199 lines
6.5 KiB
Plaintext
199 lines
6.5 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 2023 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_sat"
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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/sat/assignment_groups_sat.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/sat/samples/assignment_groups_sat.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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"Solves an 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.sat.python import cp_model\n",
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"\n",
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"\n",
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"def main() -> None:\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 = [\n",
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" [0, 0, 1, 1], # Workers 2, 3\n",
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" [0, 1, 0, 1], # Workers 1, 3\n",
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" [0, 1, 1, 0], # Workers 1, 2\n",
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" [1, 1, 0, 0], # Workers 0, 1\n",
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" [1, 0, 1, 0], # Workers 0, 2\n",
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" ]\n",
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"\n",
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" group2 = [\n",
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" [0, 0, 1, 1], # Workers 6, 7\n",
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" [0, 1, 0, 1], # Workers 5, 7\n",
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" [0, 1, 1, 0], # Workers 5, 6\n",
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" [1, 1, 0, 0], # Workers 4, 5\n",
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" [1, 0, 0, 1], # Workers 4, 7\n",
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" ]\n",
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"\n",
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" group3 = [\n",
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" [0, 0, 1, 1], # Workers 10, 11\n",
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" [0, 1, 0, 1], # Workers 9, 11\n",
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" [0, 1, 1, 0], # Workers 9, 10\n",
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" [1, 0, 1, 0], # Workers 8, 10\n",
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" [1, 0, 0, 1], # Workers 8, 11\n",
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" ]\n",
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"\n",
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" # Model\n",
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" model = cp_model.CpModel()\n",
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"\n",
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" # Variables\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] = model.new_bool_var(f\"x[{worker},{task}]\")\n",
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"\n",
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" # Constraints\n",
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" # Each worker is assigned to at most one task.\n",
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" for worker in range(num_workers):\n",
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" model.add_at_most_one(x[worker, task] for task in range(num_tasks))\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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" model.add_exactly_one(x[worker, task] for worker in range(num_workers))\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] = model.new_bool_var(f\"work[{worker}]\")\n",
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"\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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" model.add(work[worker] == sum(x[worker, task] for task in range(num_tasks)))\n",
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"\n",
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" # Define the allowed groups of worders\n",
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" model.add_allowed_assignments([work[0], work[1], work[2], work[3]], group1)\n",
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" model.add_allowed_assignments([work[4], work[5], work[6], work[7]], group2)\n",
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" model.add_allowed_assignments([work[8], work[9], work[10], work[11]], group3)\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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" model.minimize(sum(objective_terms))\n",
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"\n",
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" # Solve\n",
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" solver = cp_model.CpSolver()\n",
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" status = solver.solve(model)\n",
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"\n",
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" # Print solution.\n",
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" if status == cp_model.OPTIMAL or status == cp_model.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 solver.boolean_value(x[worker, task]):\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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"nbformat": 4,
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"nbformat_minor": 5
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}
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