model_implementation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preliminary operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5057a4be",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import main libraries\n",
    "#import folium\n",
    "import requests\n",
    "import json\n",
    "#import geopandas as geo\n",
    "#fom io import StringIO\n",
    "import io\n",
    "import pandas as pd\n",
    "from ortools.linear_solver import pywraplp\n",
    "from numpy import average, std\n",
    "from statistics import *\n",
    "import folium\n",
    "import numpy as np\n",
    "from sklearn.preprocessing import MinMaxScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "df851ec5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# degine vehicle types\n",
    "vehicle_types = [\"engine\", \"ladder\", \"rescue\", \"squad\", \"hazardous\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "de0e7204",
   "metadata": {},
   "outputs": [],
   "source": [
    "# get station capacities\n",
    "capacities = {}\n",
    "\n",
    "response2 = requests.get(\"https://gitlab.com/drvicsana/cop-proyecto-2023/-/raw/main/located_firehouses.json\")\n",
    "stations = json.loads(response2.text)\n",
    "\n",
    "for station in stations[\"features\"]:\n",
    "    station_address = station[\"properties\"][\"FacilityAddress\"]\n",
    "    capacities[station_address] = station[\"properties\"][\"capacity\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "913cbdc2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# define serviceability distances (from neighborhoods_serviceability.ipynb)\n",
    "serviceability_distances = {\n",
    "    \"engine\": 800.24,\n",
    "    \"ladder\": 800.24,\n",
    "    \"rescue\": 2675.74,\n",
    "    \"squad\": 2339.26,\n",
    "    \"hazardous\": 4537.84,\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8fef3754",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>42 South Street</th>\n",
       "      <th>49 Beekman Street</th>\n",
       "      <th>100 Duane Street</th>\n",
       "      <th>14 N. Moore Street</th>\n",
       "      <th>75 Canal Street</th>\n",
       "      <th>25 Pitt Street</th>\n",
       "      <th>222 East 2 Street</th>\n",
       "      <th>340 East 14 Street</th>\n",
       "      <th>253 Lafayette Street</th>\n",
       "      <th>42 Great Jones Street</th>\n",
       "      <th>...</th>\n",
       "      <th>256 Hylan Blvd.</th>\n",
       "      <th>278 McClean Avenue</th>\n",
       "      <th>1850 Clove Road</th>\n",
       "      <th>1592 Richmond Road</th>\n",
       "      <th>256 Nelson Ave.</th>\n",
       "      <th>345 Annadale Road</th>\n",
       "      <th>1560 Drumgoole Road West</th>\n",
       "      <th>7219 Amboy Road</th>\n",
       "      <th>1100 Rossville Ave</th>\n",
       "      <th>305 Front Street</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>42 South Street</th>\n",
       "      <td>0.00</td>\n",
       "      <td>228.56</td>\n",
       "      <td>282.07</td>\n",
       "      <td>367.00</td>\n",
       "      <td>299.82</td>\n",
       "      <td>397.01</td>\n",
       "      <td>523.64</td>\n",
       "      <td>609.91</td>\n",
       "      <td>444.76</td>\n",
       "      <td>511.11</td>\n",
       "      <td>...</td>\n",
       "      <td>1384.71</td>\n",
       "      <td>1348.97</td>\n",
       "      <td>1337.57</td>\n",
       "      <td>1553.31</td>\n",
       "      <td>2392.53</td>\n",
       "      <td>2406.78</td>\n",
       "      <td>2697.62</td>\n",
       "      <td>2833.72</td>\n",
       "      <td>2500.30</td>\n",
       "      <td>1567.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49 Beekman Street</th>\n",
       "      <td>154.94</td>\n",
       "      <td>0.00</td>\n",
       "      <td>175.70</td>\n",
       "      <td>260.63</td>\n",
       "      <td>261.52</td>\n",
       "      <td>391.57</td>\n",
       "      <td>494.09</td>\n",
       "      <td>549.25</td>\n",
       "      <td>330.31</td>\n",
       "      <td>403.98</td>\n",
       "      <td>...</td>\n",
       "      <td>1401.76</td>\n",
       "      <td>1366.02</td>\n",
       "      <td>1354.62</td>\n",
       "      <td>1570.37</td>\n",
       "      <td>2409.58</td>\n",
       "      <td>2423.84</td>\n",
       "      <td>2609.88</td>\n",
       "      <td>2719.26</td>\n",
       "      <td>2396.89</td>\n",
       "      <td>1584.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100 Duane Street</th>\n",
       "      <td>299.43</td>\n",
       "      <td>180.79</td>\n",
       "      <td>0.00</td>\n",
       "      <td>96.76</td>\n",
       "      <td>272.78</td>\n",
       "      <td>413.52</td>\n",
       "      <td>467.01</td>\n",
       "      <td>447.83</td>\n",
       "      <td>228.89</td>\n",
       "      <td>302.56</td>\n",
       "      <td>...</td>\n",
       "      <td>1411.62</td>\n",
       "      <td>1375.88</td>\n",
       "      <td>1364.48</td>\n",
       "      <td>1580.22</td>\n",
       "      <td>2419.44</td>\n",
       "      <td>2341.17</td>\n",
       "      <td>2469.12</td>\n",
       "      <td>2578.51</td>\n",
       "      <td>2256.14</td>\n",
       "      <td>1593.91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14 N. Moore Street</th>\n",
       "      <td>408.12</td>\n",
       "      <td>289.48</td>\n",
       "      <td>174.89</td>\n",
       "      <td>0.00</td>\n",
       "      <td>339.69</td>\n",
       "      <td>444.26</td>\n",
       "      <td>450.79</td>\n",
       "      <td>431.61</td>\n",
       "      <td>212.68</td>\n",
       "      <td>286.35</td>\n",
       "      <td>...</td>\n",
       "      <td>1520.31</td>\n",
       "      <td>1484.57</td>\n",
