{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Copyright 2010-2017 Google\n",
    "# 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",
    "from __future__ import print_function\n",
    "from ortools.sat.python import cp_model\n",
    "\n",
    "\n",
    "# Data.\n",
    "cost = [[90, 76, 75, 70, 50, 74], [35, 85, 55, 65, 48,\n",
    "                                   101], [125, 95, 90, 105, 59, 120],\n",
    "        [45, 110, 95, 115, 104, 83], [60, 105, 80, 75, 59, 62], [\n",
    "            45, 65, 110, 95, 47, 31\n",
    "        ], [38, 51, 107, 41, 69, 99], [47, 85, 57, 71,\n",
    "                                       92, 77], [39, 63, 97, 49, 118, 56],\n",
    "        [47, 101, 71, 60, 88, 109], [17, 39, 103, 64, 61,\n",
    "                                     92], [101, 45, 83, 59, 92, 27]]\n",
    "\n",
    "group1 = [\n",
    "    [0, 0, 1, 1],  # Workers 2, 3\n",
    "    [0, 1, 0, 1],  # Workers 1, 3\n",
    "    [0, 1, 1, 0],  # Workers 1, 2\n",
    "    [1, 1, 0, 0],  # Workers 0, 1\n",
    "    [1, 0, 1, 0]\n",
    "]  # Workers 0, 2\n",
    "\n",
    "group2 = [\n",
    "    [0, 0, 1, 1],  # Workers 6, 7\n",
    "    [0, 1, 0, 1],  # Workers 5, 7\n",
    "    [0, 1, 1, 0],  # Workers 5, 6\n",
    "    [1, 1, 0, 0],  # Workers 4, 5\n",
    "    [1, 0, 0, 1]\n",
    "]  # Workers 4, 7\n",
    "\n",
    "group3 = [\n",
    "    [0, 0, 1, 1],  # Workers 10, 11\n",
    "    [0, 1, 0, 1],  # Workers 9, 11\n",
    "    [0, 1, 1, 0],  # Workers 9, 10\n",
    "    [1, 0, 1, 0],  # Workers 8, 10\n",
    "    [1, 0, 0, 1]\n",
    "]  # Workers 8, 11\n",
    "\n",
    "sizes = [10, 7, 3, 12, 15, 4, 11, 5]\n",
    "total_size_max = 15\n",
    "num_workers = len(cost)\n",
    "num_tasks = len(cost[1])\n",
    "all_workers = range(num_workers)\n",
    "all_tasks = range(num_tasks)\n",
    "\n",
    "# Model.\n",
    "\n",
    "model = cp_model.CpModel()\n",
    "# Variables\n",
    "total_cost = model.NewIntVar(0, 1000, 'total_cost')\n",
    "x = [[model.NewBoolVar('x[%i,%i]' % (i, j))\n",
    "      for j in all_tasks]\n",
    "     for i in all_workers]\n",
    "works = [model.NewBoolVar('works[%i]' % i) for i in all_workers]\n",
    "\n",
    "# Constraints\n",
    "\n",
    "# Link x and workers.\n",
    "for i in range(num_workers):\n",
    "  model.AddMaxEquality(works[i], x[i])\n",
    "\n",
    "# Each task is assigned to at least one worker.\n",
    "for j in all_tasks:\n",
    "  model.Add(sum(x[i][j] for i in all_workers) >= 1)\n",
    "\n",
    "# Total task size for each worker is at most total_size_max\n",
    "for i in all_workers:\n",
    "  model.Add(sum(sizes[j] * x[i][j] for j in all_tasks) <= total_size_max)\n",
    "\n",
    "# Group constraints.\n",
    "model.AddAllowedAssignments([works[0], works[1], works[2], works[3]], group1)\n",
    "model.AddAllowedAssignments([works[4], works[5], works[6], works[7]], group2)\n",
    "model.AddAllowedAssignments([works[8], works[9], works[10], works[11]],\n",
    "                            group3)\n",
    "\n",
    "# Total cost\n",
    "model.Add(total_cost == sum(\n",
    "    x[i][j] * cost[i][j] for j in all_tasks for i in all_workers))\n",
    "model.Minimize(total_cost)\n",
    "\n",
    "# Solve and output solution.\n",
    "solver = cp_model.CpSolver()\n",
    "status = solver.Solve(model)\n",
    "\n",
    "if status == cp_model.OPTIMAL:\n",
    "  print('Total cost = %i' % solver.ObjectiveValue())\n",
    "  print()\n",
    "  for i in all_workers:\n",
    "    for j in all_tasks:\n",
    "      if solver.Value(x[i][j]) == 1:\n",
    "        print('Worker ', i, ' assigned to task ', j, '  Cost = ', cost[i][j])\n",
    "\n",
    "  print()\n",
    "\n",
    "print('Statistics')\n",
    "print('  - conflicts : %i' % solver.NumConflicts())\n",
    "print('  - branches  : %i' % solver.NumBranches())\n",
    "print('  - wall time : %f ms' % solver.WallTime())\n",
    "\n"
   ]
  }
 ],
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