235 lines
7.7 KiB
Plaintext
235 lines
7.7 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "408a7040",
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"metadata": {},
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"source": [
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"##### Copyright 2021 Google LLC."
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]
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},
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{
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"cell_type": "markdown",
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"id": "1a76cac9",
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"metadata": {},
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"source": [
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"Licensed under the Apache License, Version 2.0 (the \"License\");\n",
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"you may not use this file except in compliance with the License.\n",
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"You may obtain a copy of the License at\n",
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"\n",
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" http://www.apache.org/licenses/LICENSE-2.0\n",
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"\n",
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"Unless required by applicable law or agreed to in writing, software\n",
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"distributed under the License is distributed on an \"AS IS\" BASIS,\n",
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"WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
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"See the License for the specific language governing permissions and\n",
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"limitations under the License.\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a94ef0e4",
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"metadata": {},
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"source": [
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"# assignment_groups_mip"
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]
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},
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{
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"cell_type": "markdown",
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"id": "77e471f0",
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"metadata": {},
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"source": [
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"<table align=\"left\">\n",
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"<td>\n",
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"<a href=\"https://colab.research.google.com/github/google/or-tools/blob/master/examples/notebook/linear_solver/assignment_groups_mip.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
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"</td>\n",
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"<td>\n",
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"<a href=\"https://github.com/google/or-tools/blob/master/ortools/linear_solver/samples/assignment_groups_mip.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/tools/github_32px.png\"/>View source on GitHub</a>\n",
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"</td>\n",
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"</table>"
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]
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},
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{
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"cell_type": "markdown",
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"id": "6f4db2f2",
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"metadata": {},
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"source": [
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"First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
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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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"id": "e9575cb8",
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"metadata": {},
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"outputs": [],
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"source": [
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"!pip install ortools"
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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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"id": "754869c9",
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"metadata": {},
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"outputs": [],
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"source": [
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"#!/usr/bin/env python3\n",
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"# Copyright 2010-2021 Google LLC\n",
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"# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
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"# you may not use this file except in compliance with the License.\n",
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"# You may obtain a copy of the License at\n",
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"#\n",
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"# http://www.apache.org/licenses/LICENSE-2.0\n",
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"#\n",
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"# Unless required by applicable law or agreed to in writing, software\n",
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"# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
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"# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
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"# See the License for the specific language governing permissions and\n",
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"# limitations under the License.\n",
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"# [START program]\n",
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"\"\"\"Solve assignment problem for given group of workers.\"\"\"\n",
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"# [START import]\n",
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"from ortools.linear_solver import pywraplp\n",
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"# [END import]\n",
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"\n",
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"\n",
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"# Data\n",
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"# [START data]\n",
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"costs = [\n",
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" [90, 76, 75, 70, 50, 74],\n",
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" [35, 85, 55, 65, 48, 101],\n",
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" [125, 95, 90, 105, 59, 120],\n",
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" [45, 110, 95, 115, 104, 83],\n",
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" [60, 105, 80, 75, 59, 62],\n",
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" [45, 65, 110, 95, 47, 31],\n",
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" [38, 51, 107, 41, 69, 99],\n",
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" [47, 85, 57, 71, 92, 77],\n",
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" [39, 63, 97, 49, 118, 56],\n",
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" [47, 101, 71, 60, 88, 109],\n",
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" [17, 39, 103, 64, 61, 92],\n",
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" [101, 45, 83, 59, 92, 27],\n",
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"]\n",
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"# [END data]\n",
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"\n",
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"# Allowed groups of workers:\n",
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"# [START allowed_groups]\n",
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"group1 = [ # Subgroups of workers 0 - 3\n",
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" [2, 3],\n",
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" [1, 3],\n",
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" [1, 2],\n",
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" [0, 1],\n",
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" [0, 2],\n",
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"]\n",