       "      <td>1473.17</td>\n",
       "      <td>1688.91</td>\n",
       "      <td>2405.59</td>\n",
       "      <td>2246.56</td>\n",
       "      <td>2374.51</td>\n",
       "      <td>2483.90</td>\n",
       "      <td>2161.52</td>\n",
       "      <td>1702.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75 Canal Street</th>\n",
       "      <td>296.75</td>\n",
       "      <td>295.70</td>\n",
       "      <td>275.65</td>\n",
       "      <td>283.51</td>\n",
       "      <td>0.00</td>\n",
       "      <td>195.55</td>\n",
       "      <td>260.18</td>\n",
       "      <td>346.45</td>\n",
       "      <td>260.93</td>\n",
       "      <td>293.16</td>\n",
       "      <td>...</td>\n",
       "      <td>1563.49</td>\n",
       "      <td>1522.61</td>\n",
       "      <td>1516.35</td>\n",
       "      <td>1732.10</td>\n",
       "      <td>2571.31</td>\n",
       "      <td>2470.82</td>\n",
       "      <td>2598.77</td>\n",
       "      <td>2708.16</td>\n",
       "      <td>2385.79</td>\n",
       "      <td>1745.79</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 219 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                    42 South Street  49 Beekman Street  100 Duane Street  \\\n",
       "42 South Street                0.00             228.56            282.07   \n",
       "49 Beekman Street            154.94               0.00            175.70   \n",
       "100 Duane Street             299.43             180.79              0.00   \n",
       "14 N. Moore Street           408.12             289.48            174.89   \n",
       "75 Canal Street              296.75             295.70            275.65   \n",
       "\n",
       "                    14 N. Moore Street  75 Canal Street  25 Pitt Street  \\\n",
       "42 South Street                 367.00           299.82          397.01   \n",
       "49 Beekman Street               260.63           261.52          391.57   \n",
       "100 Duane Street                 96.76           272.78          413.52   \n",
       "14 N. Moore Street                0.00           339.69          444.26   \n",
       "75 Canal Street                 283.51             0.00          195.55   \n",
       "\n",
       "                    222 East 2 Street  340 East 14 Street  \\\n",
       "42 South Street                523.64              609.91   \n",
       "49 Beekman Street              494.09              549.25   \n",
       "100 Duane Street               467.01              447.83   \n",
       "14 N. Moore Street             450.79              431.61   \n",
       "75 Canal Street                260.18              346.45   \n",
       "\n",
       "                    253 Lafayette Street  42 Great Jones Street  ...  \\\n",
       "42 South Street                   444.76                 511.11  ...   \n",
       "49 Beekman Street                 330.31                 403.98  ...   \n",
       "100 Duane Street                  228.89                 302.56  ...   \n",
       "14 N. Moore Street                212.68                 286.35  ...   \n",
       "75 Canal Street                   260.93                 293.16  ...   \n",
       "\n",
       "                    256 Hylan Blvd.  278 McClean Avenue  1850 Clove Road  \\\n",
       "42 South Street             1384.71             1348.97          1337.57   \n",
       "49 Beekman Street           1401.76             1366.02          1354.62   \n",
       "100 Duane Street            1411.62             1375.88          1364.48   \n",
       "14 N. Moore Street          1520.31             1484.57          1473.17   \n",
       "75 Canal Street             1563.49             1522.61          1516.35   \n",
       "\n",
       "                    1592 Richmond Road  256 Nelson Ave.  345 Annadale Road  \\\n",
       "42 South Street                1553.31          2392.53            2406.78   \n",
       "49 Beekman Street              1570.37          2409.58            2423.84   \n",
       "100 Duane Street               1580.22          2419.44            2341.17   \n",
       "14 N. Moore Street             1688.91          2405.59            2246.56   \n",
       "75 Canal Street                1732.10          2571.31            2470.82   \n",
       "\n",
       "                    1560 Drumgoole Road West  7219 Amboy Road  \\\n",
       "42 South Street                      2697.62          2833.72   \n",
       "49 Beekman Street                    2609.88          2719.26   \n",
       "100 Duane Street                     2469.12          2578.51   \n",
       "14 N. Moore Street                   2374.51          2483.90   \n",
       "75 Canal Street                      2598.77          2708.16   \n",
       "\n",
       "                    1100 Rossville Ave  305 Front Street  \n",
       "42 South Street                2500.30           1567.00  \n",
       "49 Beekman Street              2396.89           1584.06  \n",
       "100 Duane Street               2256.14           1593.91  \n",
       "14 N. Moore Street             2161.52           1702.60  \n",
       "75 Canal Street                2385.79           1745.79  \n",
       "\n",
       "[5 rows x 219 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get distances between stations\n",
    "response = requests.get(\"https://gitlab.com/drvicsana/cop-proyecto-2023/-/raw/main/project_data/distancias_estaciones.json\")\n",
    "distances_stations_db = json.loads(response.text)\n",
    "\n",
    "# convert json to dataframe\n",
    "df_distances_stations = pd.DataFrame(distances_stations_db)\n",
    "# solve an error in the columns order\n",
    "df_distances_stations =  pd.concat([df_distances_stations.iloc[-1:], df_distances_stations.iloc[:-1]], axis=0)\n",
