From 4f8a23c03c76639a77f614143b71837b39b8eab9 Mon Sep 17 00:00:00 2001 From: Pavel Akhmetchanov Date: Mon, 31 Jul 2023 16:00:16 +0300 Subject: [PATCH 01/14] Method Monte Carlo --- .../job/tasks/planning/_category_.yml | 1 - .../Monte-Carlo-Burndown-cahrt-full.jpg | Bin 0 -> 198346 bytes .../assets/Monte-Carlo-Burndown-chart.jpg | Bin 0 -> 48553 bytes .../planning/assets/Monte-Carlo-S-Curve.png | Bin 0 -> 215427 bytes .../assets/Monte-Carlo-Table-Results-Full.png | Bin 0 -> 40920 bytes .../assets/Monte-Carlo-Table-Results.png | Bin 0 -> 25018 bytes .../planning/assets/Monte-Carlo-Througput.png | Bin 0 -> 20691 bytes .../assets/Monte-Carlo-with-risks.png | Bin 0 -> 696227 bytes .../assets/Monte-carlo-all-experiments.png | Bin 0 -> 572516 bytes .../job/tasks/planning/monte-carlo-method.md | 379 +++++++++++++++++- 10 files changed, 378 insertions(+), 2 deletions(-) create mode 100644 docs/roadmap/management/job/tasks/planning/assets/Monte-Carlo-Burndown-cahrt-full.jpg create mode 100644 docs/roadmap/management/job/tasks/planning/assets/Monte-Carlo-Burndown-chart.jpg create mode 100644 docs/roadmap/management/job/tasks/planning/assets/Monte-Carlo-S-Curve.png create mode 100644 docs/roadmap/management/job/tasks/planning/assets/Monte-Carlo-Table-Results-Full.png create mode 100644 docs/roadmap/management/job/tasks/planning/assets/Monte-Carlo-Table-Results.png create mode 100644 docs/roadmap/management/job/tasks/planning/assets/Monte-Carlo-Througput.png create mode 100644 docs/roadmap/management/job/tasks/planning/assets/Monte-Carlo-with-risks.png create mode 100644 docs/roadmap/management/job/tasks/planning/assets/Monte-carlo-all-experiments.png diff --git a/docs/roadmap/management/job/tasks/planning/_category_.yml b/docs/roadmap/management/job/tasks/planning/_category_.yml index f0b648e..bbec7e3 100644 --- a/docs/roadmap/management/job/tasks/planning/_category_.yml +++ b/docs/roadmap/management/job/tasks/planning/_category_.yml @@ -1,4 +1,3 @@ label: Планирование 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система функций и выбранный порядок их расчёта +* Опыт — эксперимент, одна из проб расчёта по выбранной модели и получения результата +* Исход — это результат проведенного опыта +* Событие — явление, которое может произойти или не произойти в результате опыта, при сопоставлении предпологаемого результата с фактическим наблюдением +* Свертка данных — это приведение нескольких значений к одному, например выбрать "среднее" или "медиану" или другие математические операции, позволяющие дать характеристику набору данных в одном значении. + + +Метод Монте-Карло представляет собой перебор возможных исходов событий. А для его использования в планировании необходимо сначала выбрать модель по которой будет производиться расчет. + +Для примера понимания того как работает метод, попробуем его использовать для решения задачи прогнозирования завершения проекта интеллектуальной работы. + +Есть несколько важных замечаний при использовании метода для прогнозирования интеллектуальной работы. + +Когда мы говорим о прогнозировании сроков интеллектуальной работы команды, например в ИТ, то лучшим отрезком свертки данных, будет является неделя. А связано это с тем, что количество задач выполненных за день будет сильно изменятся от дня в день, по причине высокой волатильности результатов зависящих как от эмоционального состояния людей, так и разной сложности решаемых задач и многих других параметров. + +## Метод Монте-Карло для прогнозирования сроков завершения проекта на основе пропускной способности + +Для примера необходимо взять достаточный набор данных, предлагаю использовать периоды от 7 до 26 недель. + +С чем может быть связано? + +7 недель, это чуть более чем полтора месяца, меньше данных для использования метода Монте-Карло приведет высокой степени недостоверности результата. + +А брать более чем 26 недель, что соответствует половине года, не имеет смысла, так как в интеллектуальной работе происходят постоянные изменения, которые так же могут внести повысить недостоверность прогнозов. С другой стороны такого набора данных вполне достаточно для хорошего прогнозирования. + +Будет ли работать метод, с учетом того, что интеллектуальные задачи очень разные по сложности и времени выполнения? + +Да, конечно будет. Главное чтобы объемы этих задач не отличались кратно. Например если в наборе данных мы имеем задачу которую можно решить в течении пары часов и задачу которую будут решать более 120 дней, то это может привести к недостоверности результата прогнозирования внося огромную дисперсию в результат. + +По этому рекомендуется использовать декомпозицию задач, которые будут нивелировать огромный разрыв в характеристиках поставленных заданий. + +### Пример планирования + +И так рассмотрим пример прогнозирования сроков выполнения проекта, который декомпозирован на 40 задач. + +Есть набор данных в виде количества завершенных задач суммированных понедельно — это данные пропускной способности “Throughput”: + +``` +[4, 1, 2, 1, 4, 3, 2, 3, 6, 3, 2, 1, 6, 13, 3, 1, 6, 1, 4, 4, 6, 3, 6, 2, 6, 2] +``` + +Каждое число в этом наборе — это количество задач завершенных за одну неделю. Общее количество данных мы взяли за последние 26 неделю. + +![Chart Throughput](./assets/Monte-Carlo-Througput.png) + +#### Алгоритм метода + +##### Шаг первый. + +Выбираем случайное число из набора данных пропускной способности. + +Например, 8 число из набора. Это будет "3" + +``` +[4, 1, 2, 1, 4, 3, 2, |3|, 6, 3, 2, 1, 6, 13, 3, 1, 6, 1, 4, 4, 6, 3, 6, 2, 6, 2] → 3 +``` +##### Шаг второй. + +Считаем что в первую неделю работы над проектом сервис выполнит 3 задачи. И от 40 исходных задач проекта отнимаем это же количество, получим 37. + +![Burn Cahrt of Project](./assets/Monte-Carlo-Burndown-chart.jpg) + +##### Шаг третий. + +Повторяем первый шаг, и второй до тех пор, пока в исходном наборе 40 задач проекта не останется их совсем. Так мы получим вероятное количество недель за которое будет выполнен проект, запоминаем это количество недель. А добавив этот отрезок времени к планируемой дате начала проекта, можем получить дату завершения. + +![Burn Cahrt of Project](./assets/Monte-Carlo-Burndown-cahrt-full.jpg) + +На примере просчета первого эксперимента (на картинке), проект завершится за 17 недель. Запоминаем этот срок. + +##### Шаг четвертый. + +Алгоритм шагов от первого до третьего повторяем от 10000. После каждого расчета сроков, мы получим число недель за которое может закрыться проект. Собираем эти сроки и считаем сколько раз проект закрылся за этот срок. + +![All Experiments](./assets/Monte-carlo-all-experiments.png) + +Так получаем распределение данных показывающих за какое количество недель может быть выполнен проект, и какое количество исходов получилось при моделировании в одно и тоже количество недель. + +![Table Results](./assets/Monte-Carlo-Table-Results.png) + +Для каждой недели имеем количество раз, сколько раз завершился проект в эту неделю. + +Используя эти данные мы можем рассчитать вероятность завершения проекта к каждой неделе в которую он завершился. + +По формуле `P = (∑[1-n]s)/N`, + +где s — количество исходов на текущей неделе. Т.