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‎16.02. ЦЛП. Задача составления расписания.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "view-in-github",
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"colab_type": "text"
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},
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"source": [
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"<a href=\"https://colab.research.google.com/github/NikolaiZolotykh/ScientificPython/blob/master/16.02.%20%D0%A6%D0%9B%D0%9F.%20%D0%97%D0%B0%D0%B4%D0%B0%D1%87%D0%B0%20%D1%81%D0%BE%D1%81%D1%82%D0%B0%D0%B2%D0%BB%D0%B5%D0%BD%D0%B8%D1%8F%20%D1%80%D0%B0%D1%81%D0%BF%D0%B8%D1%81%D0%B0%D0%BD%D0%B8%D1%8F.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "Gc00N6R5gSE2",
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"outputId": "1eeccf29-163d-4828-c904-ccf369dc7519"
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},
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"outputs": [
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{
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"output_type": "stream",
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"name": "stdout",
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"text": [
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"Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
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"Collecting pulp\n",
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" Downloading PuLP-2.7.0-py3-none-any.whl (14.3 MB)\n",
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"\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m14.3/14.3 MB\u001b[0m \u001b[31m71.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
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"\u001b[?25hInstalling collected packages: pulp\n",
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"Successfully installed pulp-2.7.0\n"
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]
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}
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],
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"source": [
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"!pip install pulp\n",
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"import pulp"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"id": "Mk4ulvLhgSE4"
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},
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"outputs": [],
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"source": [
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"m = 3 # количество учебных дисциплин (преподавателей)\n",
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"n = 3 # количество академических групп\n",
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"p = 4 # количество тактов времени"
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]
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},
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{
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"cell_type": "code",
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"source": [
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"#m = 10 # количество учебных дисциплин (преподавателей)\n",
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"#n = 10 # количество академических групп\n",
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"#p = 12 # количество тактов времени"
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],
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"metadata": {
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"id": "6I0a9VO6jG7F"
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},
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"id": "sRYl8NAigSE5"
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},
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"outputs": [],
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"source": [
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"I = range(m) # множество учебных дисциплин\n",
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"J = range(n) # множество академических групп\n",
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"T = range(p) # множество тактов\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"id": "hh55eWddgSE5"
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},
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"outputs": [],
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"source": [
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"# x[i][j][k] = 1 означает, что в k-й такт у j-й группы проходит занятие по i-й дисциплине */\n",
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"x = pulp.LpVariable.dicts(\"x\", (I, J, T), 0, 1, pulp.LpInteger)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "QOhqX9t4gSE6",
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"outputId": "b0159373-b512-4dc3-d286-1daac23902dc"
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},
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"outputs": [
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{
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"output_type": "execute_result",
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"data": {
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"text/plain": [
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"x_0_2_2"
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]
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},
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"metadata": {},
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"execution_count": 5
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}
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],
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"source": [
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"x[0][2][2]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "ll8i2ENPgSE7",
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"outputId": "643ddd4c-ec3f-4a82-ff5d-8efad5a19076"
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},
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"outputs": [
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{
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"output_type": "stream",
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"name": "stderr",
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"text": [
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"/usr/local/lib/python3.8/dist-packages/pulp/pulp.py:1352: UserWarning: Spaces are not permitted in the name. Converted to '_'\n",
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" warnings.warn(\"Spaces are not permitted in the name. Converted to '_'\")\n"
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]
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}
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],
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"source": [
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"prob = pulp.LpProblem(\"School Scheduling Problem\", pulp.LpMinimize)\n",
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"#prob += 0, \"Arbitrary Objective Function\" "
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"id": "jIVKJPmvgSE8"
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},
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"outputs": [],
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"source": [
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"# У каждой группы по каждой дисциплине должно пройти ровно одно занятие:\n",
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"for i in I:\n",
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" for j in J:\n",
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" prob += pulp.lpSum([x[i][j][t] for t in T]) == 1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"id": "X8jQ5WKbgSE8"