    "df_distances_stations.fillna(0, inplace=True)\n",
    "df_distances_stations.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "facb8520",
   "metadata": {},
   "outputs": [],
   "source": [
    "# get ntas-station distances dataset\n",
    "distance = pd.read_csv(\"dataset/distance_stations_neighborhoods.csv\", index_col=0)\n",
    "# get standardized neighborhoods info dataset\n",
    "neighborhood = pd.read_csv(\"dataset/neighborhoods_info_standardized.csv\")\n",
    "# define a serviceability dictionary\n",
    "serviceability = {}\n",
    "\n",
    "# get the serviceability table for each vehicle type\n",
    "for vehicle_type in vehicle_types:\n",
    "    serviceability[vehicle_type] = pd.read_csv(\"dataset/serviceability/\" + vehicle_type +\"_ntas_serviceability.csv\", index_col=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6062f0b7",
   "metadata": {},
   "source": [
    "## Creating an instance of the Solver class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "745c774f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# define the solver type\n",
    "solver = pywraplp.Solver.CreateSolver(\"SCIP\")\n",
    "# define a time limit for the solver (30 min)\n",
    "solver.set_time_limit(60*1000*30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- type of vehicles$: i=1\\dots 5$\n",
    "\n",
    "- stations: $j=1\\dots 219$\n",
    "\n",
    "- shifts: $k=1\\dots 2$\n",
    "\n",
    "- neighborhoods: $n=1 \\dots 195$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "18d53c2d",
   "metadata": {},
   "outputs": [],
   "source": [
    "response = requests.get(\"https://gitlab.com/drvicsana/cop-proyecto-2023/-/raw/main/project_data/incidentes2019.json\")\n",
    "incidents = json.loads(response.text)\n",
    "\n",
    "I = [\"engine\", \"ladder\", \"rescue\", \"squad\", \"hazardous\"]\n",
    "N = list(neighborhood.nta)\n",
    "J = list(distance.columns)\n",
    "K = [1,2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8a56bbc",
   "metadata": {},
   "source": [
    "## Creating decision variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$X_{i, j, k}: $  number of vehicles of type ${i}$ deployed in station ${j}$ during shift ${k}$\n",
    "\n",
    "$X_{i, j, k} \\geq 0$, $X_{i, j, k} \\in \\mathbb{Z}$\n",
    "\n",
    "$ i \\in I, j \\in J, k \\in K$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0038e46e",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = {}\n",
    "for i in I:\n",
    "    for j in J:\n",
    "        for k in K:\n",
    "            v = solver.IntVar(0, solver.infinity(), \"Number of vehicles of type \" + str(i) + \" deployed at station \"+ str(j)+ \" during shift \" + str(k))\n",
    "            X[(i,j,k)] = v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$Y_{i, a, b}:$  number of vehicles of type ${i}$ moved from station ${a}$ to station ${b}$ at shift change\n",
    "\n",
    "$Y_{i, a, b} \\geq 0$, $Y_{i, a, b} \\in \\mathbb{Z}$\n",
    "\n",
    "$ i \\in I, a \\in J, b \\in J$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ae40d52b",
   "metadata": {},
   "outputs": [],
   "source": [
    "Y = {}\n",
    "for i in I:\n",
    "    for a in J:\n",
    "        for b in J:\n",
    "            v = solver.IntVar(0, solver.infinity(), \"Number of vehicles of type \" + str(i) + \" moved from station \"+ str(a)+ \" to station \" + str(b))\n",
    "            Y[(i,a,b)] = v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$T_{i, j, k}: 1$ if a vehicle of type ${i}$ is deployed in station ${j}$ during shift ${k}$, $0$ otherwise\n",
    "\n",
    "$T_{i, j, k} \\geq 0$, $T_{i, j, k} \\in  \\{0,1\\}$\n",
    "\n",
    "$ i \\in I, j \\in J, k \\in K$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "13f46831",
   "metadata": {},
   "outputs": [],
   "source": [
    "T = {}\n",
    "for i in I:\n",
    "    for j in J:\n",
    "        for k in K:\n",
    "            v = solver.BoolVar(\"if a vehicle of type\" + str(i)  + \" is deployed in station \" + str(j) + \" during shift \" + str(k))\n",
    "            T[(i,j,k)] = v"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e32b03a",
   "metadata": {},
   "source": [
    "$Q_{j, k}: 1$ if there are more than two vehicles in station $j$ during shift $k$, $0$ otherwise\n",
    "\n",
    "$Q_{j, k} \\geq 0$, $Q_{j, k} \\in \\{0,1\\}$\n",
    "\n",
    "$ j \\in J, k \\in K$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6a5afa46",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q = {}\n",
    "for j in J:\n",
    "    for k in K:\n",
    "        v = solver.BoolVar(\"if there are two or more vehicles in station \" + str(j) + \" during shift \" + str(k))\n",
    "        Q[(j,k)] = v"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ece64324",
   "metadata": {},
   "source": [
    "## Creating constraints"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Linking constraints"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.1. Linking Variable T\n",
    "\n",
    "$T_{i, j, k} \\leq X_{i, j, k} \\leq c_{j}T_{i, j, k}, \\forall i \\in I, j \\in J, k \\in K$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9ec8b9be",
   "metadata": {},
   "outputs": [],
   "source": [
    "T_lower_linking_constraints = []\n",
    "T_upper_linking_constraints = []\n",
    "\n",
    "for i in I:\n",
    "    for j in J:\n",
    "        capacity = capacities[j]\n",
    "        for k in K:\n",
    "            v_T = T[(i, j, k)]\n",
    "            v_X = X[(i, j, k)]\n",
    "\n",
    "            c_lower = solver.Constraint(-solver.infinity(), 0)\n",
    "\n",
    "            c_lower.SetCoefficient(v_T, 1)\n",
    "            c_lower.SetCoefficient(v_X, -1)\n",