е. сумма общих исходов до текущей даты, делённая на N —количество экспериментов, в рассматриваемом случае это 10000. + +![Table Results](./assets/Monte-Carlo-Table-Results-Full.png) + +Можем увидеть, что количественная вероятность завершить проект в 15 неделю уже превышает 90%, а на 16 уже превысить 95%. + +Выбрав удовлетворяющую вас вероятность завершения проекта, вы определяете и срок завершения. + +Из опыта, хорошей вероятностью для интеллектуальной работы является вероятность в пределах от 85% до 98%. + +В данном случае можно взять в качестве сроков выполнения проекта **16 неделю**. + +#### Алгоритм метода на JavaScript + +Вот пример кода на JavaScript для этой простой модуляции. + +```javascript +// Данные по пропускной способности по итерациям времени +// итерация - минимальная единица времени в которой хотим считать +// длительность проекта +const historicalDataThroughput = [ + 4, 1, 2, 1, 4, 3, 2, 3, 2, 3, 6, + 3, 2, 1, 6, 13, 3, 1, 6, 1, 2, + 4, 4, 6, 3, 1, 3, 3, 6, 6, 2, + 6, 2, 1 + ]; + + // количество задач в проекте + const countTaskInProject = 40; + const result = MonteCarloForProject(historicalDataThroughput, countTaskInProject, 10000); + console.table(result) + + /** + * Получить распределение вероятности завершения проекта + * на основе количества решаемых задач за итерацию + * + * @param {Array} historicalDataThroughput Набор испторических данных по пропускной способности + * @param {Number} countTaskInProject Количество задач в проекте + * @param {Number} numberOfExperiments Количество проводимх эксперимантов + * @returns {Array} key - количество фич в итерации, value - частота + */ + function MonteCarloForProject( + historicalDataThroughput, + countTaskInProject, + numberOfExperiments + ) { + const result = new Map(); + const len = historicalDataThroughput.length + let experiment = 1; + + for (; experiment <= numberOfExperiments; experiment++) { + let prjTasks = countTaskInProject; + // индекс начинается с "0" + let IndexIteration = 0; + while (prjTasks > 0) { + let randomIndex = Math.floor(Math.random() * len); + let countTasks = historicalDataThroughput[randomIndex]; + IndexIteration += 1; + prjTasks = prjTasks - countTasks; + } + + let i = result.get(IndexIteration); + result.set(IndexIteration, i ? i + 1 : 1); + } + let sum = 0; + // Из Map переводим в тип Массив, расчитываем вероятность + return Array.from(result, ([name, value]) => ({ iteration: name, count: value})) + .sort((a, b) => a.iteration - b.iteration) + .map((i,j) => { + sum += i.count; + return { + ...i, + probability: sum/numberOfExperiments + } + }) + } +``` + +[Пример на Gist Github](https://gist.github.com/pavelpower/97625088b6cdbde9cfdd4f181fb33a39) + +Код написан так, чтобы можно было его запустить в браузере. + +Пример вывода результата программы: + +``` +┌─────────┬───────────┬───────┬─────────────┐ +│ (index) │ iteration │ count │ probability │ +├─────────┼───────────┼───────┼─────────────┤ +│ 0 │ 4 │ 1 │ 0.0001 │ +│ 1 │ 5 │ 11 │ 0.0012 │ +│ 2 │ 6 │ 51 │ 0.0063 │ +│ 3 │ 7 │ 125 │ 0.0188 │ +│ 4 │ 8 │ 341 │ 0.0529 │ +│ 5 │ 9 │ 646 │ 0.1175 │ +│ 6 │ 10 │ 1087 │ 0.2262 │ +│ 7 │ 11 │ 1492 │ 0.3754 │ +│ 8 │ 12 │ 1630 │ 0.5384 │ +│ 9 │ 13 │ 1528 │ 0.6912 │ +│ 10 │ 14 │ 1289 │ 0.8201 │ +│ 11 │ 15 │ 892 │ 0.9093 │ +│ 12 │ 16 │ 515 │ 0.9608 │ +│ 13 │ 17 │ 242 │ 0.985 │ +│ 14 │ 18 │ 96 │ 0.9946 │ +│ 15 │ 19 │ 37 │ 0.9983 │ +│ 16 │ 20 │ 13 │ 0.9996 │ +│ 17 │ 21 │ 3 │ 0.9999 │ +│ 18 │ 22 │ 1 │ 1 │ +└─────────┴───────────┴───────┴─────────────┘ +``` + +Где + +* **iteration** — это количество недель (итераций) которое понадобится на реализацию проекта из **40** задач +* **count** — количество исходов, результатов завершения проекта за этот срок из заданных **10000** повторений +* **probability** — рассчитанная количественная вероятность завершения за этот срок + +#### Можно ли в модели учесть неожиданные события? + +Да, вполне, вы так же можете задать случайно возникающие риски которые могут случится с какой-то вероятностью. + +Тогда в эту модель вы добавить функциональность которая может сработать с какой-то вероятностью и добавить еще задач к проекту при наступлении риска. + +Тогда нам нужно определить заранее предполагаемую вероятность наступления риска, и предположить сколько задач он может добавить. + +Так же какой-то риск и убавить задач из проекта. + +#### Алгоритм метода на JavaScript с учетом рисков + +```javascript +// Данные по пропускной способности по итерациям времени +// итерация - минимальная единица времени в которой хотим считать +// длительность проекта +const historicalDataThroughput = [ + 4, 1, 2, 1, 4, 3, 2, 3, 2, 3, 6, + 3, 2, 1, 6, 13, 3, 1, 6, 1, 2, + 4, 4, 6, 3, 1, 3, 3, 6, 6, 2, + 6, 2, 1 + ]; + + // количество задач в проекте + const countTaskInProject = 40; + + // Риски которые могут случится с какой-то вероятностью + // И добавить новых задач к проекту + // Предполагаем что риск может сработать один раз + const risks = [ + // С вероятностью 2% наступления риска, к проекту добавится 20 задач + { probability: 2, countNewTasks: 20}, + // С вероятностью 12% наступления риска, к проекту добавится 4 задач + { probability: 12, countNewTasks: 4}, + // С вероятностью 5% наступления риска, к проекту добавится 2 задач + { probability: 5, countNewTasks: 2}, + // С вероятностью 4% наступления риска, от проекта отнимется 8 задач + { probability: 4, countNewTasks: -8}, + ] + + const result = MonteCarloForProject( + historicalDataThroughput, + countTaskInProject, + risks, + 10000 + ); + + console.table(result) + + /** + * Получить распределение вероятности завершения проекта + * на основе количества решаемых задач за итерацию + * + * @param {Array} historicalDataThroughput Набор испторических данных по пропускной способности + * @param {Number} countTaskInProject Количество задач в проекте + * @param {Array<{probability: Number, countNewTasks: Number}>} risks Риски + * @param {Number} numberOfExperiments Количество проводимх эксперимантов + * @returns {Array} key - количество фич в итерации, value - частота + */ + function