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},
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"outputs": [],
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"source": [
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"# в любой такт по каждой дисциплине проходит не более одного занятия во всех группах:\n",
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"for i in I:\n",
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" for t in T:\n",
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" prob += pulp.lpSum([x[i][j][t] for j in J]) <= 1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"id": "vs4J2k1VgSE8"
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},
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"outputs": [],
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"source": [
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"# в любой такт у любой группы проходит не более одного занятия:\n",
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"for j in J:\n",
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" for t in T:\n",
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" prob += pulp.lpSum([x[i][j][t] for i in I]) <= 1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"id": "K5F2WbMcgSE9"
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},
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"outputs": [],
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"source": [
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"# 1-й преподаватель не может проводить занятия 4-й парой:\n",
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"for j in J:\n",
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" prob += x[0][j][3] == 0\n",
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"\n",
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"# 2-й преподаватель не может проводить занятия 3-й парой:\n",
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"for j in J:\n",
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" prob += x[1][j][2] == 0\n",
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"\n",
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"# 2-я группа не может учиться 1-й парой:\n",
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"for i in I:\n",
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" prob += x[i][1][0] == 0 \n",
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"\n",
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"# 3-я группа не может учиться 4-й парой \n",
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"for i in I:\n",
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" prob += x[i][2][3] == 0"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "ULj4NxC6gSE9",
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"outputId": "810ac2e0-08ed-4e5d-ecbe-7fbe85090160"
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},
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"outputs": [
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{
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"output_type": "stream",
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"name": "stdout",
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"text": [
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"Status: Optimal\n"
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]
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}
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],
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"source": [
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"prob.solve()\n",
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"print(\"Status:\", pulp.LpStatus[prob.status])\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "jve6S5sagSE9",
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"outputId": "307deb26-e340-441d-e842-c6320716c824"
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},
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"outputs": [
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{
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"output_type": "stream",
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"name": "stdout",
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"text": [
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"\n",
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" Solution:\n",
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"\n",
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" \\\n",
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" \\ Groups\n",
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" t \\\n",
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" \\\n",
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" 0 1 2 3 4 5 6 7 8 9\n",
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" 0 2 . 7 5 1 0 4 6 8 9\n",
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" 1 7 6 8 9 3 . 0 1 4 5\n",
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" 2 3 2 9 8 6 4 7 . 5 0\n",
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" 3 . 5 . 4 2 8 3 7 6 .\n",
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" 4 . 7 4 . 9 5 2 3 1 6\n",
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" 5 0 9 5 6 . 2 1 8 3 7\n",
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" 6 4 8 6 1 0 7 5 9 . 3\n",
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" 7 6 1 2 0 8 . 9 5 7 4\n",
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" 8 9 . . 3 . 1 . 2 0 8\n",
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" 9 8 3 0 . 4 9 6 . 2 1\n",
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"10 1 0 3 7 5 6 8 4 . 2\n",
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"11 5 4 1 2 7 3 . 0 9 .\n",
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"\n"
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]
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}
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],
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"source": [
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"print(\"\\n Solution:\\n\\n \\\\\\n \\\\ Groups\\n t \\\\\\n \\\\\")\n",
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"print(\" \", end=\"\")\n",
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"for j in J:\n",
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" print(\"{:2d}\".format(j), end=\"\")\n",
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"print()\n",
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"\n",
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"for t in T:\n",
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" print(\"{:2d} \".format(t), end=\"\")\n",
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" for j in J:\n",
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" lesson = False\n",
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" for i in I:\n",
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" if pulp.value(x[i][j][t]) == 1:\n",
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" print(\"{:2d}\".format(i), end=\"\")\n",
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" lesson = True\n",
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" break\n",
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" if not lesson:\n",
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" print(\" .\", end=\"\") \n",
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" print()\n",
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"print()\n"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.3"
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},
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"colab": {
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"provenance": [],
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"include_colab_link": true
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}

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