{"id":308,"date":"2022-02-27T17:50:00","date_gmt":"2022-02-27T17:50:00","guid":{"rendered":"https:\/\/dev.dtrees.com\/?page_id=308"},"modified":"2022-03-07T10:02:48","modified_gmt":"2022-03-07T10:02:48","slug":"methodologie","status":"publish","type":"page","link":"https:\/\/dtrees.com\/en\/methodology\/","title":{"rendered":"Methodology"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"308\" class=\"elementor elementor-308\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-629507ff elementor-section-height-min-height elementor-section-stretched elementor-section-boxed elementor-section-height-default elementor-section-items-middle\" data-id=\"629507ff\" data-element_type=\"section\" data-settings=\"{&quot;stretch_section&quot;:&quot;section-stretched&quot;,&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1e996e3d\" data-id=\"1e996e3d\" data-element_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-5d228640 elementor-widget elementor-widget-spacer\" data-id=\"5d228640\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4ef62856 elementor-widget__width-auto elementor-widget elementor-widget-heading\" data-id=\"4ef62856\" data-element_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\">Methodology<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-10f9b5c0 elementor-widget elementor-widget-spacer\" data-id=\"10f9b5c0\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-207881a elementor-widget__width-auto elementor-widget elementor-widget-heading\" data-id=\"207881a\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Multidimensional scenario trees<\/h3>\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-15ae787f elementor-section-stretched elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"15ae787f\" data-element_type=\"section\" data-settings=\"{&quot;stretch_section&quot;:&quot;section-stretched&quot;}\">\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-5316b837\" data-id=\"5316b837\" data-element_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-2dd44468 elementor-widget elementor-widget-text-editor\" data-id=\"2dd44468\" data-element_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 class=\"translation-block\">Rather than generating multiple separate scenarios, stochastic optimization is based on the generation of scenario trees, where various scenarios share a common history before they branch apart. There are different mathematical concepts for the generation of these trees, which can alternatively be applied in DTrees' products. Each single node of the scenario tree holds the future states of crucial uncertain impacts that are key to a utilities generation system and trading portfolio operation. These uncertainties involve such as<\/p><ul><li>spot market prices<\/li><li>forward market prices<\/li><li>retail load<\/li><li>wind generation<\/li><li>inflows to hydro reservoirs<\/li><li>&#8230;<\/li><\/ul><p class=\"translation-block\">Each path of the scenario tree represents a joint discrete evolution of all these impacts, which altogether result in a multidimensional scenario tree. The values for all the multidimensional nodes are calculated based on information of<\/p><ul><li>expected<\/li><li>evolution<\/li><li>volatility<\/li><li>dynamics<\/li><li>correlation<\/li><\/ul><p>of all the uncertain impacts. For price evolutions, in particular, special stochastic processes including jump diffusion and mean reversion processes are applied for the generation of the price components of the multidimensional tree. \u00a0<\/p><p>The spot price component of such a multidimensional scenario tree is shown below. Depending on the expected evolution and volatility, the spot price scenarios are scattered over a more or less broad range. \u00a0<\/p><p>With respect to what objective needs to be accomplished by the optimization model that the scenario tree is applied to, the timely granularity could be months, weeks, days or hours or a combination of these.