MonteCarloForProject( + historicalDataThroughput, + countTaskInProject, + risks, + numberOfExperiments + ) { + const result = new Map(); + const len = historicalDataThroughput.length + let experiment = 1; + + for (; experiment <= numberOfExperiments; experiment++) { + let prjTasks = countTaskInProject; + + // если сгенерированное число меньше чем указанный процент вероятности, + // считаем что риск случился + risks.forEach(r => { + // получаем случайное число от 1 до 100 + // вычисляем случайное число отдельно для каждого риска + let randomForRisk = Math.floor(Math.random() * 100) + 1; + + // Если вероятность риска больше полученного числа, + // то добавляются новые задачи к проекту + if (r.probability > randomForRisk) { + prjTasks += r.countNewTasks; + } + }); + + // индекс начинается с "0" + let IndexIteration = 0; + while (prjTasks > 0) { + let randomIndex = Math.floor(Math.random() * len); + let countTasks = historicalDataThroughput[randomIndex]; + IndexIteration += 1; + prjTasks = prjTasks - countTasks; + } + + let i = result.get(IndexIteration); + result.set(IndexIteration, i ? i + 1 : 1); + } + let sum = 0; + // Из Map переводим в тип Массив, расчитываем вероятность + return Array.from(result, ([name, value]) => ({ iteration: name, count: value})) + .sort((a, b) => a.iteration - b.iteration) + .map((i) => { + sum += i.count; + return { + ...i, + probability: sum/numberOfExperiments + } + }) + } +``` +[Пример на Gist Github](https://gist.github.com/pavelpower/4c22b470f1e78030802963d61ae6b8e1) + +Пример вывода результата программы: + +``` +┌─────────┬───────────┬───────┬─────────────┐ +│ (index) │ iteration │ count │ probability │ +├─────────┼───────────┼───────┼─────────────┤ +│ 0 │ 4 │ 2 │ 0.0002 │ +│ 1 │ 5 │ 10 │ 0.0012 │ +│ 2 │ 6 │ 41 │ 0.0053 │ +│ 3 │ 7 │ 135 │ 0.0188 │ +│ 4 │ 8 │ 324 │ 0.0512 │ +│ 5 │ 9 │ 659 │ 0.1171 │ +│ 6 │ 10 │ 1004 │ 0.2175 │ +│ 7 │ 11 │ 1411 │ 0.3586 │ +│ 8 │ 12 │ 1525 │ 0.5111 │ +│ 9 │ 13 │ 1571 │ 0.6682 │ +│ 10 │ 14 │ 1342 │ 0.8024 │ +│ 11 │ 15 │ 899 │ 0.8923 │ +│ 12 │ 16 │ 531 │ 0.9454 │ +│ 13 │ 17 │ 276 │ 0.973 │ +│ 14 │ 18 │ 151 │ 0.9881 │ +│ 15 │ 19 │ 58 │ 0.9939 │ +│ 16 │ 20 │ 37 │ 0.9976 │ +│ 17 │ 21 │ 9 │ 0.9985 │ +│ 18 │ 22 │ 4 │ 0.9989 │ +│ 19 │ 23 │ 6 │ 0.9995 │ +│ 20 │ 24 │ 1 │ 0.9996 │ +│ 21 │ 25 │ 2 │ 0.9998 │ +│ 22 │ 26 │ 1 │ 0.9999 │ +│ 23 │ 27 │ 1 │ 1 │ +└─────────┴───────────┴───────┴─────────────┘ +``` + +Идею с рисками можно конечно обыграть и тем, что мы можем добавить вероятность добавления случайного количества задач при наступлении риска в каких-то пределах. + +Например, если мы предполагаем, что риск наступим с вероятностью "p", но при этом этот риск может добавить к проекту от "k" задач до "2k", но сколько мы не знаем. + +В этом случае мы так же может задать расчет вероятности сколько количества задач добавит нам этот риск. + +## Выводы +Даже используя простые модели для моделирования сроков завершения проектов, вы можете при помощи метода Монте-Карло, определить вероятность завершения проекта. + +И такая вероятность будет достаточно точной, с учетом того, что ваша система (процессы создания ценности) не изменялись со временем. + +Хотя, вы уже понимаете, что моделировать при помощи Монте-Крало можно и более сложные модели, в том, числе и с учетом предполагаемых изменений. Но надо иметь ввиду, что изменения вводимые в процессы очень сложно прогнозируются, и вы можете построить ошибочную модель. + +Мир математики численных методов, на самом деле куда более широк, чем изложен в этой статье. Чего только стоят Байесовские методы, которые могли бы вам помочь в моделировании более сложных процессов. + +Начинайте с простого. + +Если же вы плохо понимаете в коде, то могу предложить посмотреть проект созданный Rodrigo Rosauro на основе работ Troy Magennis и Dimitar Bakardzhiev's вот в этой Excel + +Попробуйте воспользоваться этой страницей https://rodrigozr.github.io/ProjectForecaster/ + +#### Примечание +Проекты, на самом деле завершаются не так линейно как показано в этих примерах. Они могут так завершатся только в одном случае, если команда занимается только этим проектом. Однако часто это не так. + +Если исследовать динамику завершения проектов, часто можно обнаружить S-образную функцию (s-curve) завершения проекта, связанную с тем, что в начале проекта неизвестно до конца сколько будет добавлено задач к проекту. + +![S-Curve](./assets/Monte-Carlo-S-Curve.png) From a1de4f5552203e23f234e9b038c0c49dd8100b5b Mon Sep 17 00:00:00 2001 From: Pavel Akhmetchanov Date: Mon, 31 Jul 2023 16:10:41 +0300 Subject: [PATCH 02/14] fixed small error in text --- .../management/job/tasks/planning/monte-carlo-method.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md index d7dded0..2655178 100644 --- a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md +++ b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md @@ -7,8 +7,9 @@ sidebar_class_name: enabled-page * Модель расчёта — функция или система функций и выбранный порядок их расчёта * Опыт — эксперимент, одна из проб расчёта по выбранной модели и получения результата * Исход — это результат проведенного опыта -* Событие — явление, которое может произойти или не произойти в результате опыта, при сопоставлении предпологаемого результата с фактическим наблюдением +* Событие — явление, которое может произойти или не произойти в результате опыта, при сопоставлении предполагаемого результата с фактическим наблюдением * Свертка данных — это приведение нескольких значений к одному, например выбрать "среднее" или "медиану" или другие математические операции, позволяющие дать характеристику набору данных в одном значении. +* Волатильность — изменчивость данных измеряемой величены Метод Монте-Карло представляет собой перебор возможных исходов событий. А для его использования в планировании необходимо сначала выбрать модель по которой будет производиться расчет. From c904ebfa88715fbbebc29927453adc6ef63395d4 Mon Sep 17 00:00:00 2001 From: Pavel Akhmetchanov Date: Mon, 31 Jul 2023 18:40:38 +0300 Subject: [PATCH 03/14] added KTex plugin for math formuls --- docusaurus.config.js | 22 +++++++++++++++------- package.json | 3 +++ 2 files changed, 18 insertions(+), 7 deletions(-) diff --git a/docusaurus.config.js b/docusaurus.config.js index 9582e35..ff6b086 100644 --- a/docusaurus.config.js +++ b/docusaurus.config.js @@ -1,4 +1,6 @@ /** @type {import('@docusaurus/types').DocusaurusConfig} */ +const math = require('remark-math'); +const katex = require('rehype-katex'); module.exports = { title: 'Деливери менеджер', tagline: 'Кто это, задачи, обязанности, как им стать, карта развития', @@ -16,7 +18,7 @@ module.exports = { themes: ['@docusaurus/theme-mermaid'], themeConfig: { mermaid: { - theme: {light: 'base', dark: 'dark'}, + theme: { light: 'base', dark: 'dark' }, options: { flowchart: { curve: 'monotoneX', @@ -49,14 +51,13 @@ module.exports = { alt: 'База знаний профессии Деливери менеджер', src: 'img/logo.svg', }, - items: [ - { + items: [{ type: 'doc', docId: 'profession/about', position: 'left', label: 'Документация', }, - {to: 'blog', label: 'Блог', position: 'left'}, + { to: 'blog', label: 'Блог', position: 'left' }, { type: 'docsVersionDropdown', position: 'right', @@ -88,8 +89,9 @@ module.exports = { }, sidebarPath: require.resolve('./sidebars.js'), // Please change this to your repo. - editUrl: - 'https://github.com/Tinkoff/dm-knowledgebase/edit/main/', + editUrl: 'https://github.com/Tinkoff/dm-knowledgebase/edit/main/', + remarkPlugins: [math], + rehypePlugins: [katex], }, gtag: { trackingID: 'G-CNJ52NL21B', @@ -101,6 +103,12 @@ module.exports = { }, ], ], + stylesheets: [{ + href: 'https://cdn.jsdelivr.net/npm/katex@0.13.24/dist/katex.min.css', + type: 'text/css', + integrity: 'sha384-odtC+0UGzzFL/6PNoE8rX/SPcQDXBJ+uRepguP4QkPCm2LBxH3FA3y+fKSiJ+AmM', + crossorigin: 'anonymous', + }, ], plugins: [ [ require.resolve('docusaurus-lunr-search'), @@ -109,4 +117,4 @@ module.exports = { }, ], ], -}; +}; \ No newline at end of file diff --git a/package.json b/package.json index 310166e..7a39058 100644 --- a/package.json +++ b/package.json @@ -23,9 +23,12 @@ "clsx": "^1.1.1", "docusaurus-lunr-search": "^2.3.2", "file-loader": "^6.2.0", + "hast-util-is-element": "^1.1.0", "react": "^17.0.2", "react-dom": "^17.0.2", "react-popper": "^2.3.0", + "rehype-katex": "^5.0.0", + "remark-math": "^3.0.1", "url-loader": "^4.1.1" }, "browserslist": { From 9c62f66929af5fbf38e6b9e2b49b786e29beb62f Mon Sep 17 00:00:00 2001 From: Pavel Akhmetchanov Date: Mon, 31 Jul 2023 18:44:34 +0300 Subject: [PATCH 04/14] update Monte-Carlo^ new images, change image table on table mdx --- ...pg => Monte-Carlo-Burndown-chart-full.jpg} | Bin .../assets/Monte-Carlo-Result-Probably.png | Bin 0 -> 127612 bytes .../assets/Monte-Carlo-Table-Results-Full.png | Bin 40920 -> 0 bytes .../assets/Monte-Carlo-Table-Results.png | Bin 25018 -> 0 bytes ...rougput.png => Monte-Carlo-Throughput.png} | Bin .../job/tasks/planning/monte-carlo-method.md | 142 ++++++++++++++---- .../planning/monte-carlo-method.module.css | 13 ++ 7 files changed, 122 insertions(+), 33 deletions(-) rename docs/roadmap/management/job/tasks/planning/assets/{Monte-Carlo-Burndown-cahrt-full.jpg => Monte-Carlo-Burndown-chart-full.jpg} (100%) create mode 100644 docs/roadmap/management/job/tasks/planning/assets/Monte-Carlo-Result-Probably.png delete mode 100644 docs/roadmap/management/job/tasks/planning/assets/Monte-Carlo-Table-Results-Full.png delete mode 100644 docs/roadmap/management/job/tasks/planning/assets/Monte-Carlo-Table-Results.png rename docs/roadmap/management/job/tasks/planning/assets/{Monte-Carlo-Througput.png => Monte-Carlo-Throughput.png} (100%) create mode 100644 docs/roadmap/management/job/tasks/planning/monte-carlo-method.module.css diff --git a/docs/roadmap/management/job/tasks/planning/assets/Monte-Carlo-Burndown-cahrt-full.jpg 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z{?zAxcY7rq)6v85kZyo!`%`!M8Sg)@Ewr~_?Sson@1Otj&-W2f1lA%7_$>>7|KDEk d#>KYJwwax4DA8ooa`nWK{{g1CB)0$n diff --git a/docs/roadmap/management/job/tasks/planning/assets/Monte-Carlo-Througput.png b/docs/roadmap/management/job/tasks/planning/assets/Monte-Carlo-Throughput.png similarity index 100% rename from docs/roadmap/management/job/tasks/planning/assets/Monte-Carlo-Througput.png rename to docs/roadmap/management/job/tasks/planning/assets/Monte-Carlo-Throughput.png diff --git a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md index 2655178..e2e0e75 100644 --- a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md +++ b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md @@ -1,18 +1,27 @@ --- sidebar_class_name: enabled-page +description: Как работает метод Монте-Карло --- -# Метод Монте-Карло +import MonteCarloThroughput from './assets/Monte-Carlo-Throughput.png'; +import MonteCarloBurndownChart from './assets/Monte-Carlo-Burndown-chart.jpg'; +import MonteCarloBurndownChartFull from './assets/Monte-Carlo-Burndown-chart-full.jpg'; +import MonteCarloAllExperiments from './assets/Monte-carlo-all-experiments.png'; +import MonteCarloResultProbably from './assets/Monte-Carlo-Result-Probably.png'; +import styles from './monte-carlo-method.module.css'; -Для начала введем термины: -* Модель расчёта — функция или система функций и выбранный порядок их расчёта -* Опыт — эксперимент, одна из проб расчёта по выбранной модели и получения результата -* Исход — это результат проведенного опыта -* Событие — явление, которое может произойти или не произойти в результате опыта, при сопоставлении предполагаемого результата с фактическим наблюдением -* Свертка данных — это приведение нескольких значений к одному, например выбрать "среднее" или "медиану" или другие математические операции, позволяющие дать характеристику набору данных в одном значении. -* Волатильность — изменчивость данных измеряемой величены +# Метод Монте-Карло +:::note +Для начала введем термины: +* **Модель расчёта** — функция или система функций и выбранный порядок их расчёта +* **Опыт** — эксперимент, одна из проб расчёта по выбранной модели и получения результата +* **Исход** — это результат проведенного опыта +* **Событие** — явление, которое может произойти или не произойти в результате опыта, при сопоставлении предполагаемого результата с фактическим наблюдением +* **Свертка данных** — это приведение нескольких значений к одному, например выбрать "среднее" или "медиану" или другие математические операции, позволяющие дать характеристику набору данных в одном значении. +* **Волатильность** — изменчивость данных измеряемой величены +::: -Метод Монте-Карло представляет собой перебор возможных исходов событий. А для его использования в планировании необходимо сначала выбрать модель по которой будет производиться расчет. +Метод Монте-Карло представляет собой перебор возможных исходов событий. А для его использования в планировании необходимо сначала выбрать модель по которой будет производиться расчет. Для примера понимания того как работает метод, попробуем его использовать для решения задачи прогнозирования завершения проекта интеллектуальной работы. @@ -20,13 +29,13 @@ sidebar_class_name: enabled-page Когда мы говорим о прогнозировании сроков интеллектуальной работы команды, например в ИТ, то лучшим отрезком свертки данных, будет является неделя. А