Express_Air_hrz.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1fb3a6e0",
   "metadata": {},
   "source": [
    "Code for solving the Express Air Cargo Operation Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1780,
   "id": "8edb2f2d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from gurobipy import *\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1701,
   "id": "8929373c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# initiate cargo comes in for each day\n",
    "Monday = np.array([[0,100,50],[25,0,25],[40,400,0]])\n",
    "Tuesday = np.array([[0,200,50],[25,0,25],[40,200,0]])\n",
    "Wednesday = np.array([[0,100,50],[25,0,25],[40,300,0]])\n",
    "Thursday = np.array([[0,400,50],[25,0,25],[40,200,0]])\n",
    "Friday = np.array([[0,300,50],[25,0,25],[40,400,0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1702,
   "id": "a5198c08",
   "metadata": {},
   "outputs": [],
   "source": [
    "cargo_lst = [Monday, Tuesday, Wednesday, Thursday, Friday]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1703,
   "id": "cf948b48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[  0, 100,  50],\n",
       "        [ 25,   0,  25],\n",
       "        [ 40, 400,   0]]),\n",
       " array([[  0, 200,  50],\n",
       "        [ 25,   0,  25],\n",
       "        [ 40, 200,   0]]),\n",
       " array([[  0, 100,  50],\n",
       "        [ 25,   0,  25],\n",
       "        [ 40, 300,   0]]),\n",
       " array([[  0, 400,  50],\n",
       "        [ 25,   0,  25],\n",
       "        [ 40, 200,   0]]),\n",
       " array([[  0, 300,  50],\n",
       "        [ 25,   0,  25],\n",
       "        [ 40, 400,   0]])]"
      ]
     },
     "execution_count": 1703,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cargo_lst"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1704,
   "id": "3ab2aced",
   "metadata": {},
   "outputs": [],
   "source": [
    "# cost for empty repositioning flight\n",
    "repositioning_cost = np.array([[0,7,3],[7,0,6],[3,6,0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1705,
   "id": "92c6cac8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 7, 3],\n",
       "       [7, 0, 6],\n",
       "       [3, 6, 0]])"
      ]
     },
     "execution_count": 1705,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "repositioning_cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1706,
   "id": "98c79e25",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_airports = 3\n",
    "num_days = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1707,
   "id": "84eb0b1a",
   "metadata": {},
   "outputs": [],
   "source": [
    "myVars = [[[0 for j in range (num_airports)] for i in range (num_airports)] for d in range(num_days)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1708,
   "id": "28e9a153",
   "metadata": {},
   "outputs": [],
   "source": [
    "#myVars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1709,
   "id": "ac6d998f",
   "metadata": {},
   "outputs": [],
   "source": [
    "airport_names = ['A','B','C']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1710,
   "id": "7d56700c",
   "metadata": {},
   "outputs": [],
   "source": [
    "days = ['Monday','Tuesday','Wednesday','Thursday','Friday']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1711,
   "id": "0381b915",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a new model\n",
    "myModel = Model(\"Express_Air\")\n",
    "\n",
    "# create decision variables and store them in the array myVars\n",
    "# decision variables Xijt denote number of flights with cargos from airport i to airport j on day t\n",
    "# Xijt is integer\n",
