UFLP (with and without Disruptions).ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "UFLP (with and without Disruptions)",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyPz9hRrZHOWRFV76yaIrmMY",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Jeevesh28/Facility-Location-Problem/blob/main/UFLP%20(with%20and%20without%20Disruptions).ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2AvLvidA-7pW"
      },
      "source": [
        "The **Gurobi Optimizer** is an optimization solver for linear programming (LP), quadratic programming (QP), quadratically constrained programming (QCP), mixed-integer linear programming (MILP), mixed-integer quadratic programming (MIQP), and mixed-integer quadratically constrained programming (MIQCP)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DAFOA6W4UB5g"
      },
      "source": [
        "%%capture\n",
        "!pip install gurobipy;"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K6ugudi4_r2Y"
      },
      "source": [
        "Importing python libraries:\n",
        "\n",
        "*   **NumPy:** Matrix operations\n",
        "*   **Matplotlib:** Plotting\n",
        "*   **Random:** Randomising facility and customer coordinates"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ev-1BFO-XFjU"
      },
      "source": [
        "import random\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "rnd = np.random\n",
        "rnd.seed(42) # Change seed value to randomise "
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fWr_OjjBBCbi"
      },
      "source": [
        "**Initialising Customers and Facility with random coordinates**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Duxl5c7sXIbj"
      },
      "source": [
        "n = 20 # Number of Customer\n",
        "xc = rnd.rand(n) * 200 # x-coordinate\n",
        "yc = rnd.rand(n) * 100 # y-coordinate\n",
        "\n",
        "m = 5  # Numebr of Facility\n",
        "xf = rnd.rand(m) * 200 # x-coordiante \n",
        "yf = rnd.rand(m) * 100 # y-coordiante"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zCwKXF_ZBVRb"
      },
      "source": [
        "**Plotting Customers (Blue - Circle) and Facility (Red - Square)**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 267
        },
        "id": "2YkUNcYxXRlG",
        "outputId": "8f36098c-0502-4053-8c02-2f16bd7b5702"
      },
      "source": [
        "plt.scatter(xc[0:], yc[0:], c='b', label = 'Customer') # Customer\n",
        "plt.scatter(xf[0:], yf[0:], c='r', marker='s', label = 'Facility') # Facility\n",
        "plt.legend()\n",
        "plt.show();"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
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        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NHUKa9B_CGWI"
      },
      "source": [
        "**1. Building the Cost Function for Undisrupted Uncapacitated Facility Location Problem**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jI-QPsDWXZfL"
      },
      "source": [
        "I = [i for i in range(0, n)] # Customer\n",
        "J = [i for i in range(0, m)] # Facility\n",
        "h = {i: rnd.randint(1, 10) for i in I} # Demand of Customer\n",
        "A = [(i, j) for i in I for j in J] # 2-D cartesian product\n",
        "f = {j: 100 for j in J} # Fixed setup cost of Facility\n",
        "c = {(i, j): 1*np.hypot(xc[i]-xf[j], yc[i]-yf[j]) for (i, j) in A} # Cost to reach customer from Facility"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QqnAEDfVXoXx"
      },
      "source": [
        "from gurobipy import Model, GRB, quicksum"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7BD1qhusXpF9"
      },
      "source": [
        "%%capture\n",
        "mdl = Model('UFLP');"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zIM3XHDgXqjy"
      },
      "source": [
        "x = mdl.addVars(J, vtype = GRB.BINARY)\n",
        "y = mdl.addVars(A, vtype = GRB.CONTINUOUS) "
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hTB8ou5gXwD8"
      },
      "source": [
        "mdl.ModelSense = GRB.MINIMIZE # Minimisation model\n",
        "mdl.setObjective(quicksum(f[j]*x[j] for j in J) + quicksum(h[i]*c[i,j]*y[i,j] for i,j in A)) # Cost Function"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ya57kW7aXyuT"
      },
      "source": [
        "mdl.addConstrs(quicksum(y[i,j] for j in J) == 1 for i in I);\n",
        "mdl.addConstrs(y[i,j] <= x[j] for i,j in A);"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GPO917ANDo5x"
      },
      "source": [
        "**Model Optimization**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EomwipKAX4NX",
        "outputId": "6942d08e-d696-4941-e2e8-8920929be58c"
      },