<\/p><figure class=\"w-richtext-figure-type-image w-richtext-align-center\" data-rt-type=\"image\" data-rt-align=\"center\"><div><img decoding=\"async\" src=\"https:\/\/assets.website-files.com\/5c6fd02e6978d217448b286f\/5c71bc0a6e5e6842b1eba28f_StochasticOptimizationMetho1_01.png\" \/><\/div><\/figure><h3>From scenario trees to decision trees<\/h3><p>The concept of stochastic optimization is now based on the determination of optimal decisions in each node of the scenario tree. These decisions are\n\n<li>based on one unique history of impacts and decisions<\/li>\n\n<li>optimal with respect to all subsequent scenarios.<\/li><\/p><p>Obviously, in each of the nodes of a particular time step, different decisions are determined based on the individual situation. With these decisions being linked to previous decisions by such as portfolio book balances or resource balances, all previous decisions are optimally matched to the different future decisions in each of the various scenarios. Therewith, in particular today's decision is then optimally determined with respect to all future uncertain evolutions and all future potential decisions to be taken in order to respond to these scenarios.<\/p><p>With the optimization of decisions based on scenario trees, we obtain decision trees from which can be derived what to do in a particular scenario path and - more importantly - what to do now.<\/p><figure class=\"w-richtext-figure-type-image w-richtext-align-center\" data-rt-type=\"image\" data-rt-align=\"center\"><div><img decoding=\"async\" src=\"https:\/\/assets.website-files.com\/5c6fd02e6978d217448b286f\/5c71bc0a331282bc5a3b534a_StochasticOptimizationMetho2_01.png\" \/><\/div><\/figure><h3>Mathematical model formulation<\/h3><p>The multidimensional scenario tree together with the mathematical formulation of the optimization problem, which is composed by an objective function and a number of constraints, defines the overall mathematical model to be solved. Thereby, the objective function can focus on the minimization of procurement costs or the maximization of sales profits.<\/p><p>Crucially, each scenario enters the objective function with a certain probability. All restrictions to the model, such as resource or book balance equations, limits on power production, procurement and sales need to hold for each of the individual scenarios. The illustration below shows the growth of the mathematical model with respect to the subsequent branching of the scenario tree, since all restrictions need to hold for all scenarios.<\/p><p>With this mathematical modeling approach, decisions that are taken early and impact points in time far in the future, as it holds for forward trading, can be represented. These unique decisions are optimized with respect to all possible price scenarios that may be realized in the future.<\/p><figure class=\"w-richtext-figure-type-image w-richtext-align-center\" data-rt-type=\"image\" data-rt-align=\"center\"><div><img decoding=\"async\" src=\"https:\/\/assets.website-files.com\/5c6fd02e6978d217448b286f\/5c71bc0a331282b4523b534b_StochasticOptimizationMetho3_01.png\" \/><\/div><\/figure><h3>Solution of the mathematical model<\/h3><p>As illustrated below, the mathematical model is passed to IBM ILOG CPLEX or to Gurobi to be solved. Decision Trees has vast experience in configuration of CPLEX to reduce the solution time of the model to a minimum. Various solver options are available that can be chosen dependent on the structure of the model to be solved.<\/p><p>Finally, after the solution of the model, all optimized decisions are quantified. But only the first time stage's decisions are applied in practice, all future stages' decisions in potential scenarios would only apply if one of the scenarios then would become reality. Therefore, in future situations new models are set up based on new information on uncertainties. This approach is called rolling optimization.