связано это с тем, что количество задач выполненных за день будет сильно изменятся от дня в день, по причине высокой волатильности результатов зависящих как от эмоционального состояния людей, так и разной сложности решаемых задач и многих других параметров. -## Метод Монте-Карло для прогнозирования сроков завершения проекта на основе пропускной способности +## Прогнозирования сроков завершения проекта на основе пропускной способности Для примера необходимо взять достаточный набор данных, предлагаю использовать периоды от 7 до 26 недель. С чем может быть связано? -7 недель, это чуть более чем полтора месяца, меньше данных для использования метода Монте-Карло приведет высокой степени недостоверности результата. +7 недель, это чуть более чем полтора месяца, меньше данных для использования метода Монте-Карло приведет высокой степени недостоверности результата. А брать более чем 26 недель, что соответствует половине года, не имеет смысла, так как в интеллектуальной работе происходят постоянные изменения, которые так же могут внести повысить недостоверность прогнозов. С другой стороны такого набора данных вполне достаточно для хорошего прогнозирования. @@ -36,7 +45,7 @@ sidebar_class_name: enabled-page По этому рекомендуется использовать декомпозицию задач, которые будут нивелировать огромный разрыв в характеристиках поставленных заданий. -### Пример планирования +### Постановка задачи для примера И так рассмотрим пример прогнозирования сроков выполнения проекта, который декомпозирован на 40 задач. @@ -48,11 +57,11 @@ sidebar_class_name: enabled-page Каждое число в этом наборе — это количество задач завершенных за одну неделю. Общее количество данных мы взяли за последние 26 неделю. -![Chart Throughput](./assets/Monte-Carlo-Througput.png) +Chart Throughput -#### Алгоритм метода +### Алгоритм метода -##### Шаг первый. +#### Шаг первый. Выбираем случайное число из набора данных пропускной способности. @@ -61,39 +70,70 @@ sidebar_class_name: enabled-page ``` [4, 1, 2, 1, 4, 3, 2, |3|, 6, 3, 2, 1, 6, 13, 3, 1, 6, 1, 4, 4, 6, 3, 6, 2, 6, 2] → 3 ``` -##### Шаг второй. +#### Шаг второй. Считаем что в первую неделю работы над проектом сервис выполнит 3 задачи. И от 40 исходных задач проекта отнимаем это же количество, получим 37. -![Burn Cahrt of Project](./assets/Monte-Carlo-Burndown-chart.jpg) +Burn Cahrt of Project -##### Шаг третий. +#### Шаг третий. Повторяем первый шаг, и второй до тех пор, пока в исходном наборе 40 задач проекта не останется их совсем. Так мы получим вероятное количество недель за которое будет выполнен проект, запоминаем это количество недель. А добавив этот отрезок времени к планируемой дате начала проекта, можем получить дату завершения. -![Burn Cahrt of Project](./assets/Monte-Carlo-Burndown-cahrt-full.jpg) +Burn Cahrt of Project На примере просчета первого эксперимента (на картинке), проект завершится за 17 недель. Запоминаем этот срок. -##### Шаг четвертый. +#### Шаг четвертый. Алгоритм шагов от первого до третьего повторяем от 10000. После каждого расчета сроков, мы получим число недель за которое может закрыться проект. Собираем эти сроки и считаем сколько раз проект закрылся за этот срок. -![All Experiments](./assets/Monte-carlo-all-experiments.png) +All Experiments Так получаем распределение данных показывающих за какое количество недель может быть выполнен проект, и какое количество исходов получилось при моделировании в одно и тоже количество недель. -![Table Results](./assets/Monte-Carlo-Table-Results.png) + + + + + + + + + + + +
Количество недель5678910111213141516171819202122
Количество исходов7411533206541070142016641631122691154121597251032
+ Для каждой недели имеем количество раз, сколько раз завершился проект в эту неделю. Используя эти данные мы можем рассчитать вероятность завершения проекта к каждой неделе в которую он завершился. -По формуле `P = (∑[1-n]s)/N`, +По формуле +$$ +P = \dfrac{\sum_{n=1}^{10000} s}{N} +$$ где s — количество исходов на текущей неделе. Т.е. сумма общих исходов до текущей даты, делённая на N —количество экспериментов, в рассматриваемом случае это 10000. -![Table Results](./assets/Monte-Carlo-Table-Results-Full.png) + + + + + + + + + + + + + + + + +
Количество недель5678910111213141516171819202122
Количество исходов "s"7411533206541070142016641631122691154121597251032
Вероятность "P"0.00070.00480.02010.05210.11750.22450.36650.53290.6960.81960.91070.96480.98630.9960.99850.99950.99981
Можем увидеть, что количественная вероятность завершить проект в 15 неделю уже превышает 90%, а на 16 уже превысить 95%. @@ -101,11 +141,18 @@ sidebar_class_name: enabled-page Из опыта, хорошей вероятностью для интеллектуальной работы является вероятность в пределах от 85% до 98%. -В данном случае можно взять в качестве сроков выполнения проекта **16 неделю**. +Если отобразить этот результат на графике, то получим следующее + +График вероятности завершения -#### Алгоритм метода на JavaScript +В данном случае можно взять в качестве сроков выполнения проекта **16 неделю**, где вероятность завершения проекта равна `0.9648`, +что соответствует **96.48%**. -Вот пример кода на JavaScript для этой простой модуляции. +### Алгоритм метода на JavaScript + +

+ Вот пример кода на JavaScript для этой простой модуляции. +
```javascript // Данные по пропускной способности по итерациям времени @@ -169,11 +216,18 @@ const historicalDataThroughput = [ } ``` + +
+
+ [Пример на Gist Github](https://gist.github.com/pavelpower/97625088b6cdbde9cfdd4f181fb33a39) Код написан так, чтобы можно было его запустить в браузере. -Пример вывода результата программы: + +
+ Пример вывода результата программы: +
``` ┌─────────┬───────────┬───────┬─────────────┐ @@ -201,13 +255,16 @@ const historicalDataThroughput = [ └─────────┴───────────┴───────┴─────────────┘ ``` +
+
+ Где * **iteration** — это количество недель (итераций) которое понадобится на реализацию проекта из **40** задач * **count** — количество исходов, результатов завершения проекта за этот срок из заданных **10000** повторений * **probability** — рассчитанная количественная вероятность завершения за этот срок -#### Можно ли в модели учесть неожиданные события? +### Можно ли в модели учесть неожиданные события? Да, вполне, вы так же можете задать случайно возникающие риски которые могут случится с какой-то вероятностью. @@ -217,7 +274,11 @@ const historicalDataThroughput = [ Так же какой-то риск и убавить задач из проекта. -#### Алгоритм метода на JavaScript с учетом рисков +### Алгоритм метода на JavaScript с учетом рисков + +
+ Алгоритм метода на JavaScript с учетом рисков +