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"\n",
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"group2 = [ # Subgroups of workers 4 - 7\n",
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" [6, 7],\n",
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" [5, 7],\n",
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" [5, 6],\n",
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" [4, 5],\n",
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" [4, 7],\n",
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"]\n",
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"\n",
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"group3 = [ # Subgroups of workers 8 - 11\n",
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" [10, 11],\n",
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" [9, 11],\n",
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" [9, 10],\n",
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" [8, 10],\n",
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" [8, 11],\n",
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"]\n",
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"\n",
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"allowed_groups = []\n",
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"for workers_g1 in group1:\n",
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" for workers_g2 in group2:\n",
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" for workers_g3 in group3:\n",
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" allowed_groups.append(workers_g1 + workers_g2 + workers_g3)\n",
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"# [END allowed_groups]\n",
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"\n",
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"# [START solves]\n",
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"min_val = 1e6\n",
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"total_time = 0\n",
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"for group in allowed_groups:\n",
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" res = assignment(costs, group)\n",
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" status_tmp = res[0]\n",
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" solver_tmp = res[1]\n",
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" x_tmp = res[2]\n",
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" if status_tmp == pywraplp.Solver.OPTIMAL or status_tmp == pywraplp.Solver.FEASIBLE:\n",
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" if solver_tmp.Objective().Value() < min_val:\n",
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" min_val = solver_tmp.Objective().Value()\n",
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" min_group = group\n",
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" min_solver = solver_tmp\n",
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" min_x = x_tmp\n",
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" total_time += solver_tmp.WallTime()\n",
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"# [END solves]\n",
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"\n",
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"# Print best solution.\n",
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"# [START print_solution]\n",
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"if min_val < 1e6:\n",
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" print(f'Total cost = {min_solver.Objective().Value()}\\n')\n",
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" num_tasks = len(costs[0])\n",
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" for worker in min_group:\n",
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" for task in range(num_tasks):\n",
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" if min_x[worker, task].solution_value() > 0.5:\n",
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" print(f'Worker {worker} assigned to task {task}.' +\n",
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" f' Cost = {costs[worker][task]}')\n",
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"else:\n",
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" print('No solution found.')\n",
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"print(f'Time = {total_time} ms')\n",
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"# [END print_solution]\n",
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"\n",
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"def assignment(costs, group):\n",
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" \"\"\"Solve the assignment problem for one allowed group combinaison.\"\"\"\n",
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" num_tasks = len(costs[1])\n",
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" # Solver\n",
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" # [START solver]\n",
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" # Create the mip solver with the SCIP backend.\n",
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" solver = pywraplp.Solver.CreateSolver('SCIP')\n",
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" # [END solver]\n",
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"\n",
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" # Variables\n",
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" # [START variables]\n",
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" # x[worker, task] is an array of 0-1 variables, which will be 1\n",
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" # if the worker is assigned to the task.\n",
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" x = {}\n",
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" for worker in group:\n",
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" for task in range(num_tasks):\n",
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" x[worker, task] = solver.BoolVar(f'x[{worker},{task}]')\n",
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" # [END variables]\n",
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"\n",
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" # Constraints\n",
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" # [START constraints]\n",
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" # The total size of the tasks each worker takes on is at most total_size_max.\n",
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" for worker in group:\n",
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" solver.Add(\n",
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" solver.Sum([x[worker, task] for task in range(num_tasks)]) <= 1)\n",
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"\n",
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" # Each task is assigned to exactly one worker.\n",
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" for task in range(num_tasks):\n",
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" solver.Add(solver.Sum([x[worker, task] for worker in group]) == 1)\n",
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" # [END constraints]\n",
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"\n",
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" # Objective\n",
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" # [START objective]\n",
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" objective_terms = []\n",
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" for worker in group:\n",
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" for task in range(num_tasks):\n",
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" objective_terms.append(costs[worker][task] * x[worker, task])\n",
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" solver.Minimize(solver.Sum(objective_terms))\n",
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" # [END objective]\n",
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"\n",
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" # Solve\n",
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" # [START solve]\n",
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" status = solver.Solve()\n",
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" # [END solve]\n",
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"\n",
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" return [status, solver, x]\n",
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"\n",
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"\n"
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]
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}
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],
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"metadata": {},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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