<\/p><figure class=\"w-richtext-figure-type-image w-richtext-align-center\" data-rt-type=\"image\" data-rt-align=\"center\"><div><img decoding=\"async\" src=\"https:\/\/assets.website-files.com\/5c6fd02e6978d217448b286f\/5c71bc0afd0819a0168d9f45_csm_StochasticOptimizationMetho5_01_5d8dc82985.png\" \/><\/div><\/figure>\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-4cf945e0 elementor-section-stretched elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4cf945e0\" data-element_type=\"section\" data-settings=\"{&quot;stretch_section&quot;:&quot;section-stretched&quot;,&quot;background_background&quot;:&quot;classic&quot;}\">\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-25 elementor-top-column elementor-element elementor-element-47c292f2\" data-id=\"47c292f2\" data-element_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-3815c4a0 elementor-position-left elementor-view-default elementor-mobile-position-top elementor-widget elementor-widget-icon-box\" data-id=\"3815c4a0\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-icon-box-wrapper\">\n\n\t\t\t\t\t\t<div class=\"elementor-icon-box-icon\">\n\t\t\t\t<span  class=\"elementor-icon\">\n\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-map-marker-alt\" viewbox=\"0 0 384 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M172.268 501.67C26.97 291.031 0 269.413 0 192 0 85.961 85.961 0 192 0s192 85.961 192 192c0 77.413-26.97 99.031-172.268 309.67-9.535 13.774-29.93 13.773-39.464 0zM192 272c44.183 0 80-35.817 80-80s-35.817-80-80-80-80 35.817-80 80 35.817 80 80 80z\"><\/path><\/svg>\t\t\t\t<\/span>\n\t\t\t<\/div>\n\t\t\t\n\t\t\t\t\t\t<div class=\"elementor-icon-box-content\">\n\n\t\t\t\t\t\t\t\t\t<h3 class=\"elementor-icon-box-title\">\n\t\t\t\t\t\t<span  >\n\t\t\t\t\t\t\tOFFICE<br>MUNICH\t\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/h3>\n\t\t\t\t\n\t\t\t\t\t\t\t\t\t<p class=\"elementor-icon-box-description\">\n\t\t\t\t\t\tKonrad-Zuse-Platz 8<br>\nD-81829 M\u00fcnchen<br><br>\n\nTel.: +49 89 207042 284<br>\nFax: +49 89 207042 288<br><br>\n\noffice@dtrees.com\t\t\t\t\t<\/p>\n\t\t\t\t\n\t\t\t<\/div>\n\t\t\t\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<div class=\"elementor-column elementor-col-25 elementor-top-column elementor-element elementor-element-6138e975\" data-id=\"6138e975\" data-element_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-3bfe58cf elementor-position-left elementor-view-default elementor-mobile-position-top elementor-widget elementor-widget-icon-box\" data-id=\"3bfe58cf\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-icon-box-wrapper\">\n\n\t\t\t\t\t\t<div class=\"elementor-icon-box-icon\">\n\t\t\t\t<span  class=\"elementor-icon\">\n\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-map-marker-alt\" viewbox=\"0 0 384 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M172.268 501.67C26.97 291.031 0 269.413 0 192 0 85.961 85.961 0 192 0s192 85.961 192 192c0 77.413-26.97 99.031-172.268 309.67-9.535 13.774-29.93 13.773-39.464 0zM192 272c44.183 0 80-35.817 80-80s-35.817-80-80-80-80 35.817-80 80 35.817 80 80 80z\"><\/path><\/svg>\t\t\t\t<\/span>\n\t\t\t<\/div>\n\t\t\t\n\t\t\t\t\t\t<div class=\"elementor-icon-box-content\">\n\n\t\t\t\t\t\t\t\t\t<h3 class=\"elementor-icon-box-title\">\n\t\t\t\t\t\t<span  >\n\t\t\t\t\t\t\tOFFICE<br>ST. 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10.1h-46.6c-5.5 0-9.7-2.9-12.9-8.7l-66-120.3c2.3-4.1 36.8-64.9 103.4-182.3 3.3-5.8 7.4-8.7 12.5-8.7h46.9c5.7-.1 8.8 4.7 6 10z\"><\/path><\/svg>\t\t\t<\/a>\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\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-64a9409c\" data-id=\"64a9409c\" data-element_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-529f2c00 elementor-widget elementor-widget-text-editor\" data-id=\"529f2c00\" data-element_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>\u00a9 Decision Trees GmbH &#8211; All rights reserved<\/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<div 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elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f753b5c\" data-element_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-14b4fb9\" data-id=\"14b4fb9\" data-element_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-616c667 elementor-grid-1 elementor-grid-tablet-1 elementor-grid-mobile-1 elementor-posts--thumbnail-top elementor-card-shadow-yes elementor-posts__hover-gradient load-more-align-center elementor-widget