{"id":6843,"date":"2019-04-10T12:37:03","date_gmt":"2019-04-10T11:37:03","guid":{"rendered":"http:\/\/smart--grid.net\/?page_id=6843"},"modified":"2022-12-03T23:02:05","modified_gmt":"2022-12-03T22:02:05","slug":"analyse-post-optimale-de-sensibilite-dual","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/linear-programming-2\/post-optimal-dual-sensitivity-analysis\/","title":{"rendered":"Post-optimal sensitivity analysis (dual)"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"6843\" class=\"elementor elementor-6843\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7fd6e68 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7fd6e68\" 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 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elementor-element-25ce9e8c elementor-widget elementor-widget-text-editor\" data-id=\"25ce9e8c\" 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\/linear-programming-2\/post-optimal-dual-sensitivity-analysis\/#Analyse-post-optimale-de-sensibilite\" >Post-optimal sensitivity analysis<\/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\/linear-programming-2\/post-optimal-dual-sensitivity-analysis\/#Cas-detude-1-introduction-dune-nouvelle-variable\" >Case study 1: introduction of a new variable<\/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\/linear-programming-2\/post-optimal-dual-sensitivity-analysis\/#Cas-detude-2-introduction-dune-nouvelle-contrainte\" >Case study 2: introduction of a new constraint<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Analyse-post-optimale-de-sensibilite\"><\/span>Post-optimal sensitivity analysis<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>THE&#039;<a href=\"https:\/\/complex-systems-ai.com\/en\/linear-programming-2\/post-optimal-sensitivity-analysis\/\">post-optimal sensitivity analysis<\/a> from <a href=\"https:\/\/complex-systems-ai.com\/en\/linear-programming-2\/dual-program\/\">dual program<\/a> makes it possible to check two other measures of sensitivities: new variable and new constraint.<\/p>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Cas-detude-1-introduction-dune-nouvelle-variable\"><\/span>Case study 1: introduction of a new variable<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p>here is the <a href=\"https:\/\/complex-systems-ai.com\/en\/linear-programming-2\/\">linear program<\/a> basic :<\/p>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" class=\"alignnone wp-image-6844 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp35.png\" alt=\"simplex method sensitivity analysis post-optimal dual sensitivity analysis\" width=\"196\" height=\"148\" title=\"\"><\/figure>\n<\/div>\n\n<p>We want to add a new activity:<\/p>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" class=\"alignnone wp-image-6845 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp36.png\" alt=\"simplex method sensitivity analysis post-optimal dual sensitivity analysis\" width=\"217\" height=\"153\" title=\"\"><\/figure>\n<\/div>\n\n<p>We want to determine if the new activity is of interest or not. In other words, if it is not in his interest to do so, the optimal solution of the linear program above gives x<sub>3<\/sub>\u00a0= 0. This is equivalent to the fact that the third constraint of the dual is not satisfied: y<sub>1<\/sub> + 3 y<sub>2<\/sub> + 2y<sub>3<\/sub> \u2265 C<sub>3<\/sub>.<\/p>\n\n<p>The solution of the dual is (200\/3, 0, 100\/3), we replace in the third constraint of the dual:<\/p>\n\n<ul class=\"wp-block-list\">\n<li>If C<sub>3<\/sub>&lt;200\/3 then the new variable is zero in the primal, there is no interest in producing the new activity<\/li>\n<li>If C<sub>3<\/sub>&gt; 200\/3 then there is interest in producing the new activity, moreover the solution of the primal \/ dual will change<\/li>\n<li>If C<sub>3<\/sub>= 200\/3 then the production of the new activity will not change the value of the optimal solution.<\/li>\n<\/ul>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Cas-detude-2-introduction-dune-nouvelle-contrainte\"><\/span>Case study 2: introduction of a new constraint<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p>If the optimal solution satisfies the new constraint, the problem will admit the same solution. Otherwise the introduction of this constraint will generate a new optimal solution.<\/p>\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<\/div>","protected":false},"excerpt":{"rendered":"<p>Linear programming Wiki home page Post-optimal sensitivity analysis The post-optimal sensitivity analysis of the dual program makes it possible to verify two other measures of sensitivities: \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":486,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-6843","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/6843","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=6843"}],"version-history":[{"count":3,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/6843\/revisions"}],"predecessor-version":[{"id":16797,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/6843\/revisions\/16797"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/486"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/media?parent=6843"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}