    "\n",
    "            T_lower_linking_constraints.append(c_lower)\n",
    "\n",
    "            c_upper = solver.Constraint(-solver.infinity(), 0)\n",
    "\n",
    "            c_upper.SetCoefficient(v_T, -capacity)\n",
    "            c_upper.SetCoefficient(v_X, 1)\n",
    "\n",
    "            T_upper_linking_constraints.append(c_upper)\n",
    "\n",
    "assert len(T_lower_linking_constraints) == 2190, \"The number of constraints (\" + str(len(T_lower_linking_constraints)) + \") is NOT correct\"\n",
    "assert len(T_upper_linking_constraints) == 2190, \"The number of constraints (\" + str(len(T_upper_linking_constraints)) + \") is NOT correct\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2. Linking Variable Q\n",
    "\n",
    "$\\sum_{i \\in I} X_{i, j, k} - 1 \\leq c_{j}Q_{j, k}, \\forall j \\in J, k \\in K$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4a05af72",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q_linking_constraints = []\n",
    "\n",
    "for j in J:\n",
    "    capacity = capacities[j]\n",
    "    for k in K:\n",
    "        c = solver.Constraint(-solver.infinity(), 1)\n",
    "        v_Q = Q[(j, k)]\n",
    "        for i in I:\n",
    "            v_X = X[(i, j, k)]\n",
    "\n",
    "            c.SetCoefficient(v_X, 1)\n",
    "            \n",
    "        c.SetCoefficient(v_Q, -capacity)\n",
    "        \n",
    "        Q_linking_constraints.append(c)\n",
    "\n",
    "assert len(Q_linking_constraints) == 438, \"The number of constraints (\" + str(len(Q_linking_constraints)) + \") is NOT correct\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e2c95a6",
   "metadata": {},
   "source": [
    "### 2. Station capacity\n",
    "\n",
    "$\\sum_{i \\in I}^{}X_{i, j, k} \\leq c_{j}, \\forall j \\in J, k \\in K$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "02e4c902",
   "metadata": {},
   "outputs": [],
   "source": [
    "station_capacity_constraints = []\n",
    "\n",
    "for j in J:\n",
    "    capacity = capacities[j]\n",
    "    for k in K:\n",
    "        c = solver.Constraint(-solver.infinity(), capacity)\n",
    "    \n",
    "        for i in I:\n",
    "            v = X[(i, j, k)]\n",
    "            c.SetCoefficient(v, 1)\n",
    "\n",
    "        station_capacity_constraints.append(c)\n",
    "\n",
    "assert len(station_capacity_constraints) == 438, \"The number of constraints (\" + str(len(station_capacity_constraints)) + \") is NOT correct\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "443f9a80",
   "metadata": {},
   "source": [
    "### 3. Vehicles availability\n",
    "\n",
    "$\\sum_{j \\in J}^{}X_{i, j, k} = v_{i}, \\forall i \\in I, k \\in K$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "4ff65ae3",
   "metadata": {},
   "outputs": [],
   "source": [
    "availabilities = {'engine': 197, 'ladder': 143, 'hazardous': 1, 'squad': 8, 'rescue':5}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "6bef8548",
   "metadata": {},
   "outputs": [],
   "source": [
    "vehicles_availability_constraints = []\n",
    "\n",
    "for i in I:\n",
    "    availability = availabilities[i]\n",
    "\n",
    "    for k in K:\n",
    "        c = solver.Constraint(availability, availability)\n",
    "\n",
    "        for j in J:\n",
    "            v = X[(i, j, k)]\n",
    "            c.SetCoefficient(v, 1)\n",
    "            \n",
    "        vehicles_availability_constraints.append(c)\n",
    "\n",
    "assert len(vehicles_availability_constraints) == 10, \"The number of constraints (\" + str(len(vehicles_availability_constraints)) + \") is NOT correct\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5e49ab1",
   "metadata": {},
   "source": [
    "### 4. At least one vehicle\n",
    "\n",
    "$\\sum_{i \\in I}^{}X_{i, j, k} \\geq 1, \\forall j \\in J, k \\in K$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e7e2c65e",
   "metadata": {},
   "outputs": [],
   "source": [
    "atleast_one_vehicle_constraints = []\n",
    "\n",
    "for j in J:\n",
    "    for k in K:\n",
    "        c = solver.Constraint(1, solver.infinity())\n",
    "    \n",
    "        for i in I:\n",
    "            v = X[(i, j, k)]\n",
    "            c.SetCoefficient(v, 1)\n",
    "        atleast_one_vehicle_constraints.append(c)\n",
    "\n",
    "assert len(atleast_one_vehicle_constraints) == 438, \"The number of constraints (\" + str(len(atleast_one_vehicle_constraints)) + \") is NOT correct\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "042a1185",
   "metadata": {},
   "source": [
    "### 5. Scarce resources coverage\n",
    "\n",
    "$\\sum_{j \\in J}^{}s_{i, j, n}X_{i, j, k} \\geq  1, \\forall n \\in N, k \\in K, i \\in \\left \\{ 3, 4 \\right \\}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "68837e1a",
   "metadata": {},
   "outputs": [],
   "source": [
    "scarce_resources_availability = []\n",
    "\n",
    "for k in K:\n",
    "    for n in N:\n",
    "        for i in [\"rescue\", \"squad\"]:\n",
    "            c = solver.Constraint(1, solver.infinity())\n",
    "            \n",
    "            for j in J:\n",
    "                s = 1 if serviceability[i].loc[n, j] == True else 0\n",
    "                v = X[(i, j, k)]\n",
    "                c.SetCoefficient(v, s)\n",
    "\n",
    "            scarce_resources_availability.append(c)\n",
    "\n",
    "assert len(scarce_resources_availability) == 780, \"The number of constraints (\" + str(len(scarce_resources_availability)) + \") is NOT correct\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "060f17e9",
   "metadata": {},
   "source": [
    "### 6. Area resources concentration\n",
    "\n",