      "source": [
        "mdl.optimize() # Solution cost: 3818.43 (varies with changing seed value)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Gurobi Optimizer version 9.1.2 build v9.1.2rc0 (linux64)\n",
            "Thread count: 1 physical cores, 2 logical processors, using up to 2 threads\n",
            "Optimize a model with 120 rows, 105 columns and 300 nonzeros\n",
            "Model fingerprint: 0x08ec4171\n",
            "Variable types: 100 continuous, 5 integer (5 binary)\n",
            "Coefficient statistics:\n",
            "  Matrix range     [1e+00, 1e+00]\n",
            "  Objective range  [3e+01, 2e+03]\n",
            "  Bounds range     [1e+00, 1e+00]\n",
            "  RHS range        [1e+00, 1e+00]\n",
            "Presolve time: 0.00s\n",
            "Presolved: 120 rows, 105 columns, 300 nonzeros\n",
            "Variable types: 100 continuous, 5 integer (5 binary)\n",
            "\n",
            "Root relaxation: objective 3.818435e+03, 8 iterations, 0.00 seconds\n",
            "\n",
            "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
            " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
            "\n",
            "*    0     0               0    3818.4347491 3818.43475  0.00%     -    0s\n",
            "\n",
            "Explored 0 nodes (8 simplex iterations) in 0.08 seconds\n",
            "Thread count was 2 (of 2 available processors)\n",
            "\n",
            "Solution count 1: 3818.43 \n",
            "\n",
            "Optimal solution found (tolerance 1.00e-04)\n",
            "Best objective 3.818434749094e+03, best bound 3.818434749094e+03, gap 0.0000%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AE429dmgDwC8"
      },
      "source": [
        "**Customer - Facility mapping**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hV0M82BcX5_D"
      },
      "source": [
        "assignment = [a for a in A if y[a].X > 0.0] "
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kxzfw8w8X9Z3",
        "outputId": "161c0920-6516-4afc-8a13-5ec1e5cd310f"
      },
      "source": [
        "assignment # (i, j) == (Customer, Facility)"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[(0, 1),\n",
              " (1, 3),\n",
              " (2, 3),\n",
              " (3, 1),\n",
              " (4, 0),\n",
              " (5, 0),\n",
              " (6, 2),\n",
              " (7, 3),\n",
              " (8, 1),\n",
              " (9, 1),\n",
              " (10, 2),\n",
              " (11, 3),\n",
              " (12, 3),\n",
              " (13, 0),\n",
              " (14, 0),\n",
              " (15, 0),\n",
              " (16, 4),\n",
              " (17, 1),\n",
              " (18, 1),\n",
              " (19, 4)]"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x585asEFD7e_"
      },
      "source": [
        "**Plotting final obtained map**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 267
        },
        "id": "qc7ZTNWEX_Do",
        "outputId": "f947102b-e483-4cc2-bf74-c2abd2569f7d"
      },
      "source": [
        "for i, j in assignment:\n",
        "    plt.plot([xc[i], xf[j]], [yc[i], yf[j]], c='g', zorder=0)\n",
        "plt.scatter(xc[0:], yc[0:], c='b', label = 'Customer')\n",
        "plt.scatter(xf[0:], yf[0:], c='r',marker='s', label = 'Facility')\n",
        "plt.legend()\n",
        "plt.show();"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IcrPxaz1Ei2D"
      },
      "source": [
        "**2. Building the Cost Function for Disrupted Uncapacitated Facility Location Problem**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Oigqgxr7QyT4"
      },
      "source": [
        "max_disruption = 10000 # High penalty for disrupted facility\n",
        "I = [i for i in range(0, n)] # Customer\n",
        "J = [i for i in range(0, m)] # Facility\n",
        "h = {i: rnd.randint(1, 10) for i in I} # Demand of Customer\n",
        "A = [(i, j) for i in I for j in J] # 2-D cartesian product\n",
        "f = {j: 100 for j in J} # Fixed setup cost of Facility\n",
        "c = {(i, j): 1*np.hypot(xc[i]-xf[j], yc[i]-yf[j]) for (i, j) in A} # Cost to reach customer from Facility\n",
        "p = {j: rnd.choice(np.array((0, max_disruption // 4, max_disruption // 2, max_disruption)), p=[0.5, 0.25, 0.15, 0.1]) for j in J} # Penalty due to disruptions"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "P0X0VeOzQ33q",
        "outputId": "2ef34a45-7389-4a8a-e9d7-5874d6f83590"
      },
      "source": [
        "p # Penalty to Facility (Although used particular fixed values, any probability distribution function can be used instead)"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{0: 2500, 1: 0, 2: 2500, 3: 0, 4: 10000}"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l10IjK4lQ7vW"
