ortools-clone/examples/notebook/contrib/assignment.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "google",
   "metadata": {},
   "source": [
    "##### Copyright 2024 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": [
    "# assignment"
   ]
  },
  {
   "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/contrib/assignment.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/examples/contrib/assignment.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",
    "\n",
    "  Assignment problem in Google CP Solver.\n",
    "\n",
    "  Winston 'Operations Research', Assignment Problems, page 393f\n",
    "  (generalized version with added test column)\n",
    "\n",
    "  Compare with the following models:\n",
    "  * Comet   : http://www.hakank.org/comet/assignment.co\n",
    "  * ECLiPSE : http://www.hakank.org/eclipse/assignment.ecl\n",
    "  * Gecode  : http://www.hakank.org/gecode/assignment.cpp\n",
    "  * MiniZinc: http://www.hakank.org/minizinc/assignment.mzn\n",
    "  * Tailor/Essence': http://www.hakank.org/tailor/assignment.eprime\n",
    "  * SICStus: http://hakank.org/sicstus/assignment.pl\n",
    "\n",
    "  This model was created by Hakan Kjellerstrand (hakank@gmail.com)\n",
    "  Also see my other Google CP Solver models:\n",
    "  http://www.hakank.org/google_or_tools/\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "code",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ortools.constraint_solver import pywrapcp\n",
    "\n",
    "\n",
    "def main(cost, rows, cols):\n",
    "  # Create the solver.\n",
    "  solver = pywrapcp.Solver(\"n-queens\")\n",
    "\n",
    "  #\n",
    "  # data\n",
    "  #\n",
    "\n",
    "  # declare variables\n",
    "  total_cost = solver.IntVar(0, 100, \"total_cost\")\n",
    "  x = []\n",
    "  for i in range(rows):\n",
    "    t = []\n",
    "    for j in range(cols):\n",
    "      t.append(solver.IntVar(0, 1, \"x[%i,%i]\" % (i, j)))\n",
    "    x.append(t)\n",
    "  x_flat = [x[i][j] for i in range(rows) for j in range(cols)]\n",
    "\n",
    "  #\n",
    "  # constraints\n",
    "  #\n",
    "\n",
    "  # total_cost\n",
    "  solver.Add(total_cost == solver.Sum(\n",
    "      [solver.ScalProd(x_row, cost_row) for (x_row, cost_row) in zip(x, cost)]))\n",
    "\n",
    "  # exacly one assignment per row, all rows must be assigned\n",
    "  [\n",
    "      solver.Add(solver.Sum([x[row][j]\n",
    "                             for j in range(cols)]) == 1)\n",
    "      for row in range(rows)\n",
    "  ]\n",
    "\n",
    "  # zero or one assignments per column\n",
    "  [\n",
    "      solver.Add(solver.Sum([x[i][col]\n",
    "                             for i in range(rows)]) <= 1)\n",
    "      for col in range(cols)\n",
    "  ]\n",
    "\n",
    "  objective = solver.Minimize(total_cost, 1)\n",
    "\n",
    "  #\n",
    "  # solution and search\n",
    "  #\n",
    "  solution = solver.Assignment()\n",
    "  solution.Add(x_flat)\n",
    "  solution.Add(total_cost)\n",
    "\n",
    "  # db: DecisionBuilder\n",
    "  db = solver.Phase(x_flat, solver.INT_VAR_SIMPLE, solver.ASSIGN_MIN_VALUE)\n",
    "\n",
    "  solver.NewSearch(db, [objective])\n",
    "  num_solutions = 0\n",
    "  while solver.NextSolution():\n",
    "    print(\"total_cost:\", total_cost.Value())\n",
    "    for i in range(rows):\n",
    "      for j in range(cols):\n",
    "        print(x[i][j].Value(), end=\" \")\n",
    "      print()\n",
    "    print()\n",
    "\n",
    "    for i in range(rows):\n",
    "      print(\"Task:\", i, end=\" \")\n",
    "      for j in range(cols):\n",
    "        if x[i][j].Value() == 1:\n",
    "          print(\" is done by \", j)\n",
    "    print()\n",
    "\n",
    "    num_solutions += 1\n",
    "  solver.EndSearch()\n",
    "\n",
    "  print()\n",
    "  print(\"num_solutions:\", num_solutions)\n",
    "  print(\"failures:\", solver.Failures())\n",
    "  print(\"branches:\", solver.Branches())\n",
    "  print(\"WallTime:\", solver.WallTime())\n",
    "\n",
    "\n",
    "# Problem instance\n",
    "# hakank: I added the fifth column to make it more\n",
    "#         interesting\n",
    "rows = 4\n",
    "cols = 5\n",
    "cost = [[14, 5, 8, 7, 15], [2, 12, 6, 5, 3], [7, 8, 3, 9, 7], [2, 4, 6, 10, 1]]\n",
    "\n",
    "main(cost, rows, cols)\n",
    "\n"
   ]
  }
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