```javascript // Данные по пропускной способности по итерациям времени @@ -318,9 +379,17 @@ const historicalDataThroughput = [ }) } ``` +
+
+ [Пример на Gist Github](https://gist.github.com/pavelpower/4c22b470f1e78030802963d61ae6b8e1) -Пример вывода результата программы: +Код написан так, чтобы можно было его запустить в браузере. + +
+ Пример вывода результата программы: +
+ ``` ┌─────────┬───────────┬───────┬─────────────┐ @@ -352,6 +421,8 @@ const historicalDataThroughput = [ │ 23 │ 27 │ 1 │ 1 │ └─────────┴───────────┴───────┴─────────────┘ ``` +
+
Идею с рисками можно конечно обыграть и тем, что мы можем добавить вероятность добавления случайного количества задач при наступлении риска в каких-то пределах. @@ -360,11 +431,11 @@ const historicalDataThroughput = [ В этом случае мы так же может задать расчет вероятности сколько количества задач добавит нам этот риск. ## Выводы -Даже используя простые модели для моделирования сроков завершения проектов, вы можете при помощи метода Монте-Карло, определить вероятность завершения проекта. +Даже используя простые модели для моделирования сроков завершения проектов, вы можете при помощи метода Монте-Карло, определить вероятность завершения проекта. И такая вероятность будет достаточно точной, с учетом того, что ваша система (процессы создания ценности) не изменялись со временем. -Хотя, вы уже понимаете, что моделировать при помощи Монте-Крало можно и более сложные модели, в том, числе и с учетом предполагаемых изменений. Но надо иметь ввиду, что изменения вводимые в процессы очень сложно прогнозируются, и вы можете построить ошибочную модель. +Хотя, вы уже понимаете, что моделировать при помощи Монте-Крало можно и более сложные модели, в том, числе и с учетом предполагаемых изменений. Но надо иметь ввиду, что изменения вводимые в процессы очень сложно прогнозируются, и вы можете построить ошибочную модель. Мир математики численных методов, на самом деле куда более широк, чем изложен в этой статье. Чего только стоят Байесовские методы, которые могли бы вам помочь в моделировании более сложных процессов. @@ -374,9 +445,14 @@ const historicalDataThroughput = [ Попробуйте воспользоваться этой страницей https://rodrigozr.github.io/ProjectForecaster/ +Для тех кто пользуется Jira, есть специальный плагин для Chrome [Jira Flow Companion](https://chrome.google.com/webstore/detail/jira-flow-companion/kbppfmkmcilakibigimbnohnbefifaao). В нем уже встроен модуль Монте-Карло. Хоть он и очень простой, но для большинства задач, его будет достаточно. + + +:::note #### Примечание Проекты, на самом деле завершаются не так линейно как показано в этих примерах. Они могут так завершатся только в одном случае, если команда занимается только этим проектом. Однако часто это не так. Если исследовать динамику завершения проектов, часто можно обнаружить S-образную функцию (s-curve) завершения проекта, связанную с тем, что в начале проекта неизвестно до конца сколько будет добавлено задач к проекту. ![S-Curve](./assets/Monte-Carlo-S-Curve.png) +::: \ No newline at end of file diff --git a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.module.css b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.module.css new file mode 100644 index 0000000..b379823 --- /dev/null +++ b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.module.css @@ -0,0 +1,13 @@ +.noWrap td { + white-space: nowrap; + padding: 2px; + text-align: center; +} + +.vertical td { + white-space: nowrap; + writing-mode: vertical-rl; + transform: rotate(180deg); + padding: 2px; + text-align: center; +} \ No newline at end of file From 80c0c47727e8a2ccddac8fc86521b7c8da907930 Mon Sep 17 00:00:00 2001 From: Pavel Akhmetchanov Date: Mon, 31 Jul 2023 18:47:04 +0300 Subject: [PATCH 05/14] fixed title page Monte-Carlo --- .../roadmap/management/job/tasks/planning/monte-carlo-method.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md index e2e0e75..82e4061 100644 --- a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md +++ b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md @@ -9,7 +9,7 @@ import MonteCarloAllExperiments from './assets/Monte-carlo-all-experiments.png'; import MonteCarloResultProbably from './assets/Monte-Carlo-Result-Probably.png'; import styles from './monte-carlo-method.module.css'; -# Метод Монте-Карло +# Метод Монте-Карло :::note Для начала введем термины: From 2ba75d82b80523108822eab8ba8becd36810b52f Mon Sep 17 00:00:00 2001 From: Pavel Akhmetchanov Date: Mon, 31 Jul 2023 18:48:55 +0300 Subject: [PATCH 06/14] added copyright --- .../management/job/tasks/planning/monte-carlo-method.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md index 82e4061..645553f 100644 --- a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md +++ b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md @@ -455,4 +455,6 @@ const historicalDataThroughput = [ Если исследовать динамику завершения проектов, часто можно обнаружить S-образную функцию (s-curve) завершения проекта, связанную с тем, что в начале проекта неизвестно до конца сколько будет добавлено задач к проекту. ![S-Curve](./assets/Monte-Carlo-S-Curve.png) -::: \ No newline at end of file +::: + +[© controlchart](https://t.me/controlcharts) \ No newline at end of file From e0e6c63eef545c54bc67db29137d74b7c9beb512 Mon Sep 17 00:00:00 2001 From: Pavel Akhmetchanov Date: Tue, 1 Aug 2023 17:43:38 +0300 Subject: [PATCH 07/14] added end-space for 2 files --- .../management/job/tasks/planning/monte-carlo-method.module.css | 2 +- docusaurus.config.js | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.module.css b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.module.css index b379823..b6c17a8 100644 --- a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.module.css +++ b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.module.css @@ -10,4 +10,4 @@ transform: rotate(180deg); padding: 2px; text-align: center; -} \ No newline at end of file +} diff --git a/docusaurus.config.js b/docusaurus.config.js index ff6b086..a1e6168 100644 --- a/docusaurus.config.js +++ b/docusaurus.config.js @@ -117,4 +117,4 @@ module.exports = { }, ], ], -}; \ No newline at end of file +}; From 37b9cfee809c008ad623b9e7387513be1e477004 Mon Sep 17 00:00:00 2001 From: Pavel Akhmetchanov Date: Tue, 1 Aug 2023 17:56:31 +0300 Subject: [PATCH 08/14] update yarn.lock --- yarn.lock | 35 ++++++++++++++++++++++++++++++++--- 1 file changed, 32 insertions(+), 3 deletions(-) diff --git a/yarn.lock b/yarn.lock index c083db5..3181ead 100644 --- a/yarn.lock +++ b/yarn.lock @@ -1857,6 +1857,11 @@ version "7.0.11" resolved "https://registry.npmjs.org/@types/json-schema/-/json-schema-7.0.11.tgz" +"@types/katex@^0.11.0": + version "0.11.1" + resolved "https://registry.yarnpkg.com/@types/katex/-/katex-0.11.1.tgz#34de04477dcf79e2ef6c8d23b41a3d81f9ebeaf5" + integrity sha512-DUlIj2nk0YnJdlWgsFuVKcX27MLW0KbKmGVoUHmFr+74FYYNUDAaj9ZqTADvsbE8rfxuVmSFc7KczYn5Y09ozg== + "@types/mdast@^3.0.0": version "3.0.10" resolved "https://registry.npmjs.org/@types/mdast/-/mdast-3.0.10.tgz" @@ -2704,7 +2709,7 @@ commander@^5.1.0: version "5.1.0" resolved "https://registry.npmjs.org/commander/-/commander-5.1.0.tgz" -commander@^8.3.0: +commander@^8.0.0, commander@^8.3.0: version "8.3.0" resolved "https://registry.npmjs.org/commander/-/commander-8.3.0.tgz" @@ -4085,7 +4090,7 @@ hast-util-has-property@^1.0.0: version "1.0.4" resolved "https://registry.npmjs.org/hast-util-has-property/-/hast-util-has-property-1.0.4.tgz" -hast-util-is-element@^1.0.0: +hast-util-is-element@^1.0.0, hast-util-is-element@^1.1.0: version "1.1.0" resolved "https://registry.npmjs.org/hast-util-is-element/-/hast-util-is-element-1.1.0.tgz" @@ -4680,6 +4685,13 @@ jsonfile@^6.0.1: optionalDependencies: graceful-fs "^4.1.6" +katex@^0.13.0: + version "0.13.24" + resolved "https://registry.yarnpkg.com/katex/-/katex-0.13.24.tgz#fe55455eb455698cb24b911a353d16a3c855d905" + integrity sha512-jZxYuKCma3VS5UuxOx/rFV1QyGSl3Uy/i0kTJF3HgQ5xMinCQVF8Zd4bMY/9aI9b9A2pjIBOsjSSm68ykTAr8w== + dependencies: + commander "^8.0.0" + keyv@^3.0.0: version "3.1.0" resolved "https://registry.npmjs.org/keyv/-/keyv-3.1.0.tgz" @@ -5972,7 +5984,19 @@ regjsparser@^0.9.1: dependencies: jsesc "~0.5.0" -rehype-parse@^7.0.1: +rehype-katex@^5.0.0: + version "5.0.0" + resolved "https://registry.yarnpkg.com/rehype-katex/-/rehype-katex-5.0.0.tgz#b556f24fde918f28ba1cb642ea71c7e82f3373d7" + integrity sha512-ksSuEKCql/IiIadOHiKRMjypva9BLhuwQNascMqaoGLDVd0k2NlE2wMvgZ3rpItzRKCd6vs8s7MFbb8pcR0AEg== + dependencies: + "@types/katex" "^0.11.0" + hast-util-to-text "^2.0.0" + katex "^0.13.0" + rehype-parse "^7.0.0" + unified "^9.0.0" + unist-util-visit "^2.0.0" + +rehype-parse@^7.0.0, rehype-parse@^7.0.1: version "7.0.1" resolved "https://registry.npmjs.org/rehype-parse/-/rehype-parse-7.0.1.tgz" dependencies: @@ -5995,6 +6019,11 @@ remark-footnotes@2.0.0: version "2.0.0" resolved "https://registry.npmjs.org/remark-footnotes/-/remark-footnotes-2.0.0.tgz" +remark-math@^3.0.1: + version "3.0.1" + resolved "https://registry.yarnpkg.com/remark-math/-/remark-math-3.0.1.tgz#85a02a15b15cad34b89a27244d4887b3a95185bb" + integrity sha512-epT77R/HK0x7NqrWHdSV75uNLwn8g9qTyMqCRCDujL0vj/6T6+yhdrR7mjELWtkse+Fw02kijAaBuVcHBor1+Q== + remark-mdx@1.6.22: version "1.6.22" resolved "https://registry.npmjs.org/remark-mdx/-/remark-mdx-1.6.22.tgz" From a270bf93cf2551cc92c12a632e63766839c3dda0 Mon Sep 17 00:00:00 2001 From: Pavel Akhmetchanov Date: Tue, 1 Aug 2023 17:58:35 +0300 Subject: [PATCH 09/14] remove "sidebar_class_name: enabled-page" from file monte-carlo.md --- docs/roadmap/management/job/tasks/planning/monte-carlo-method.md | 1 - 1 file changed, 1 deletion(-) diff --git a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md index 645553f..71c8ae0 100644 --- a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md +++ b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md @@ -1,5 +1,4 @@ --- -sidebar_class_name: enabled-page description: Как работает метод Монте-Карло --- import MonteCarloThroughput from './assets/Monte-Carlo-Throughput.png'; From c0004b9f3c7a875964fb68edc175917a0798785a Mon Sep 17 00:00:00 2001 From: Pavel Akhmetchanov Date: Tue, 1 Aug 2023 18:00:41 +0300 Subject: [PATCH 10/14] move monte-carlo-method.module.css to assets folder --- .../tasks/planning/{ => assets}/monte-carlo-method.module.css | 0 .../roadmap/management/job/tasks/planning/monte-carlo-method.md | 2 +- 2 files changed, 1 insertion(+), 1 deletion(-) rename docs/roadmap/management/job/tasks/planning/{ => assets}/monte-carlo-method.module.css (100%) diff --git a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.module.css b/docs/roadmap/management/job/tasks/planning/assets/monte-carlo-method.module.css similarity index 100% rename from docs/roadmap/management/job/tasks/planning/monte-carlo-method.module.css rename to docs/roadmap/management/job/tasks/planning/assets/monte-carlo-method.module.css diff --git a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md index 71c8ae0..eb63835 100644 --- a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md +++ b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md @@ -6,7 +6,7 @@ import MonteCarloBurndownChart from './assets/Monte-Carlo-Burndown-chart.jpg'; import MonteCarloBurndownChartFull from './assets/Monte-Carlo-Burndown-chart-full.jpg'; import MonteCarloAllExperiments from './assets/Monte-carlo-all-experiments.png'; import MonteCarloResultProbably from './assets/Monte-Carlo-Result-Probably.png'; -import styles from './monte-carlo-method.module.css'; +import styles from './assets/monte-carlo-method.module.css'; # Метод Монте-Карло From 65abecd2fd36b518c5ba70a16d357e78ac3ea2b5 Mon Sep 17 00:00:00 2001 From: Pavel Akhmetchanov Date: Tue, 1 Aug 2023 18:03:07 +0300 Subject: [PATCH 11/14] remove dot in end title of paragraph --- .../management/job/tasks/planning/monte-carlo-method.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md index eb63835..d15855e 100644 --- a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md +++ b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md @@ -60,7 +60,7 @@ import styles from './assets/monte-carlo-method.module.css'; ### Алгоритм метода -#### Шаг первый. +#### Шаг первый Выбираем случайное число из набора данных пропускной способности. @@ -69,13 +69,13 @@ import styles from './assets/monte-carlo-method.module.css'; ``` [4, 1, 2, 1, 4, 3, 2, |3|, 6, 3, 2, 1, 6, 13, 3, 1, 6, 1, 4, 4, 6, 3, 6, 2, 6, 2] → 3 ``` -#### Шаг второй. +#### Шаг второй Считаем что в первую неделю работы над проектом сервис выполнит 3 задачи. И от 40 исходных задач проекта отнимаем это же количество, получим 37. Burn Cahrt of Project -#### Шаг третий. +#### Шаг третий Повторяем первый шаг, и второй до тех пор, пока в исходном наборе 40 задач проекта не останется их совсем. Так мы получим вероятное количество недель за которое будет выполнен проект, запоминаем это количество недель. А добавив этот отрезок времени к планируемой дате начала проекта, можем получить дату завершения. @@ -83,7 +83,7 @@ import styles from './assets/monte-carlo-method.module.css'; На примере просчета первого эксперимента (на картинке), проект завершится за 17 недель. Запоминаем этот срок. -#### Шаг четвертый. +#### Шаг четвертый Алгоритм шагов от первого до третьего повторяем от 10000. После каждого расчета сроков, мы получим число недель за которое может закрыться проект. Собираем эти сроки и считаем сколько раз проект закрылся за этот срок. From db7bc662ac5e12d3778cad94648a4dd454070aa5 Mon Sep 17 00:00:00 2001 From: Pavel Akhmetchanov Date: Tue, 1 Aug 2023 18:17:27 +0300 Subject: [PATCH 12/14] =?UTF-8?q?