      },
      "source": [
        "%%capture\n",
        "mdl = Model('UFLP');"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M6aqftoDRAlf"
      },
      "source": [
        "x = mdl.addVars(J, vtype = GRB.BINARY)\n",
        "y = mdl.addVars(A, vtype = GRB.CONTINUOUS)"
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xv__xeNRRDrN"
      },
      "source": [
        "mdl.ModelSense = GRB.MINIMIZE # Minimization model\n",
        "mdl.setObjective(quicksum(f[j]*x[j] for j in J) + quicksum(h[i]*c[i,j]*y[i,j] for i,j in A) + quicksum(p[j]*x[j] for j in J)) # Cost Function"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i0Xcmak2RFvT"
      },
      "source": [
        "mdl.addConstrs(quicksum(y[i,j] for j in J) == 1 for i in I);\n",
        "mdl.addConstrs(y[i,j] <= x[j] for i,j in A);"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5VoZSschFJ0y"
      },
      "source": [
        "**Model Optimization**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-s95IGGWRHua",
        "outputId": "3d50a0ac-bda4-45c7-d2fa-9bc2c0f484fa"
      },
      "source": [
        "mdl.optimize() # Solution cost: 5180.93 (varies with changing seed value)"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Gurobi Optimizer version 9.1.2 build v9.1.2rc0 (linux64)\n",
            "Thread count: 1 physical cores, 2 logical processors, using up to 2 threads\n",
            "Optimize a model with 120 rows, 105 columns and 300 nonzeros\n",
            "Model fingerprint: 0xbe58d5d7\n",
            "Variable types: 100 continuous, 5 integer (5 binary)\n",
            "Coefficient statistics:\n",
            "  Matrix range     [1e+00, 1e+00]\n",
            "  Objective range  [3e+01, 1e+04]\n",
            "  Bounds range     [1e+00, 1e+00]\n",
            "  RHS range        [1e+00, 1e+00]\n",
            "Presolve time: 0.00s\n",
            "Presolved: 120 rows, 105 columns, 300 nonzeros\n",
            "Variable types: 100 continuous, 5 integer (5 binary)\n",
            "\n",
            "Root relaxation: objective 5.180927e+03, 27 iterations, 0.00 seconds\n",
            "\n",
            "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
            " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
            "\n",
            "*    0     0               0    5180.9265793 5180.92658  0.00%     -    0s\n",
            "\n",
            "Explored 0 nodes (27 simplex iterations) in 0.05 seconds\n",
            "Thread count was 2 (of 2 available processors)\n",
            "\n",
            "Solution count 1: 5180.93 \n",
            "\n",
            "Optimal solution found (tolerance 1.00e-04)\n",
            "Best objective 5.180926579334e+03, best bound 5.180926579334e+03, gap 0.0000%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r4Siqub_FfIa"
      },
      "source": [
        "**Customer - Facility mapping**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J84LYEPHRJf3"
      },
      "source": [
        "assignment = [a for a in A if y[a].X > 0.0] "
      ],
      "execution_count": 22,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QABZiWLIRLXm",
        "outputId": "f6903451-922b-4cce-997e-672fcfba127a"
      },
      "source": [
        "assignment # (i, j) == (Customer, Facility)"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[(0, 1),\n",
              " (1, 3),\n",
              " (2, 3),\n",
              " (3, 1),\n",
              " (4, 1),\n",
              " (5, 1),\n",
              " (6, 1),\n",
              " (7, 3),\n",
              " (8, 1),\n",
              " (9, 1),\n",
              " (10, 1),\n",
              " (11, 3),\n",
              " (12, 3),\n",
              " (13, 1),\n",
              " (14, 1),\n",
              " (15, 1),\n",
              " (16, 1),\n",
              " (17, 1),\n",
              " (18, 1),\n",
              " (19, 1)]"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FBLWjxWmFjLm"
      },
      "source": [
        "**Plotting final obtained map**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 267
        },
        "id": "QZ6tOZE5RMtW",
        "outputId": "d0b050e7-20e5-489b-9a40-9fd25a9f70f5"
      },
      "source": [
        "for i, j in assignment:\n",
        "    plt.plot([xc[i], xf[j]], [yc[i], yf[j]], c='g', zorder=0)\n",
        "plt.scatter(xc[0:], yc[0:], c='b', label = 'Customer')\n",
        "plt.scatter(xf[0:], yf[0:], c='r',marker='s', label = 'Facility')\n",
        "plt.legend()\n",
        "plt.show();"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}