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   "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",
    "def main():\n",
    "  # Data.\n",
    "  cost = [[90, 76, 75, 70, 50, 74],\n",
    "          [35, 85, 55, 65, 48, 101],\n",
    "          [125, 95, 90, 105, 59, 120],\n",
    "          [45, 110, 95, 115, 104, 83],\n",
    "          [60, 105, 80, 75, 59, 62],\n",
    "          [45, 65, 110, 95, 47, 31],\n",
    "          [38, 51, 107, 41, 69, 99],\n",
    "          [47, 85, 57, 71, 92, 77],\n",
    "          [39, 63, 97, 49, 118, 56],\n",
    "          [47, 101, 71, 60, 88, 109],\n",
    "          [17, 39, 103, 64, 61, 92],\n",
    "          [101, 45, 83, 59, 92, 27]]\n",
    "\n",
    "  group1 =  [[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]]      # Workers 0, 2\n",
    "\n",
    "  group2 =  [[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]]      # Workers 4, 7\n",
    "\n",
    "  group3 =  [[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]]      # Workers 8, 11\n",
    "\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)) 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]], group3)\n",
    "\n",
    "  # Total cost\n",
    "  model.Add(total_cost ==\n",
    "            sum(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",
    "\n",
    "if __name__ == '__main__':\n",
    "  main()"
   ]
  }
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