    "$\\theta = \\sum_{j \\in J}^{}s_{i, j, n}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 6.1 Area resource concentration for Engine and Ladder\n",
    "\n",
    "$\\frac{\\theta}{2}\\leq \\sum_{j \\in J}^{}s_{i, j, n}X_{i, j, k} \\leq \\theta, \\forall n \\in N, k \\in K, i \\in \\left \\{ 1, 2 \\right \\}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d022f263",
   "metadata": {},
   "outputs": [],
   "source": [
    "area_resources_concentration_constraints = []\n",
    "\n",
    "for k in K:\n",
    "    for n in N:\n",
    "        for i in [\"engine\", \"ladder\"]:\n",
    "            s_max = 0\n",
    "            \n",
    "            for j in J:\n",
    "                s_max += 1 if serviceability[i].loc[n, j] == True else 0\n",
    "            \n",
    "            c = solver.Constraint(s_max / 2, s_max)\n",
    "            \n",
    "            for j in J:\n",
    "                s = 1 if serviceability[i].loc[n, j] == True else 0\n",
    "                v = X[(i, j, k)]\n",
    "                c.SetCoefficient(v, s)\n",
    "\n",
    "            area_resources_concentration_constraints.append(c)\n",
    "        \n",
    "assert len(area_resources_concentration_constraints) == 780, \"The number of constraints (\" + str(len(area_resources_concentration_constraints)) + \") is NOT correct\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 6.2 Area resource concentration for Rescue and Squad\n",
    "\n",
    "$r_{a, b} \\geq \\frac{l_{i}}{2} \\left (T_{i, a, k} + T_{i, b, k} - 1 \\right ), \\forall k \\in K, i \\in \\left \\{ 3, 4 \\right \\}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "f2dccbb2",
   "metadata": {},
   "outputs": [],
   "source": [
    "scarce_resources_concentration = []\n",
    "\n",
    "for k in K:\n",
    "    for a in J:\n",
    "        for b in J:\n",
    "            route_distance = df_distances_stations.loc[a, b]\n",
    "            for i in [\"rescue\", \"squad\"]:\n",
    "                type_distance_limit = serviceability_distances[i] / 2\n",
    "                \n",
    "                c = solver.Constraint(-solver.infinity(), route_distance + type_distance_limit)\n",
    "            \n",
    "                T_a = T[(i, a, k)]\n",
    "                T_b = T[(i, b, k)]\n",
    "\n",
    "                c.SetCoefficient(T_a, type_distance_limit)\n",
    "                c.SetCoefficient(T_b, type_distance_limit)\n",
    "\n",
    "                scarce_resources_concentration.append(c)\n",
    "\n",
    "assert len(scarce_resources_concentration) == 191844, \"The number of constraints (\" + str(len(scarce_resources_concentration)) + \") is NOT correct\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e0edf37",
   "metadata": {},
   "source": [
    "### 7. Station resources concentration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 7.1 Station resources concentration for Engine and Ladder\n",
    "\n",
    "$X_{i, j, k} \\leq  2, \\forall j \\in J, k \\in K, i \\in \\left \\{ 1, 2 \\right \\}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "32f8dc28",
   "metadata": {},
   "outputs": [],
   "source": [
    "station_resources_concentration_constraints = []\n",
    "\n",
    "for k in K:\n",
    "    for j in J:\n",
    "        for i in [\"engine\", \"ladder\"]:\n",
    "            c = solver.Constraint(-solver.infinity(), 2)\n",
    "            v = X[(i, j, k)]\n",
    "            c.SetCoefficient(v, 1)\n",
    "            station_resources_concentration_constraints.append(c)\n",
    "                    \n",
    "assert len(station_resources_concentration_constraints) == 876, \"The number of constraints (\" + str(len(station_resources_concentration_constraints)) + \") is NOT correct\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 7.2 Station resources concentration for Rescue and Squad\n",
    "\n",
    "$X_{i, j, k} \\leq  1, \\forall j \\in J, k \\in K, i \\in \\left \\{ 3, 4 \\right \\}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a61f93c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "station_resources_concentration_constraints = []\n",
    "\n",
    "for k in K:\n",
    "    for j in J:\n",
    "        for i in [\"rescue\", \"squad\"]:\n",
    "            c = solver.Constraint(-solver.infinity(), 1)\n",
    "            v = X[(i, j, k)]\n",
    "            c.SetCoefficient(v, 1)\n",
    "            station_resources_concentration_constraints.append(c)\n",
    "                    \n",
    "assert len(station_resources_concentration_constraints) == 876, \"The number of constraints (\" + str(len(station_resources_concentration_constraints)) + \") is NOT correct\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73831d9e",
   "metadata": {},
   "source": [
    "### 8. At least two vehicle types\n",
    "\n",
    "$\\sum_{i \\in I} T_{i, j, k} \\geq 2Q_{j, k}, \\forall j \\in J, k \\in K$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "8ab84ae0",
   "metadata": {},
   "outputs": [],
   "source": [
    "atleast_two_types_of_vehicle_constraints = []\n",
    "\n",
    "for j in J:\n",
    "    capacity = capacities[j]\n",
    "    for k in K:\n",
    "        c = solver.Constraint(0, solver.infinity())\n",
    "        v_Q = Q[(j, k)]\n",
    "        for i in I:\n",
    "            v_T = T[(i, j, k)]\n",
    "\n",
    "            c.SetCoefficient(v_T, 1)\n",
    "        c.SetCoefficient(v_Q, -2)\n",
    "        atleast_two_types_of_vehicle_constraints.append(c)\n",
    "\n",
    "assert len(atleast_two_types_of_vehicle_constraints) == 438, \"The number of constraints (\" + str(len(atleast_two_types_of_vehicle_constraints)) + \") is NOT correct\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cb2f656",
   "metadata": {},
   "source": [
