{"id":6884,"date":"2019-08-27T10:05:19","date_gmt":"2019-08-27T09:05:19","guid":{"rendered":"http:\/\/smart--grid.net\/?page_id=6884"},"modified":"2022-12-03T23:02:05","modified_gmt":"2022-12-03T22:02:05","slug":"resolution-flot-maximum-avec-excel","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/maximum-flow-problem\/maximum-flow-resolution-with-excel\/","title":{"rendered":"Maximum Stream Resolution with Excel"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"6884\" class=\"elementor elementor-6884\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8309e91 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8309e91\" 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-1ffbbfd\" data-id=\"1ffbbfd\" 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-3f77e43 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"3f77e43\" 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\/maximum-flow-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\">Maximum flow 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-5bb7e30\" data-id=\"5bb7e30\" 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-64f1c4a elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"64f1c4a\" 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-0ed8762\" data-id=\"0ed8762\" 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-42fbf68 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"42fbf68\" 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\/Probl%C3%A8me_de_flot_maximum\" 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-1779238a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1779238a\" 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-71611374\" data-id=\"71611374\" 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-772d92ae elementor-widget elementor-widget-text-editor\" data-id=\"772d92ae\" 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 solver solves the problem of <a href=\"https:\/\/complex-systems-ai.com\/en\/maximum-flow-problem\/\">maximum flow<\/a> with Excel from an S node to a T node in a <a href=\"https:\/\/complex-systems-ai.com\/en\/graph-theory-2\/\">graph<\/a> oriented.<\/p><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\/maximum-flow-problem\/maximum-flow-resolution-with-excel\/#Formuler-le-probleme-de-flot-maximum-avec-Excel\" >Formulate the maximum flow problem with Excel<\/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\/maximum-flow-problem\/maximum-flow-resolution-with-excel\/#Resoudre-le-modele\" >Solve the model<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Formuler-le-probleme-de-flot-maximum-avec-Excel\"><\/span>Formulate the maximum flow problem with Excel<span class=\"ez-toc-section-end\"><\/span><\/h2><p>To formulate the flow problem, it is necessary to answer these three questions.<\/p><ul><li>What are the decisions to be made? For this problem, we need Excel to find the flow on each arc. For example, if the flow on SB is equal to 2, cell D5 is equal to 2. (in yellow)<\/li><li>What are the constraints on these decisions? The net flow (Outgoing flow - Incoming flow) of nodes A, B, C, D and E must be equal to 0. In other words, Outgoing flow = Incoming flow. In addition, each bow has a fixed capacity. The flow rate on each arc must be less than this capacity. (in light blue)<\/li><li>What is the overall measure of performance for these decisions? The overall measure of performance is maximum throughput, so the objective is to maximize this quantity. The maximum flow is equal to the output of node S. (in dark blue)<\/li><\/ul><p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-6876 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp49.png\" alt=\"maximum flow resolution with excel\" width=\"604\" height=\"392\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp49.png 604w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp49-300x195.png 300w\" sizes=\"(max-width: 604px) 100vw, 604px\" \/><\/p><p>Let us name the following ranges:<\/p><table class=\"gridtable\" width=\"292\"><tbody><tr><th width=\"178\">Beach name<\/th><th width=\"114\">Cells<\/th><\/tr><tr><td>From<\/td><td>B4: B15<\/td><\/tr><tr><td>To<\/td><td>C4: C15<\/td><\/tr><tr><td>Flow<\/td><td>D4: D15<\/td><\/tr><tr><td>Capacity<\/td><td>F4: F15<\/td><\/tr><tr><td>SupplyDemand<\/td><td>K5: K9<\/td><\/tr><tr><td>MaximumFlow<\/td><td>D17<\/td><\/tr><\/tbody><\/table><p>And let&#039;s insert the following functions:<\/p><p><img decoding=\"async\" class=\"alignnone wp-image-6877 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp50.png\" alt=\"maximum flow resolution with excel\" width=\"604\" height=\"341\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp50.png 604w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp50-300x169.png 300w\" sizes=\"(max-width: 604px) 100vw, 604px\" \/><\/p><h2><span class=\"ez-toc-section\" id=\"Resoudre-le-modele\"><\/span>Solve the model<span class=\"ez-toc-section-end\"><\/span><\/h2><p>Let\u2019s enter the solver parameters:<\/p><p><img decoding=\"async\" class=\"alignnone wp-image-6878 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp51.png\" alt=\"maximum flow resolution with excel\" width=\"570\" height=\"599\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp51.png 570w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp51-285x300.png 285w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p><p>The optimal solution is:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-6879 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp52.png\" alt=\"maximum flow resolution with excel\" width=\"604\" height=\"392\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp52.png 604w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2019\/04\/lp52-300x195.png 300w\" sizes=\"(max-width: 604px) 100vw, 604px\" \/><\/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>Maximum flow problem Wiki home page The solver allows you to solve the maximum flow problem with Excel from a node S to a node ... <\/p>","protected":false},"author":1,"featured_media":0,"parent":3587,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-6884","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/6884","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=6884"}],"version-history":[{"count":3,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/6884\/revisions"}],"predecessor-version":[{"id":17070,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/6884\/revisions\/17070"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/3587"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/media?parent=6884"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}