ortools-clone/examples/notebook/graph/simple_min_cost_flow_program.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Copyright 2021 Google LLC."
   ]
  },
  {
   "cell_type": "markdown",
   "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",
   "metadata": {},
   "source": [
    "# simple_min_cost_flow_program"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "<td>\n",
    "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/master/examples/notebook/graph/simple_min_cost_flow_program.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
    "</td>\n",
    "<td>\n",
    "<a href=\"https://github.com/google/or-tools/blob/master/ortools/graph/samples/simple_min_cost_flow_program.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/tools/github_32px.png\"/>View source on GitHub</a>\n",
    "</td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install ortools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#!/usr/bin/env python3\n",
    "# Copyright 2010-2021 Google LLC\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",
    "# [START program]\n",
    "\"\"\"From Bradley, H. and M., 'Applied Mathematical Programming', figure 8.1.\"\"\"\n",
    "# [START import]\n",
    "from ortools.graph import pywrapgraph\n",
    "# [END import]\n",
    "\n",
    "\n",
    "\"\"\"MinCostFlow simple interface example.\"\"\"\n",
    "# [START data]\n",
    "# Define four parallel arrays: sources, destinations, capacities,\n",
    "# and unit costs between each pair. For instance, the arc from node 0\n",
    "# to node 1 has a capacity of 15.\n",
    "start_nodes = [0, 0, 1, 1, 1, 2, 2, 3, 4]\n",
    "end_nodes = [1, 2, 2, 3, 4, 3, 4, 4, 2]\n",
    "capacities = [15, 8, 20, 4, 10, 15, 4, 20, 5]\n",
    "unit_costs = [4, 4, 2, 2, 6, 1, 3, 2, 3]\n",
    "\n",
    "# Define an array of supplies at each node.\n",
    "supplies = [20, 0, 0, -5, -15]\n",
    "# [END data]\n",
    "\n",
    "# [START constraints]\n",
    "# Instantiate a SimpleMinCostFlow solver.\n",
    "min_cost_flow = pywrapgraph.SimpleMinCostFlow()\n",
    "\n",
    "# Add each arc.\n",
    "for arc in zip(start_nodes, end_nodes, capacities, unit_costs):\n",
    "    min_cost_flow.AddArcWithCapacityAndUnitCost(arc[0], arc[1], arc[2],\n",
    "                                                arc[3])\n",
    "\n",
    "# Add node supplies.\n",
    "for count, supply in enumerate(supplies):\n",
    "    min_cost_flow.SetNodeSupply(count, supply)\n",
    "# [END constraints]\n",
    "\n",
    "# [START solve]\n",
    "# Find the min cost flow.\n",
    "solve_status = min_cost_flow.Solve()\n",
    "# [END solve]\n",
    "\n",
    "# [START print_solution]\n",
    "if solve_status == min_cost_flow.OPTIMAL:\n",
    "    print('Minimum cost: ', min_cost_flow.OptimalCost())\n",
    "    print('')\n",
    "    print(' Arc   Flow / Capacity  Cost')\n",
    "    for i in range(min_cost_flow.NumArcs()):\n",
    "        cost = min_cost_flow.Flow(i) * min_cost_flow.UnitCost(i)\n",
    "        print('%1s -> %1s    %3s   / %3s   %3s' %\n",
    "              (min_cost_flow.Tail(i), min_cost_flow.Head(i),\n",
    "               min_cost_flow.Flow(i), min_cost_flow.Capacity(i), cost))\n",
    "else:\n",
    "    print('Solving the min cost flow problem failed. Solver status: ',\n",
    "          solve_status)\n",
    "# [END print_solution]\n",
    "\n"
   ]
  }
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