    "### 9. Vehicles transfer\n",
    "\n",
    "$X_{i, a, 1} - X_{i, a, 2} = \\sum_{j \\in J} \\left ( Y_{i, a, j} - Y_{i, j, a} \\right ), \\forall i \\in I, a \\in J$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "36f7dbcf",
   "metadata": {},
   "outputs": [],
   "source": [
    "vehicles_transfer_constraints = []\n",
    "\n",
    "for i in I:\n",
    "    for a in J:\n",
    "        c = solver.Constraint(0, 0)\n",
    "\n",
    "        for j in J:\n",
    "            Y_aj = Y[(i, a, j)]\n",
    "            Y_ja = Y[(i, j, a)]\n",
    "\n",
    "            c.SetCoefficient(Y_aj, 1)\n",
    "            c.SetCoefficient(Y_ja, -1)\n",
    "        \n",
    "        X_a1 = X[(i, a, 1)]\n",
    "        X_a2 = X[(i, a, 2)]\n",
    "\n",
    "        c.SetCoefficient(X_a1, -1)\n",
    "        c.SetCoefficient(X_a2, 1)\n",
    "\n",
    "        vehicles_transfer_constraints.append(c)\n",
    "\n",
    "assert len(vehicles_transfer_constraints) == 1095, \"The number of constraints (\" + str(len(vehicles_transfer_constraints)) + \") is NOT correct\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1013c380",
   "metadata": {},
   "source": [
    "### 10. Maximum transfer distance\n",
    "\n",
    "$r_{a, b}Y_{i, a, b} \\leq l_{i} Y_{i, a, b}, \\forall i \\in \\left \\{ 1, 2, 3, 4 \\right \\}, a \\in J, b \\in J$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "a6e1e130",
   "metadata": {},
   "outputs": [],
   "source": [
    "max_transfer_distance_constraints = []\n",
    "a_counter = -1\n",
    "\n",
    "for a in J:\n",
    "    for b in J:\n",
    "        for i in [\"engine\", \"ladder\", \"rescue\", \"squad\"]:\n",
    "        \n",
    "            route_distance = df_distances_stations.loc[a, b]\n",
    "\n",
    "            #type_distance_limit = serviceability_distances[i] if i in [\"engine\", \"ladder\"] else (serviceability_distances[i] / 2)\n",
    "            type_distance_limit = serviceability_distances[i]\n",
    "\n",
    "            c = solver.Constraint(-solver.infinity(), 0)\n",
    "            \n",
    "            v = Y[(i, a, b)]\n",
    "\n",
    "            c.SetCoefficient(v, route_distance - type_distance_limit)\n",
    "\n",
    "            max_transfer_distance_constraints.append(c)\n",
    "\n",
    "assert len(max_transfer_distance_constraints) == 191844, \"The number of constraints (\" + str(len(max_transfer_distance_constraints)) + \") is NOT correct\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2a7309b",
   "metadata": {},
   "source": [
    "## Objective Function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c905e77a",
   "metadata": {},
   "source": [
    "$maxZ: \\sum_{k \\in K}\\sum_{i \\in I}\\sum_{j \\in J}X_{j, i, k} \\left ( \\sum_{n \\in N}s_{i, j, n} importance_{j, i, k, n} \\right )$\n",
    "\n",
    "$importance_{j, i, k, n} = w_{p} p^{\\varsigma}_{n} + w_{e} e^{\\varsigma}_{i, k, n} - w_{d} d^{\\varsigma}_{j, n} - v^{\\varsigma}_{i}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "6d68b229",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "    .dataframe tbody tr th {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>42 South Street</th>\n",
       "      <th>49 Beekman Street</th>\n",
       "      <th>100 Duane Street</th>\n",
       "      <th>14 N. Moore Street</th>\n",
       "      <th>75 Canal Street</th>\n",
       "      <th>25 Pitt Street</th>\n",
       "      <th>222 East 2 Street</th>\n",
       "      <th>340 East 14 Street</th>\n",
       "      <th>253 Lafayette Street</th>\n",
       "      <th>42 Great Jones Street</th>\n",
       "      <th>...</th>\n",
       "      <th>256 Hylan Blvd.</th>\n",
       "      <th>278 McClean Avenue</th>\n",
       "      <th>1850 Clove Road</th>\n",
       "      <th>1592 Richmond Road</th>\n",
       "      <th>256 Nelson Ave.</th>\n",
       "      <th>345 Annadale Road</th>\n",
       "      <th>1560 Drumgoole Road West</th>\n",
       "      <th>7219 Amboy Road</th>\n",
       "      <th>1100 Rossville Ave</th>\n",
       "      <th>305 Front Street</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>QN08</th>\n",
       "      <td>0.712966</td>\n",
       "      <td>0.694468</td>\n",
       "      <td>0.704228</td>\n",
       "      <td>0.707264</td>\n",
       "      <td>0.681702</td>\n",
       "      <td>0.661229</td>\n",
       "      <td>0.645215</td>\n",
       "      <td>0.637852</td>\n",
       "      <td>0.689578</td>\n",
       "      <td>0.678506</td>\n",
       "      <td>...</td>\n",
       "      <td>0.646414</td>\n",
       "      <td>0.649381</td>\n",
       "      <td>0.645223</td>\n",
       "      <td>0.654903</td>\n",
       "      <td>0.810685</td>\n",
       "      <td>0.807546</td>\n",
       "      <td>0.847927</td>\n",
       "      <td>0.872241</td>\n",
       "      <td>0.840141</td>\n",
       "      <td>0.663432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BX28</th>\n",
       "      <td>0.631054</td>\n",
       "      <td>0.599836</td>\n",
       "      <td>0.643624</td>\n",
       "      <td>0.688625</td>\n",
       "      <td>0.648207</td>\n",
       "      <td>0.612963</td>\n",
       "      <td>0.569798</td>\n",
       "      <td>0.538405</td>\n",
       "      <td>0.619114</td>\n",
       "      <td>0.599397</td>\n",
       "      <td>...</td>\n",
       "      <td>0.855937</td>\n",
       "      <td>0.859395</td>\n",
       "      <td>0.835534</td>\n",
       "      <td>0.841614</td>\n",
       "      <td>0.847833</td>\n",
       "      <td>0.758353</td>\n",
       "      <td>0.727975</td>\n",
       "      <td>0.709328</td>\n",
       "      <td>0.711457</td>\n",
       "      <td>0.862873</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>QN55</th>\n",
