From 81f1ef81044e215df2b9a204753793b677ce6cdf Mon Sep 17 00:00:00 2001 From: Fabricio Oliveira Date: Mon, 3 Jun 2024 10:32:48 +0200 Subject: [PATCH] Add chp2 part 2 --- course/content/chapter_2/1-scenario_trees.md | 40 +------------------ .../content/chapter_2/2-quality_measures.md | 37 +++++++++++++++++ 2 files changed, 38 insertions(+), 39 deletions(-) create mode 100644 course/content/chapter_2/2-quality_measures.md diff --git a/course/content/chapter_2/1-scenario_trees.md b/course/content/chapter_2/1-scenario_trees.md index 2912087..30bb30d 100644 --- a/course/content/chapter_2/1-scenario_trees.md +++ b/course/content/chapter_2/1-scenario_trees.md @@ -69,42 +69,4 @@ In practical settings, we often can rely on pre-existent models of the stochasti Often, the process of generating scenarios involves a combination of the above. In particular, provided that enough data is available, it is often common that one would define some parametric (e.g., statistical machine learning) model from which observations, or samples, are then generated. -Clearly, this involves considerable care regarding modelling premises, statistical analyses, and experiment design. Questions such as which model better represent the stochastic phenomena, how to sample scenarios and many scenarios are necessary are only some of the questions that must be answered *before* we even obtain a stochastic programming model. - -## Quality measures for scenario trees - -One crucial aspect related to stochastic programming is that scenario generation plays a significant part of the modelling process. This is a point that is often overlooked in the literature on stochastic programming applications, which has nonnegligible consequences to the quality of the model obtained. - -Figure {ref}`SP_flowchart` illustrates how should think about the process of developing stochastic programming models. That diagram highlights the central role that scenario generation has in the process. - -(SP_flowchart)= -```{mermaid} -:align: center -:caption: A flowchart representing the modelling process using stochastic programming -%%{ init: { 'flowchart': { 'curve': 'stepAfter' } } }%% - -flowchart TB - id1[Decision process] - id2[Stochastic process] - id3[Scenario tree] - id4[Stochastic programming model] - id1 --> id3 - id2 --> id3 - id3 --> id4 - -classDef default fill:white, stroke:black, stroke-width:2px; -```` - -As such, one common saying related to stochastic programming model is "garbage in equals garbage out". This refers to the fact that, having a sophisticated stochastic programming model, perhaps including many of the features we will discuss in the next chapters, is not enough for one to have a reliable model for analyses. One must, just as carefully, consider whether the quality of the uncertainty representation, as they majorly influence the quality of the solutions obtained. - -### Measuring error and stability of scenario trees - -There are two measures that one must consider when generating scenario trees: - -1. Error: scenario trees naturally encode an inherent amount of error, as they are *approximations* of the a stochastic process. On the other hand, -2. Stability - - - - - +Clearly, this involves considerable care regarding modelling premises, statistical analyses, and experiment design. Questions such as which model better represent the stochastic phenomena, how to sample scenarios and many scenarios are necessary are only some of the questions that must be answered *before* we even obtain a stochastic programming model. diff --git a/course/content/chapter_2/2-quality_measures.md b/course/content/chapter_2/2-quality_measures.md new file mode 100644 index 0000000..08a756c --- /dev/null +++ b/course/content/chapter_2/2-quality_measures.md @@ -0,0 +1,37 @@ +# Quality measures for scenario trees + +One crucial aspect related to stochastic programming is that scenario generation plays a significant part of the modelling process. This is a point that is often overlooked in the literature on stochastic programming applications, which has nonnegligible consequences to the quality of the model obtained. + +Figure {ref}`SP_flowchart` illustrates how should think about the process of developing stochastic programming models. That diagram highlights the central role that scenario generation has in the process. + +(SP_flowchart)= +```{mermaid} +:align: center +:caption: A flowchart representing the modelling process using stochastic programming +%%{ init: { 'flowchart': { 'curve': 'stepAfter' } } }%% + +flowchart TB + id1[Decision process] + id2[Stochastic process] + id3[Scenario tree] + id4[Stochastic programming model] + id1 --> id3 + id2 --> id3 + id3 --> id4 + +classDef default fill:white, stroke:black, stroke-width:2px; +```` + +As such, one common saying related to stochastic programming model is "garbage in equals garbage out". This refers to the fact that, having a sophisticated stochastic programming model, perhaps including many of the features we will discuss in the next chapters, is not enough for one to have a reliable model for analyses. One must, just as carefully, consider whether the quality of the uncertainty representation, as they majorly influence the quality of the solutions obtained. + +## Error and stability of scenario trees + +There are two measures that one must consider when generating scenario trees: + +1. Error: scenario trees naturally encode an inherent amount of error, as they are *approximations* of the a stochastic process. On the other hand, +2. Stability + + + + +