=D0=B8=D1=81=D0=BF=D1=80=D0=B0=D0=B2?= =?UTF-8?q?=D0=B8=D0=BB=20=D0=BF=D0=BE=20=D1=80=D0=B5=D0=BA=D0=BE=D0=BC?= =?UTF-8?q?=D0=B5=D0=BD=D0=B4=D0=B0=D1=86=D0=B8=D0=B8=20"=D0=9D=D0=B5?= =?UTF-8?q?=D1=81=D0=BA=D0=BE=D0=BB=D1=8C=D0=BA=D0=BE=3F=20=D0=9D=D0=B8?= =?UTF-8?q?=D0=B6=D0=B5=20=D1=82=D0=BE=D0=BB=D1=8C=D0=BA=D0=BE=20=D0=BE?= =?UTF-8?q?=D0=B4=D0=B8=D0=BD=20=D0=BF=D1=80=D0=BE=20=D0=BD=D0=B5=D0=B4?= =?UTF-8?q?=D0=B5=D0=BB=D1=8E",=20=D0=BF=D0=BE=D0=BF=D1=80=D0=B0=D0=B2?= =?UTF-8?q?=D0=B8=D0=BB=20=D1=82=D0=B5=D0=BA=D1=81=D1=82=20=D1=83=D0=BC?= =?UTF-8?q?=D0=B5=D0=BD=D1=8C=D1=88=D0=B8=D0=B2=20=D0=BA=D0=BE=D0=BB=D0=B8?= =?UTF-8?q?=D1=87=D0=B5=D1=81=D1=82=D0=B2=D0=BE?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../management/job/tasks/planning/monte-carlo-method.md | 9 ++++++--- 1 file changed, 6 insertions(+), 3 deletions(-) diff --git a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md index d15855e..16c96a9 100644 --- a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md +++ b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md @@ -22,11 +22,14 @@ import styles from './assets/monte-carlo-method.module.css'; Метод Монте-Карло представляет собой перебор возможных исходов событий. А для его использования в планировании необходимо сначала выбрать модель по которой будет производиться расчет. -Для примера понимания того как работает метод, попробуем его использовать для решения задачи прогнозирования завершения проекта интеллектуальной работы. +Для понимания того как работает метод используем его для решения задачи "прогнозирования сроков завершения проекта интеллектуальной работы". -Есть несколько важных замечаний при использовании метода для прогнозирования интеллектуальной работы. +:::info +Есть важное замечание при использовании метода в ИТ! -Когда мы говорим о прогнозировании сроков интеллектуальной работы команды, например в ИТ, то лучшим отрезком свертки данных, будет является неделя. А связано это с тем, что количество задач выполненных за день будет сильно изменятся от дня в день, по причине высокой волатильности результатов зависящих как от эмоционального состояния людей, так и разной сложности решаемых задач и многих других параметров. +Когда мы говорим о прогнозировании сроков ИТ команды лучшим отрезком свертки данных по пропускной способности будет является неделя. +Свзяано это с тем, что количество задач выполненных за день будет сильно изменятся от дня ко дню, по причине высокой волатильности результатов зависящих как от эмоционального состояния людей, так и разной сложности решаемых задач и многих других параметров. +::: ## Прогнозирования сроков завершения проекта на основе пропускной способности From 60a5c552382e1b1f7256a22731fe60359c2ff26c Mon Sep 17 00:00:00 2001 From: Pavel Akhmetchanov Date: Tue, 1 Aug 2023 18:23:17 +0300 Subject: [PATCH 13/14] =?UTF-8?q?=D1=83=D0=BC=D0=B5=D0=BD=D1=8C=D1=88?= =?UTF-8?q?=D0=B8=D0=BB=20=D0=BA=D0=BE=D0=BB=D0=B8=D1=87=D0=B5=D1=81=D1=82?= =?UTF-8?q?=D0=B2=D0=BE=20=D0=B0=D0=B1=D0=B7=D0=B0=D1=86=D0=B5=D0=B2=20?= =?UTF-8?q?=D0=B2=20"=D0=9F=D1=80=D0=BE=D0=B3=D0=BD=D0=BE=D0=B7=D0=B8?= =?UTF-8?q?=D1=80=D0=BE=D0=B2=D0=B0=D0=BD=D0=B8=D1=8F=20=D1=81=D1=80=D0=BE?= =?UTF-8?q?=D0=BA=D0=BE=D0=B2=20=D0=B7=D0=B0=D0=B2=D0=B5=D1=80=D1=88=D0=B5?= =?UTF-8?q?=D0=BD=D0=B8=D1=8F=20=D0=BF=D1=80=D0=BE=D0=B5=D0=BA=D1=82=D0=B0?= =?UTF-8?q?=20=D0=BD=D0=B0=20=D0=BE=D1=81=D0=BD=D0=BE=D0=B2=D0=B5=20=D0=BF?= =?UTF-8?q?=D1=80=D0=BE=D0=BF=D1=83=D1=81=D0=BA=D0=BD=D0=BE=D0=B9=20=D1=81?= =?UTF-8?q?=D0=BF=D0=BE=D1=81=D0=BE=D0=B1=D0=BD=D0=BE=D1=81=D1=82=D0=B8"?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../management/job/tasks/planning/monte-carlo-method.md | 8 +------- 1 file changed, 1 insertion(+), 7 deletions(-) diff --git a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md index 16c96a9..eec790e 100644 --- a/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md +++ b/docs/roadmap/management/job/tasks/planning/monte-carlo-method.md @@ -33,18 +33,12 @@ import styles from './assets/monte-carlo-method.module.css'; ## Прогнозирования сроков завершения проекта на основе пропускной способности -Для примера необходимо взять достаточный набор данных, предлагаю использовать периоды от 7 до 26 недель. - -С чем может быть связано? - +Для примера необходимо взять достаточный набор данных, предлагаю использовать периоды от 7 до 26 недель. С чем может быть связано? 7 недель, это чуть более чем полтора месяца, меньше данных для использования метода Монте-Карло приведет высокой степени недостоверности результата. - А брать более чем 26 недель, что соответствует половине года, не имеет смысла, так как в интеллектуальной работе происходят постоянные изменения, которые так же могут внести повысить недостоверность прогнозов. С другой стороны такого набора данных вполне достаточно для хорошего прогнозирования. Будет ли работать метод, с учетом того, что интеллектуальные задачи очень разные по сложности и времени выполнения? - Да, конечно будет. Главное чтобы объемы этих задач не отличались кратно. Например если в наборе данных мы имеем задачу которую можно решить в течении пары часов и задачу которую будут решать более 120 дней, то это может привести к недостоверности результата прогнозирования внося огромную дисперсию в результат. - По этому рекомендуется использовать декомпозицию задач, которые будут нивелировать огромный разрыв в характеристиках поставленных заданий. ### Постановка задачи для примера From 196a5dd1a39fd576d5333822a772950625987713 Mon Sep 17 00:00:00 2001 From: Pavel Akhmetchanov Date: Tue, 1 Aug 2023 19:22:57 +0300 Subject: [PATCH 14/14] fixed rotate table value --- .../job/tasks/planning/assets/monte-carlo-method.module.css | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/roadmap/management/job/tasks/planning/assets/monte-carlo-method.module.css b/docs/roadmap/management/job/tasks/planning/assets/monte-carlo-method.module.css index b6c17a8..4cef8c3 100644 --- a/docs/roadmap/management/job/tasks/planning/assets/monte-carlo-method.module.css +++ b/docs/roadmap/management/job/tasks/planning/assets/monte-carlo-method.module.css @@ -6,8 +6,8 @@ .vertical td { white-space: nowrap; - writing-mode: vertical-rl; - transform: rotate(180deg); + writing-mode: bt-rl; + transform: rotate(-90deg); padding: 2px; text-align: center; }