       "      <td>0.623278</td>\n",
       "      <td>0.563582</td>\n",
       "      <td>0.599072</td>\n",
       "      <td>0.618132</td>\n",
       "      <td>0.585069</td>\n",
       "      <td>0.568148</td>\n",
       "      <td>0.549079</td>\n",
       "      <td>0.547624</td>\n",
       "      <td>0.595334</td>\n",
       "      <td>0.585267</td>\n",
       "      <td>...</td>\n",
       "      <td>0.548713</td>\n",
       "      <td>0.554022</td>\n",
       "      <td>0.547603</td>\n",
       "      <td>0.559543</td>\n",
       "      <td>0.728941</td>\n",
       "      <td>0.724448</td>\n",
       "      <td>0.769168</td>\n",
       "      <td>0.788933</td>\n",
       "      <td>0.757351</td>\n",
       "      <td>0.570430</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BK50</th>\n",
       "      <td>0.501529</td>\n",
       "      <td>0.493496</td>\n",
       "      <td>0.528346</td>\n",
       "      <td>0.550370</td>\n",
       "      <td>0.547323</td>\n",
       "      <td>0.531786</td>\n",
       "      <td>0.511528</td>\n",
       "      <td>0.560687</td>\n",
       "      <td>0.558523</td>\n",
       "      <td>0.577703</td>\n",
       "      <td>...</td>\n",
       "      <td>0.436172</td>\n",
       "      <td>0.444186</td>\n",
       "      <td>0.435160</td>\n",
       "      <td>0.449707</td>\n",
       "      <td>0.634785</td>\n",
       "      <td>0.628735</td>\n",
       "      <td>0.678453</td>\n",
       "      <td>0.692978</td>\n",
       "      <td>0.661992</td>\n",
       "      <td>0.463308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BX41</th>\n",
       "      <td>0.588020</td>\n",
       "      <td>0.555329</td>\n",
       "      <td>0.600535</td>\n",
       "      <td>0.645981</td>\n",
       "      <td>0.601837</td>\n",
       "      <td>0.568300</td>\n",
       "      <td>0.523666</td>\n",
       "      <td>0.494979</td>\n",
       "      <td>0.573894</td>\n",
       "      <td>0.554524</td>\n",
       "      <td>...</td>\n",
       "      <td>0.820951</td>\n",
       "      <td>0.825249</td>\n",
       "      <td>0.789806</td>\n",
       "      <td>0.796946</td>\n",
       "      <td>0.809545</td>\n",
       "      <td>0.719431</td>\n",
       "      <td>0.691083</td>\n",
       "      <td>0.670305</td>\n",
       "      <td>0.672679</td>\n",
       "      <td>0.821289</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 219 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      42 South Street  49 Beekman Street  100 Duane Street  \\\n",
       "QN08         0.712966           0.694468          0.704228   \n",
       "BX28         0.631054           0.599836          0.643624   \n",
       "QN55         0.623278           0.563582          0.599072   \n",
       "BK50         0.501529           0.493496          0.528346   \n",
       "BX41         0.588020           0.555329          0.600535   \n",
       "\n",
       "      14 N. Moore Street  75 Canal Street  25 Pitt Street  222 East 2 Street  \\\n",
       "QN08            0.707264         0.681702        0.661229           0.645215   \n",
       "BX28            0.688625         0.648207        0.612963           0.569798   \n",
       "QN55            0.618132         0.585069        0.568148           0.549079   \n",
       "BK50            0.550370         0.547323        0.531786           0.511528   \n",
       "BX41            0.645981         0.601837        0.568300           0.523666   \n",
       "\n",
       "      340 East 14 Street  253 Lafayette Street  42 Great Jones Street  ...  \\\n",
       "QN08            0.637852              0.689578               0.678506  ...   \n",
       "BX28            0.538405              0.619114               0.599397  ...   \n",
       "QN55            0.547624              0.595334               0.585267  ...   \n",
       "BK50            0.560687              0.558523               0.577703  ...   \n",
       "BX41            0.494979              0.573894               0.554524  ...   \n",
       "\n",
       "      256 Hylan Blvd.  278 McClean Avenue  1850 Clove Road  \\\n",
       "QN08         0.646414            0.649381         0.645223   \n",
       "BX28         0.855937            0.859395         0.835534   \n",
       "QN55         0.548713            0.554022         0.547603   \n",
       "BK50         0.436172            0.444186         0.435160   \n",
       "BX41         0.820951            0.825249         0.789806   \n",
       "\n",
       "      1592 Richmond Road  256 Nelson Ave.  345 Annadale Road  \\\n",
       "QN08            0.654903         0.810685           0.807546   \n",
       "BX28            0.841614         0.847833           0.758353   \n",
       "QN55            0.559543         0.728941           0.724448   \n",
       "BK50            0.449707         0.634785           0.628735   \n",
       "BX41            0.796946         0.809545           0.719431   \n",
       "\n",
       "      1560 Drumgoole Road West  7219 Amboy Road  1100 Rossville Ave  \\\n",
       "QN08                  0.847927         0.872241            0.840141   \n",
       "BX28                  0.727975         0.709328            0.711457   \n",
       "QN55                  0.769168         0.788933            0.757351   \n",
       "BK50                  0.678453         0.692978            0.661992   \n",
       "BX41                  0.691083         0.670305            0.672679   \n",
       "\n",
       "      305 Front Street  \n",
       "QN08          0.663432  \n",
       "BX28          0.862873  \n",
       "QN55          0.570430  \n",
       "BK50          0.463308  \n",
       "BX41          0.821289  \n",
       "\n",