elementor-widget-posts\" data-id=\"616c667\" data-element_type=\"widget\" data-settings=\"{&quot;cards_columns&quot;:&quot;1&quot;,&quot;pagination_type&quot;:&quot;load_more_on_click&quot;,&quot;cards_columns_tablet&quot;:&quot;1&quot;,&quot;cards_columns_mobile&quot;:&quot;1&quot;,&quot;cards_row_gap&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:35,&quot;sizes&quot;:[]},&quot;cards_row_gap_tablet&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]},&quot;cards_row_gap_mobile&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:&quot;&quot;,&quot;sizes&quot;:[]},&quot;load_more_spinner&quot;:{&quot;value&quot;:&quot;fas fa-spinner&quot;,&quot;library&quot;:&quot;fa-solid&quot;}}\" data-widget_type=\"posts.cards\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-posts-container elementor-posts elementor-posts--skin-cards elementor-grid\">\n\t\t\t\t<article class=\"elementor-post elementor-grid-item post-1318 post type-post status-publish format-standard hentry category-nicht-kategorisiert-de wpbf-post\">\n\t\t\t<div class=\"elementor-post__card\">\n\t\t\t\t<div class=\"elementor-post__text\">\n\t\t\t\t<h3 class=\"elementor-post__title\">\n\t\t\t<a href=\"https:\/\/dtrees.com\/en\/waermepumpen-demand-side-management\/\" >\n\t\t\t\tW\u00e4rmepumpen Demand Side Management\t\t\t<\/a>\n\t\t<\/h3>\n\t\t\t\t<div class=\"elementor-post__excerpt\">\n\t\t\t<p>Der Politik voraus<\/p>\n\t\t<\/div>\n\t\t\n\t\t<a class=\"elementor-post__read-more\" href=\"https:\/\/dtrees.com\/en\/waermepumpen-demand-side-management\/\" >\n\t\t\t&gt; Read more...\t\t<\/a>\n\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/article>\n\t\t\t\t<\/div>\n\n\n\t\t\t\t\t<span class=\"e-load-more-spinner\">\n\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-spinner\" viewbox=\"0 0 512 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M304 48c0 26.51-21.49 48-48 48s-48-21.49-48-48 21.49-48 48-48 48 21.49 48 48zm-48 368c-26.51 0-48 21.49-48 48s21.49 48 48 48 48-21.49 48-48-21.49-48-48-48zm208-208c-26.51 0-48 21.49-48 48s21.49 48 48 48 48-21.49 48-48-21.49-48-48-48zM96 256c0-26.51-21.49-48-48-48S0 229.49 0 256s21.49 48 48 48 48-21.49 48-48zm12.922 99.078c-26.51 0-48 21.49-48 48s21.49 48 48 48 48-21.49 48-48c0-26.509-21.491-48-48-48zm294.156 0c-26.51 0-48 21.49-48 48s21.49 48 48 48 48-21.49 48-48c0-26.509-21.49-48-48-48zM108.922 60.922c-26.51 0-48 21.49-48 48s21.49 48 48 48 48-21.49 48-48-21.491-48-48-48z\"><\/path><\/svg>\t\t\t<\/span>\n\t\t\n\t\t\t\t<div class=\"e-load-more-anchor\" data-page=\"1\" data-max-page=\"5\" data-next-page=\"https:\/\/dtrees.com\/en\/wp-json\/wp\/v2\/pages\/308\/page\/2\/\"><\/div>\n\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"#\" class=\"elementor-button-link elementor-button\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">&gt; More posts<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<div class=\"e-load-more-message\"><\/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>Methodologie Mehrdimensionale Szenarienb\u00e4ume Die stochastische Optimierung basiert auf der Erzeugung von\u00a0Szenariob\u00e4umen, bei denen unterschiedliche Szenarios einen gemeinsamen Ursprung haben, bevor sie sich ver\u00e4steln. Dies ist ein wesentlicher Unterschied zur Monte-Carlo-Simulation, bei der viele unabh\u00e4ngige, einzelne Szenariopfade verwendet werden. Es gibt verschiedene mathematische Konzepte zur Erzeugung von Szenariob\u00e4umen, die alternativ in den Produkten von DTrees eingesetzt [&hellip;]<\/p>","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-308","page","type-page","status-publish","hentry","wpbf-post"],"_links":{"self":[{"href":"https:\/\/dtrees.com\/en\/wp-json\/wp\/v2\/pages\/308","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dtrees.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/dtrees.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/dtrees.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/dtrees.com\/en\/wp-json\/wp\/v2\/comments?post=308"}],"version-history":[{"count":4,"href":"https:\/\/dtrees.com\/en\/wp-json\/wp\/v2\/pages\/308\/revisions"}],"predecessor-version":[{"id":827,"href":"https:\/\/dtrees.com\/en\/wp-json\/wp\/v2\/pages\/308\/revisions\/827"}],"wp:attachment":[{"href":"https:\/\/dtrees.com\/en\/wp-json\/wp\/v2\/media?parent=308"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}