    "myVars = [[[0 for j in range (num_airports)] for i in range (num_airports)] for t in range(num_days)]\n",
    "for i in range(num_airports):\n",
    "    for j in range(num_airports):\n",
    "        for t in range(num_days):\n",
    "            if i != j:\n",
    "                curVar = myModel.addVar(vtype = GRB.INTEGER,\n",
    "                                           name = \"x\" + airport_names[i] + airport_names[j] + str(t+1))\n",
    "                myVars[t][i][j] = curVar\n",
    "\n",
    "# integrate decision variables into the model\n",
    "myModel.update()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1712,
   "id": "ec931ecc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[[0, <gurobi.Var xAB1>, <gurobi.Var xAC1>],\n",
       "  [<gurobi.Var xBA1>, 0, <gurobi.Var xBC1>],\n",
       "  [<gurobi.Var xCA1>, <gurobi.Var xCB1>, 0]],\n",
       " [[0, <gurobi.Var xAB2>, <gurobi.Var xAC2>],\n",
       "  [<gurobi.Var xBA2>, 0, <gurobi.Var xBC2>],\n",
       "  [<gurobi.Var xCA2>, <gurobi.Var xCB2>, 0]],\n",
       " [[0, <gurobi.Var xAB3>, <gurobi.Var xAC3>],\n",
       "  [<gurobi.Var xBA3>, 0, <gurobi.Var xBC3>],\n",
       "  [<gurobi.Var xCA3>, <gurobi.Var xCB3>, 0]],\n",
       " [[0, <gurobi.Var xAB4>, <gurobi.Var xAC4>],\n",
       "  [<gurobi.Var xBA4>, 0, <gurobi.Var xBC4>],\n",
       "  [<gurobi.Var xCA4>, <gurobi.Var xCB4>, 0]],\n",
       " [[0, <gurobi.Var xAB5>, <gurobi.Var xAC5>],\n",
       "  [<gurobi.Var xBA5>, 0, <gurobi.Var xBC5>],\n",
       "  [<gurobi.Var xCA5>, <gurobi.Var xCB5>, 0]]]"
      ]
     },
     "execution_count": 1712,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "myVars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1713,
   "id": "63232d53",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create decision variables Eijt denote empty flights from airport i to airport j on day t\n",
    "E_Vars = [[[0 for j in range (num_airports)] for i in range (num_airports)] for t in range(num_days)]\n",
    "for i in range(num_airports):\n",
    "    for j in range(num_airports):\n",
    "        for t in range(num_days):\n",
    "            #if i != j:\n",
    "                curVar = myModel.addVar(vtype = GRB.INTEGER,\n",
    "                                           name = \"E\" + airport_names[i] + airport_names[j] + str(t+1))\n",
    "                E_Vars[t][i][j] = curVar\n",
    "\n",
    "# integrate decision variables into the model\n",
    "myModel.update()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1714,
   "id": "60eebb9c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[[<gurobi.Var EAA1>, <gurobi.Var EAB1>, <gurobi.Var EAC1>],\n",
       "  [<gurobi.Var EBA1>, <gurobi.Var EBB1>, <gurobi.Var EBC1>],\n",
       "  [<gurobi.Var ECA1>, <gurobi.Var ECB1>, <gurobi.Var ECC1>]],\n",
       " [[<gurobi.Var EAA2>, <gurobi.Var EAB2>, <gurobi.Var EAC2>],\n",
       "  [<gurobi.Var EBA2>, <gurobi.Var EBB2>, <gurobi.Var EBC2>],\n",
       "  [<gurobi.Var ECA2>, <gurobi.Var ECB2>, <gurobi.Var ECC2>]],\n",
       " [[<gurobi.Var EAA3>, <gurobi.Var EAB3>, <gurobi.Var EAC3>],\n",
       "  [<gurobi.Var EBA3>, <gurobi.Var EBB3>, <gurobi.Var EBC3>],\n",
       "  [<gurobi.Var ECA3>, <gurobi.Var ECB3>, <gurobi.Var ECC3>]],\n",
       " [[<gurobi.Var EAA4>, <gurobi.Var EAB4>, <gurobi.Var EAC4>],\n",
       "  [<gurobi.Var EBA4>, <gurobi.Var EBB4>, <gurobi.Var EBC4>],\n",
       "  [<gurobi.Var ECA4>, <gurobi.Var ECB4>, <gurobi.Var ECC4>]],\n",
       " [[<gurobi.Var EAA5>, <gurobi.Var EAB5>, <gurobi.Var EAC5>],\n",
       "  [<gurobi.Var EBA5>, <gurobi.Var EBB5>, <gurobi.Var EBC5>],\n",
       "  [<gurobi.Var ECA5>, <gurobi.Var ECB5>, <gurobi.Var ECC5>]]]"
      ]