       "[5 rows x 219 columns]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MM_scaler = MinMaxScaler()\n",
    "distance_scaled = MM_scaler.fit_transform(distance)\n",
    "df_distance_scaled = distance.copy()\n",
    "df_distance_scaled[:] = distance_scaled\n",
    "df_distance_scaled.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "1075d2d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        ],\n",
       "       [0.7244898 ],\n",
       "       [0.        ],\n",
       "       [0.03571429],\n",
       "       [0.02040816]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "availabilities_list = np.array(list(availabilities.values())).reshape(-1, 1)\n",
    "vehicle_availabilities_scaled = MM_scaler.fit_transform(availabilities_list)\n",
    "vehicle_availabilities_scaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "feaa4ce6",
   "metadata": {},
   "outputs": [],
   "source": [
    "availabilities_scaled = {'engine': 1.0, 'ladder': 0.7244898, 'hazardous': 0.0, 'squad': 0.03571429, 'rescue':0.02040816}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "c49a94ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "def set_objective_function(wp, we, wd):\n",
    "    objective = solver.Objective()\n",
    "    objective.SetMaximization()\n",
    "\n",
    "\n",
    "    for k in K:\n",
    "        shift_str = 'first' if k == 1 else 'second'\n",
    "        for i in I:\n",
    "            for j in J:\n",
    "                v = X[(i, j, k)]\n",
    "                overall_importance = 0\n",
    "                \n",
    "                for n in N:\n",
    "                    #computing the coefficient\n",
    "                    area_importance = 0\n",
    "\n",
    "                    s = 1 if serviceability[i].loc[n][j] else 0\n",
    "\n",
    "                    if s == 1:  \n",
    "                        current_n = neighborhood[neighborhood['nta'] == n]\n",
    "                        column_name = f\"{i}_needed_{shift_str}_shift\"\n",
    "\n",
    "                        p = current_n['population_density'].values[0]\n",
    "                        e = current_n[column_name].values[0]\n",
    "                        d = df_distance_scaled.loc[n][j]\n",
    "                        q = availabilities_scaled[i]\n",
    "                        \n",
    "                        importance = (wp * p) + (we * e) - (wd * d) - q\n",
    "                        area_importance += importance\n",
    "\n",
    "                    overall_importance += area_importance\n",
    "                objective.SetCoefficient(v, overall_importance)\n",
    "    \n",
    "    return objective"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "f68a5c48",
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_problem(wp, we, wd):\n",
    "    deployments_first_shift = pd.DataFrame(0, index=I, columns=J)\n",
    "    deployments_second_shift = pd.DataFrame(0, index=I, columns=J)\n",
    "\n",
    "    objective = set_objective_function(wp, we, wd)\n",
    "    result = solver.Solve()\n",
    "\n",
    "    if result == solver.ABNORMAL :\n",
    "        print(\"Execution finished by an error\")\n",
    "        \n",
    "    elif result == solver.FEASIBLE :\n",
    "        print(\"In the specified time limit the solver has found a feasible solution\")\n",
    "        for k in K:\n",
    "            for i in I:\n",
    "                for j in J:\n",
    "                    v = X[(i,j, k)]\n",
    "                    if v.SolutionValue()>0:\n",
    "                        print(v, v.solution_value())\n",
    "        print(\"The value for the objective function is\", objective.Value())\n",
    "            \n",
    "    elif result == solver.INFEASIBLE :\n",
    "        print(\"There is no feasible solution for the problem\")\n",
    "            \n",
    "    elif result == solver.NOT_SOLVED :\n",
    "        print(\"In the specified time limit the solver has not found any feasible solution\")\n",
    "            \n",
    "    elif result == solver.OPTIMAL :\n",
    "        print(\"In the specified time limit the solver has found a feasible solution\")\n",
    "        for k in K:\n",
    "            for i in I:\n",
    "                for j in J:\n",
    "                    v = X[(i,j,k)]\n",
    "                    if v.SolutionValue()>0:\n",
    "                        if k == 1:\n",
    "                            deployments_first_shift.loc[i, j] = v.solution_value()\n",
    "                        else:\n",
    "                            deployments_second_shift.loc[i, j] = v.solution_value()\n",
    "                        print(v, v.solution_value())\n",
    "        \n",
    "        print(\"The optimal value for the objective function is\", objective.Value())\n",
    "        \n",
    "    elif result == solver.UNBOUNDED :\n",
    "        print(\"The solution is unbounded\")\n",
    "        \n",
    "    else :\n",
    "        print(\"Unknown error code\")\n",
    "\n",
    "    return deployments_first_shift, deployments_second_shift"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "17622e86",
   "metadata": {},
   "outputs": [],
   "source": [
    "wp = 0.40\n",
    "we = 0.10\n",
    "wd = 0.50\n",
    "\n",
    "deployments_first_shift, deployments_second_shift = solve_problem(wp, we, wd)\n",
    "\n",
    "deployments_first_shift.to_csv(\"dataset/results/deployments_first_\" + str(int(wp*100)) + \"p_\" + str(int(we*100)) + \"e_\" + str(int(wd*100)) + \"d.csv\")\n",
    "deployments_second_shift.to_csv(\"dataset/results/deployments_second_\" + str(int(wp*100)) + \"p_\" + str(int(we*100)) + \"e_\" + str(int(wd*100)) + \"d.csv\")"
   ]
  }
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