linear_programming_ortools.ipynb

linear_programming_ortools.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/leobarone/30d0a2c0c34fa5f486a37a6f5185b624/linear_programming_ortools.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "f718ccbb-d2ce-4b82-8123-afddce958174",
      "metadata": {
        "id": "f718ccbb-d2ce-4b82-8123-afddce958174"
      },
      "source": [
        "Import linear solver \"pywraplp\" from ortools."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "b5d02ab6-c0ee-421c-92bc-aeccb0ad9cc1",
      "metadata": {
        "id": "b5d02ab6-c0ee-421c-92bc-aeccb0ad9cc1"
      },
      "outputs": [],
      "source": [
        "from ortools.linear_solver import pywraplp"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "7ec059fa-e0ea-4c84-981e-4255e1803798",
      "metadata": {
        "id": "7ec059fa-e0ea-4c84-981e-4255e1803798"
      },
      "source": [
        "Create a linear solver object."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "11f14f09-e5fc-4ef2-b5af-b1b9a0af6010",
      "metadata": {
        "id": "11f14f09-e5fc-4ef2-b5af-b1b9a0af6010"
      },
      "outputs": [],
      "source": [
        "# Create the linear solver with the SCIP backend.\n",
        "solver = pywraplp.Solver.CreateSolver('SCIP')"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8d4b0087-dba4-42e0-8c89-4c6ca36d1bc3",
      "metadata": {
        "id": "8d4b0087-dba4-42e0-8c89-4c6ca36d1bc3"
      },
      "source": [
        "Define a variable for infinity."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "ecfc8ed2-52d4-403a-9cd6-ce14c6b09543",
      "metadata": {
        "tags": [],
        "id": "ecfc8ed2-52d4-403a-9cd6-ce14c6b09543"
      },
      "outputs": [],
      "source": [
        "inf = solver.infinity()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "470092dc-acd9-43c3-a27a-746fae098457",
      "metadata": {
        "id": "470092dc-acd9-43c3-a27a-746fae098457"
      },
      "source": [
        "Define the 3 variables of the problem, $x_1$, $x_2$ and $x_3$ as non-negative real numbers."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "1c34a0cd-5a0c-4d18-b06e-fca8b5a44219",
      "metadata": {
        "id": "1c34a0cd-5a0c-4d18-b06e-fca8b5a44219"
      },
      "outputs": [],
      "source": [
        "# Create the variables x1, x2 and x3.\n",
        "x1 = solver.NumVar(0., inf, 'x1')\n",
        "x2 = solver.NumVar(0., inf, 'x2')\n",
        "x3 = solver.NumVar(0., inf, 'x3')"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "7317fa70-1470-4a3a-8308-3771ceac75a4",
      "metadata": {
        "id": "7317fa70-1470-4a3a-8308-3771ceac75a4"
      },
      "source": [
        "Write the four linear constraints of the problem\n",
        "\n",
        "$0.7 * x_1 + 0.8 * x_2 + 0 * x_3 >= 10$\n",
        "\n",
        "$0.9 * x_1 + 0.8 * x_2 + 0.8 * x_3 >= 12$\n",
        "\n",
        "$0.8 * x_1 + 1.5 * x_2 + 0.9 * x_3 >= 15$\n",
        "\n",
        "$0.5 * x_1 + 0.6 * x_2 + 0.4 * x_3 <= 7.5$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "1f00bfab-9f42-4c99-9df4-bb44dbf97c21",
      "metadata": {
        "id": "1f00bfab-9f42-4c99-9df4-bb44dbf97c21",
        "outputId": "a2dc0048-b3b9-4787-827b-4e4240f1ecd3"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<ortools.linear_solver.pywraplp.Constraint; proxy of <Swig Object of type 'operations_research::MPConstraint *' at 0x7f7758064720> >"
            ]
          },
          "execution_count": 29,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "solver.Add(0.7 * x1 + 0.8 * x2 + 0 * x3 >= 10)\n",
        "solver.Add(0.9 * x1 + 0.8 * x2 + 0.8 * x3 >= 12)\n",
        "solver.Add(0.8 * x1 + 1.5 * x2 + 0.9 * x3 >= 15)\n",
        "solver.Add(0.5 * x1 + 0.6 * x2 + 0.4 * x3 <= 7.5)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8d9d8ef1-aef0-4fe1-ac60-e4fefe518975",
      "metadata": {
        "id": "8d9d8ef1-aef0-4fe1-ac60-e4fefe518975"
      },
      "source": [
        "Write the objective function of the problem to be minimized:\n",
        "\n",
        "$0.25 * x_1 + 0.10 * x_2 + 0.08 * x_3$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "006bd0f4-a8e2-4359-99a4-e3c2a73d26f5",
      "metadata": {
        "id": "006bd0f4-a8e2-4359-99a4-e3c2a73d26f5"
      },
      "outputs": [],
      "source": [
        "solver.Minimize(0.25 * x1 + 0.10 * x2 + 0.08 * x3)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ae05e61f-17dd-4935-adf2-e395d0f10563",
      "metadata": {
        "id": "ae05e61f-17dd-4935-adf2-e395d0f10563"
      },
      "source": [
        "And, finally, solve it:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "f3aee2b4-fc76-4609-ab20-ab54565936d8",
      "metadata": {
        "id": "f3aee2b4-fc76-4609-ab20-ab54565936d8",
        "outputId": "747c216e-199e-4085-8ae7-65f3d48d6c6d"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Solution:\n",
            "Objective value = 2.590000000000001\n",
            "x1 = 8.000000000000007\n",
            "x2 = 5.499999999999995\n",
            "x3 = 0.49999999999999756\n"
          ]
        }
      ],
      "source": [
        "solver.Solve()\n",
        "print('Solution:')\n",
        "print('Objective value =', solver.Objective().Value())\n",
        "print('x1 =', x1.solution_value())\n",
        "print('x2 =', x2.solution_value())\n",
        "print('x3 =', x3.solution_value())"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.10"
    },
    "colab": {
      "name": "linear_programming_ortools.ipynb",
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}