     },
     "execution_count": 1714,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E_Vars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1715,
   "id": "74b5f3b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create decisons variables Lijt denote unshipped cargo from airport i to airport j on day t\n",
    "# create decision variables Eijt denote empty flights from airport i to airport j on day t\n",
    "L_Vars = [[[0 for j in range (num_airports)] for i in range (num_airports)] for t in range(num_days)]\n",
    "for i in range(num_airports):\n",
    "    for j in range(num_airports):\n",
    "        for t in range(num_days):\n",
    "            if i != j:\n",
    "                curVar = myModel.addVar(vtype = GRB.INTEGER,\n",
    "                                           name = \"L\" + airport_names[i] + airport_names[j] + str(t+1))\n",
    "                L_Vars[t][i][j] = curVar\n",
    "\n",
    "# integrate decision variables into the model\n",
    "myModel.update()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1716,
   "id": "8b667ddc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[[0, <gurobi.Var LAB1>, <gurobi.Var LAC1>],\n",
       "  [<gurobi.Var LBA1>, 0, <gurobi.Var LBC1>],\n",
       "  [<gurobi.Var LCA1>, <gurobi.Var LCB1>, 0]],\n",
       " [[0, <gurobi.Var LAB2>, <gurobi.Var LAC2>],\n",
       "  [<gurobi.Var LBA2>, 0, <gurobi.Var LBC2>],\n",
       "  [<gurobi.Var LCA2>, <gurobi.Var LCB2>, 0]],\n",
       " [[0, <gurobi.Var LAB3>, <gurobi.Var LAC3>],\n",
       "  [<gurobi.Var LBA3>, 0, <gurobi.Var LBC3>],\n",
       "  [<gurobi.Var LCA3>, <gurobi.Var LCB3>, 0]],\n",
       " [[0, <gurobi.Var LAB4>, <gurobi.Var LAC4>],\n",
       "  [<gurobi.Var LBA4>, 0, <gurobi.Var LBC4>],\n",
       "  [<gurobi.Var LCA4>, <gurobi.Var LCB4>, 0]],\n",
       " [[0, <gurobi.Var LAB5>, <gurobi.Var LAC5>],\n",
       "  [<gurobi.Var LBA5>, 0, <gurobi.Var LBC5>],\n",
       "  [<gurobi.Var LCA5>, <gurobi.Var LCB5>, 0]]]"
      ]
     },
     "execution_count": 1716,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L_Vars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1717,
   "id": "00942f44",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create decison variables Si denote starting number of aircrafts at airport i on day 1\n",
    "S_Vars = [0 for i in range (num_airports)]\n",
    "for i in range(num_airports):\n",
    "    curVar = myModel.addVar(vtype = GRB.INTEGER,\n",
    "                               name = \"S\" + airport_names[i])\n",
    "    S_Vars[i] = curVar\n",
    "\n",
    "# integrate decision variables into the model\n",
    "myModel.update()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1718,
   "id": "0115ec01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<gurobi.Var SA>, <gurobi.Var SB>, <gurobi.Var SC>]"
      ]
     },
     "execution_count": 1718,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S_Vars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1719,
   "id": "28248936",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a linear expression for the objective\n",
    "objExpr = LinExpr()\n",
    "\n",
    "# add all repositioning cost\n",
    "for i in range(num_airports):\n",
    "    for j in range(num_airports):\n",
    "        for t in range(num_days):\n",
    "            #if i != j:\n",
    "                curVar = E_Vars[t][i][j]\n",
    "                objExpr += repositioning_cost[i][j] * curVar\n",
    "                \n",
    "# add all landing cargo cost:\n",
    "for i in range(num_airports):\n",
    "    for j in range(num_airports):\n",
    "        for t in range(num_days):\n",
    "            if i != j:\n",
