244 lines
8.2 KiB
Plaintext
244 lines
8.2 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "google",
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"metadata": {},
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"source": [
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"##### Copyright 2025 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": "apache",
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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": "basename",
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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": "link",
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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/main/examples/notebook/linear_solver/assignment_groups_mip.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/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/main/ortools/linear_solver/samples/assignment_groups_mip.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/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": "doc",
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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": "install",
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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": "markdown",
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"id": "description",
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"metadata": {},
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"source": [
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"\n",
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"Solve assignment problem for given group of workers."
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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": "code",
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"metadata": {},
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"outputs": [],
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"source": [
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"from ortools.linear_solver import pywraplp\n",
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"\n",
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"\n",
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"\n",
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"def main():\n",
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" # 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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" num_workers = len(costs)\n",
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" num_tasks = len(costs[0])\n",
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"\n",
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" # Allowed groups of workers:\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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" # 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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" if not solver:\n",
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" return\n",
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"\n",
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" # 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 range(num_workers):\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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"\n",
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" # 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 range(num_workers):\n",
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" solver.Add(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 range(num_workers)]) == 1)\n",
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"\n",
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" # Create variables for each worker, indicating whether they work on some task.\n",
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" work = {}\n",
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" for worker in range(num_workers):\n",
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" work[worker] = solver.BoolVar(f\"work[{worker}]\")\n",
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"\n",
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" for worker in range(num_workers):\n",
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" solver.Add(\n",
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" work[worker] == solver.Sum([x[worker, task] for task in range(num_tasks)])\n",
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" )\n",
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"\n",
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" # Group1\n",
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" constraint_g1 = solver.Constraint(1, 1)\n",
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" for index, _ in enumerate(group1):\n",
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" # a*b can be transformed into 0 <= a + b - 2*p <= 1 with p in [0,1]\n",
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" # p is True if a AND b, False otherwise\n",
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" constraint = solver.Constraint(0, 1)\n",
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" constraint.SetCoefficient(work[group1[index][0]], 1)\n",
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" constraint.SetCoefficient(work[group1[index][1]], 1)\n",
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" p = solver.BoolVar(f\"g1_p{index}\")\n",
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" constraint.SetCoefficient(p, -2)\n",
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"\n",
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" constraint_g1.SetCoefficient(p, 1)\n",
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"\n",
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" # Group2\n",
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" constraint_g2 = solver.Constraint(1, 1)\n",
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" for index, _ in enumerate(group2):\n",
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" # a*b can be transformed into 0 <= a + b - 2*p <= 1 with p in [0,1]\n",
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" # p is True if a AND b, False otherwise\n",
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" constraint = solver.Constraint(0, 1)\n",
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" constraint.SetCoefficient(work[group2[index][0]], 1)\n",
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" constraint.SetCoefficient(work[group2[index][1]], 1)\n",
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" p = solver.BoolVar(f\"g2_p{index}\")\n",
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" constraint.SetCoefficient(p, -2)\n",
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"\n",
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" constraint_g2.SetCoefficient(p, 1)\n",
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"\n",
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" # Group3\n",
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" constraint_g3 = solver.Constraint(1, 1)\n",
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" for index, _ in enumerate(group3):\n",
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" # a*b can be transformed into 0 <= a + b - 2*p <= 1 with p in [0,1]\n",
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" # p is True if a AND b, False otherwise\n",
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" constraint = solver.Constraint(0, 1)\n",
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" constraint.SetCoefficient(work[group3[index][0]], 1)\n",
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" constraint.SetCoefficient(work[group3[index][1]], 1)\n",
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" p = solver.BoolVar(f\"g3_p{index}\")\n",
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" constraint.SetCoefficient(p, -2)\n",
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"\n",
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" constraint_g3.SetCoefficient(p, 1)\n",
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"\n",
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" # Objective\n",
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" objective_terms = []\n",
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" for worker in range(num_workers):\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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"\n",
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" # Solve\n",
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" print(f\"Solving with {solver.SolverVersion()}\")\n",
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" status = solver.Solve()\n",
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"\n",
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" # Print solution.\n",
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" if status == pywraplp.Solver.OPTIMAL or status == pywraplp.Solver.FEASIBLE:\n",
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" print(f\"Total cost = {solver.Objective().Value()}\\n\")\n",
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" for worker in range(num_workers):\n",
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" for task in range(num_tasks):\n",
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" if x[worker, task].solution_value() > 0.5:\n",
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" print(\n",
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" f\"Worker {worker} assigned to task {task}.\"\n",
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" + f\" Cost: {costs[worker][task]}\"\n",
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" )\n",
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" else:\n",
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" print(\"No solution found.\")\n",
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"\n",
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"\n",
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"main()\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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"language_info": {
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"name": "python"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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