201 lines
7.0 KiB
Plaintext
201 lines
7.0 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "google",
|
|
"metadata": {},
|
|
"source": [
|
|
"##### Copyright 2025 Google LLC."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "apache",
|
|
"metadata": {},
|
|
"source": [
|
|
"Licensed under the Apache License, Version 2.0 (the \"License\");\n",
|
|
"you may not use this file except in compliance with the License.\n",
|
|
"You may obtain a copy of the License at\n",
|
|
"\n",
|
|
" http://www.apache.org/licenses/LICENSE-2.0\n",
|
|
"\n",
|
|
"Unless required by applicable law or agreed to in writing, software\n",
|
|
"distributed under the License is distributed on an \"AS IS\" BASIS,\n",
|
|
"WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
|
|
"See the License for the specific language governing permissions and\n",
|
|
"limitations under the License.\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "basename",
|
|
"metadata": {},
|
|
"source": [
|
|
"# schedule_requests_sat"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "link",
|
|
"metadata": {},
|
|
"source": [
|
|
"<table align=\"left\">\n",
|
|
"<td>\n",
|
|
"<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/sat/schedule_requests_sat.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
|
|
"</td>\n",
|
|
"<td>\n",
|
|
"<a href=\"https://github.com/google/or-tools/blob/main/ortools/sat/samples/schedule_requests_sat.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
|
|
"</td>\n",
|
|
"</table>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "doc",
|
|
"metadata": {},
|
|
"source": [
|
|
"First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "install",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"%pip install ortools"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "description",
|
|
"metadata": {},
|
|
"source": [
|
|
"\n",
|
|
"Nurse scheduling problem with shift requests."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "code",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"from typing import Union\n",
|
|
"\n",
|
|
"from ortools.sat.python import cp_model\n",
|
|
"\n",
|
|
"\n",
|
|
"\n",
|
|
"def main() -> None:\n",
|
|
" # This program tries to find an optimal assignment of nurses to shifts\n",
|
|
" # (3 shifts per day, for 7 days), subject to some constraints (see below).\n",
|
|
" # Each nurse can request to be assigned to specific shifts.\n",
|
|
" # The optimal assignment maximizes the number of fulfilled shift requests.\n",
|
|
" num_nurses = 5\n",
|
|
" num_shifts = 3\n",
|
|
" num_days = 7\n",
|
|
" all_nurses = range(num_nurses)\n",
|
|
" all_shifts = range(num_shifts)\n",
|
|
" all_days = range(num_days)\n",
|
|
" shift_requests = [\n",
|
|
" [[0, 0, 1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 1]],\n",
|
|
" [[0, 0, 0], [0, 0, 0], [0, 1, 0], [0, 1, 0], [1, 0, 0], [0, 0, 0], [0, 0, 1]],\n",
|
|
" [[0, 1, 0], [0, 1, 0], [0, 0, 0], [1, 0, 0], [0, 0, 0], [0, 1, 0], [0, 0, 0]],\n",
|
|
" [[0, 0, 1], [0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 0], [1, 0, 0], [0, 0, 0]],\n",
|
|
" [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 0]],\n",
|
|
" ]\n",
|
|
"\n",
|
|
" # Creates the model.\n",
|
|
" model = cp_model.CpModel()\n",
|
|
"\n",
|
|
" # Creates shift variables.\n",
|
|
" # shifts[(n, d, s)]: nurse 'n' works shift 's' on day 'd'.\n",
|
|
" shifts = {}\n",
|
|
" for n in all_nurses:\n",
|
|
" for d in all_days:\n",
|
|
" for s in all_shifts:\n",
|
|
" shifts[(n, d, s)] = model.new_bool_var(f\"shift_n{n}_d{d}_s{s}\")\n",
|
|
"\n",
|
|
" # Each shift is assigned to exactly one nurse in .\n",
|
|
" for d in all_days:\n",
|
|
" for s in all_shifts:\n",
|
|
" model.add_exactly_one(shifts[(n, d, s)] for n in all_nurses)\n",
|
|
"\n",
|
|
" # Each nurse works at most one shift per day.\n",
|
|
" for n in all_nurses:\n",
|
|
" for d in all_days:\n",
|
|
" model.add_at_most_one(shifts[(n, d, s)] for s in all_shifts)\n",
|
|
"\n",
|
|
" # Try to distribute the shifts evenly, so that each nurse works\n",
|
|
" # min_shifts_per_nurse shifts. If this is not possible, because the total\n",
|
|
" # number of shifts is not divisible by the number of nurses, some nurses will\n",
|
|
" # be assigned one more shift.\n",
|
|
" min_shifts_per_nurse = (num_shifts * num_days) // num_nurses\n",
|
|
" if num_shifts * num_days % num_nurses == 0:\n",
|
|
" max_shifts_per_nurse = min_shifts_per_nurse\n",
|
|
" else:\n",
|
|
" max_shifts_per_nurse = min_shifts_per_nurse + 1\n",
|
|
" for n in all_nurses:\n",
|
|
" num_shifts_worked: Union[cp_model.LinearExpr, int] = 0\n",
|
|
" for d in all_days:\n",
|
|
" for s in all_shifts:\n",
|
|
" num_shifts_worked += shifts[(n, d, s)]\n",
|
|
" model.add(min_shifts_per_nurse <= num_shifts_worked)\n",
|
|
" model.add(num_shifts_worked <= max_shifts_per_nurse)\n",
|
|
"\n",
|
|
" model.maximize(\n",
|
|
" sum(\n",
|
|
" shift_requests[n][d][s] * shifts[(n, d, s)]\n",
|
|
" for n in all_nurses\n",
|
|
" for d in all_days\n",
|
|
" for s in all_shifts\n",
|
|
" )\n",
|
|
" )\n",
|
|
"\n",
|
|
" # Creates the solver and solve.\n",
|
|
" solver = cp_model.CpSolver()\n",
|
|
" status = solver.solve(model)\n",
|
|
"\n",
|
|
" if status == cp_model.OPTIMAL:\n",
|
|
" print(\"Solution:\")\n",
|
|
" for d in all_days:\n",
|
|
" print(\"Day\", d)\n",
|
|
" for n in all_nurses:\n",
|
|
" for s in all_shifts:\n",
|
|
" if solver.value(shifts[(n, d, s)]) == 1:\n",
|
|
" if shift_requests[n][d][s] == 1:\n",
|
|
" print(\"Nurse\", n, \"works shift\", s, \"(requested).\")\n",
|
|
" else:\n",
|
|
" print(\"Nurse\", n, \"works shift\", s, \"(not requested).\")\n",
|
|
" print()\n",
|
|
" print(\n",
|
|
" f\"Number of shift requests met = {solver.objective_value}\",\n",
|
|
" f\"(out of {num_nurses * min_shifts_per_nurse})\",\n",
|
|
" )\n",
|
|
" else:\n",
|
|
" print(\"No optimal solution found !\")\n",
|
|
"\n",
|
|
" # Statistics.\n",
|
|
" print(\"\\nStatistics\")\n",
|
|
" print(f\" - conflicts: {solver.num_conflicts}\")\n",
|
|
" print(f\" - branches : {solver.num_branches}\")\n",
|
|
" print(f\" - wall time: {solver.wall_time}s\")\n",
|
|
"\n",
|
|
"\n",
|
|
"main()\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"language_info": {
|
|
"name": "python"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|