    "                curVar = L_Vars[t][i][j]\n",
    "                objExpr += 10 * curVar\n",
    "\n",
    "myModel.setObjective(objExpr, GRB.MINIMIZE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1720,
   "id": "d17bda3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<gurobi.LinExpr: 0.0 EAA1 + 0.0 EAA2 + 0.0 EAA3 + 0.0 EAA4 + 0.0 EAA5 + 7.0 EAB1 + 7.0 EAB2 + 7.0 EAB3 + 7.0 EAB4 + 7.0 EAB5 + 3.0 EAC1 + 3.0 EAC2 + 3.0 EAC3 + 3.0 EAC4 + 3.0 EAC5 + 7.0 EBA1 + 7.0 EBA2 + 7.0 EBA3 + 7.0 EBA4 + 7.0 EBA5 + 0.0 EBB1 + 0.0 EBB2 + 0.0 EBB3 + 0.0 EBB4 + 0.0 EBB5 + 6.0 EBC1 + 6.0 EBC2 + 6.0 EBC3 + 6.0 EBC4 + 6.0 EBC5 + 3.0 ECA1 + 3.0 ECA2 + 3.0 ECA3 + 3.0 ECA4 + 3.0 ECA5 + 6.0 ECB1 + 6.0 ECB2 + 6.0 ECB3 + 6.0 ECB4 + 6.0 ECB5 + 0.0 ECC1 + 0.0 ECC2 + 0.0 ECC3 + 0.0 ECC4 + 0.0 ECC5 + 10.0 LAB1 + 10.0 LAB2 + 10.0 LAB3 + 10.0 LAB4 + 10.0 LAB5 + 10.0 LAC1 + 10.0 LAC2 + 10.0 LAC3 + 10.0 LAC4 + 10.0 LAC5 + 10.0 LBA1 + 10.0 LBA2 + 10.0 LBA3 + 10.0 LBA4 + 10.0 LBA5 + 10.0 LBC1 + 10.0 LBC2 + 10.0 LBC3 + 10.0 LBC4 + 10.0 LBC5 + 10.0 LCA1 + 10.0 LCA2 + 10.0 LCA3 + 10.0 LCA4 + 10.0 LCA5 + 10.0 LCB1 + 10.0 LCB2 + 10.0 LCB3 + 10.0 LCB4 + 10.0 LCB5 + 0.0 xAB1 + 0.0 xAB2 + 0.0 xAB3 + 0.0 xAB4 + 0.0 xAB5 + 0.0 xAC1 + 0.0 xAC2 + 0.0 xAC3 + 0.0 xAC4 + 0.0 xAC5 + 0.0 xBA1 + 0.0 xBA2 + 0.0 xBA3 + 0.0 xBA4 + 0.0 xBA5 + 0.0 xBC1 + 0.0 xBC2 + 0.0 xBC3 + 0.0 xBC4 + 0.0 xBC5 + 0.0 xCA1 + 0.0 xCA2 + 0.0 xCA3 + 0.0 xCA4 + 0.0 xCA5 + 0.0 xCB1 + 0.0 xCB2 + 0.0 xCB3 + 0.0 xCB4 + 0.0 xCB5 + 0.0 SA + 0.0 SB + 0.0 SC>"
      ]
     },
     "execution_count": 1720,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "objExpr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1721,
   "id": "aa3a9ca5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create constraint so that total number of outflow for airport i at time 1 is equal to starting number Si \n",
    "for i in range(num_airports):\n",
    "    constExpr = LinExpr()\n",
    "    for j in range(num_airports):\n",
    "        # out of node\n",
    "        curVar = myVars[0][i][j]\n",
    "        constExpr += 1*curVar\n",
    "        #if i != j:\n",
    "        curVar1 = E_Vars[0][i][j]\n",
    "        constExpr += 1*curVar1\n",
    "        \n",
    "    myModel.addConstr(lhs = constExpr, sense = GRB.EQUAL, rhs = S_Vars[i], name = \"Monday\"+ 'airport'+ airport_names[i])\n",
    "    \n",
    "myModel.update()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1722,
   "id": "c978764b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create constraint so that total number of outflow for airport i at time t is equal to inflow for airport i at time t \n",
    "for i in range(num_airports):\n",
    "    for t in range(1,num_days):\n",
    "        constExpr = LinExpr()\n",
    "        for j in range(num_airports):\n",
    "            # out of node\n",
    "            curVar = myVars[t][i][j]\n",
    "            constExpr += 1*curVar\n",
    "            #if i != j:\n",
    "            curVar1 = E_Vars[t][i][j]\n",
    "            constExpr += 1*curVar1\n",
    "            curVar2 = myVars[t-1][j][i]\n",
    "            constExpr -= curVar2\n",
    "            #if i != j:\n",
    "            curVar3 = E_Vars[t-1][j][i]\n",
    "            constExpr -= curVar3\n",
    "\n",
    "        myModel.addConstr(lhs = constExpr, sense = GRB.EQUAL, rhs = 0, name = days[t] + 'airport' + airport_names[i])\n",
    "    \n",
    "myModel.update()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1723,
   "id": "52fcb68e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create constraint so that total number of inflow for airport i at time 5 is equal to starting number Si \n",
