\" width=\"452\" height=\"195\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/04\/transport2.png 452w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/04\/transport2-300x129.png 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><\/figure>\n<\/div>\n<p><\/p>\n<p>The transport problem is often represented as a bipartite graph with a flow problem (coupling). We will show here other variants to solve this problem.<\/p>\n<p><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Theories Homepage Wiki I. Scheduling \/ Planning Gantt PERT MPM II. Assignment Hungarian algorithm Algorithm of Edmonds III. Transportation Stepping stone IV. Solvers Resolution Assignment \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-868","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/868","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=868"}],"version-history":[{"count":25,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/868\/revisions"}],"predecessor-version":[{"id":20403,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/868\/revisions\/20403"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/media?parent=868"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}