    "for i in range(num_airports):\n",
    "    constExpr = LinExpr()\n",
    "    for j in range(num_airports):\n",
    "        # out of node\n",
    "        curVar = myVars[4][j][i]\n",
    "        constExpr += 1*curVar\n",
    "        #if i != j:\n",
    "        curVar1 = E_Vars[4][j][i]\n",
    "        constExpr += 1*curVar1\n",
    "        \n",
    "    myModel.addConstr(lhs = constExpr, sense = GRB.EQUAL, rhs = S_Vars[i], name = \"EndofWeek\"+ 'airport'+ airport_names[i])\n",
    "    \n",
    "myModel.update()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1724,
   "id": "3535c803",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create constraint so that total number of flights is 1200\n",
    "constExpr = LinExpr()\n",
    "for i in range(num_airports):\n",
    "    curVar = S_Vars[i]\n",
    "    constExpr += 1*curVar\n",
    "        \n",
    "myModel.addConstr(lhs = constExpr, sense = GRB.EQUAL, rhs = 1200, name = \"NumberofAircrafts\")\n",
    "    \n",
    "myModel.update()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1725,
   "id": "c09dce62",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create constraint so that number of landing cargos equals amount need to be shipped minus amount really shipped\n",
    "# for Monday\n",
    "for i in range(num_airports):\n",
    "    for j in range(num_airports):\n",
    "        if i != j:\n",
    "            constExpr1 = LinExpr()\n",
    "            constExpr2 = LinExpr()\n",
    "            curVar = L_Vars[0][i][j]\n",
    "            curVar0 = L_Vars[4][i][j]\n",
    "            curVar1 = cargo_lst[0][i][j]\n",
    "            curVar2 = myVars[0][i][j]\n",
    "            constExpr1 += 1*curVar - 1*curVar0 + 1*curVar2\n",
    "            constExpr2 += 1*curVar1\n",
    "            myModel.addConstr(lhs = constExpr1, sense = GRB.EQUAL, rhs = constExpr2, name = 'StartLandingCargos'+'Monday'+airport_names[i]+airport_names[j])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1726,
   "id": "d4114589",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"\\nfor i in range(num_airports):\\n    for j in range(num_airports):\\n        if i != j:\\n            constExpr = LinExpr()\\n            curVar = L_Vars[4][i][j]\\n            constExpr += 1*curVar\\n            myModel.addConstr(lhs = constExpr, sense = GRB.EQUAL, rhs = 0, name = 'FinalLandingCargos'+days[t]+airport_names[i]+airport_names[j])\\n\""
      ]
     },
     "execution_count": 1726,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# for Tues,Weds,Thurs\n",
    "for i in range(num_airports):\n",
    "    for j in range(num_airports):\n",
    "        for t in range(1, num_days):\n",
    "            if i != j:\n",
    "                constExpr1 = LinExpr()\n",
    "                constExpr2 = LinExpr()\n",
    "                curVar = L_Vars[t][i][j]\n",
    "                curVar0 = L_Vars[t-1][i][j]\n",
    "                curVar1 = cargo_lst[t][i][j]\n",
    "                curVar2 = myVars[t][i][j]\n",
    "                constExpr1 += 1*curVar - 1*curVar0 + 1*curVar2\n",
    "                constExpr2 += 1*curVar1\n",
    "                myModel.addConstr(lhs = constExpr1, sense = GRB.EQUAL, rhs = constExpr2, name = 'LandingCargos'+days[t]+airport_names[i]+airport_names[j])\n",
    "# for Friday\n",
    "'''\n",
    "for i in range(num_airports):\n",
    "    for j in range(num_airports):\n",
    "        if i != j:\n",
    "            constExpr = LinExpr()\n",
    "            curVar = L_Vars[4][i][j]\n",
    "            constExpr += 1*curVar\n",
    "            myModel.addConstr(lhs = constExpr, sense = GRB.EQUAL, rhs = 0, name = 'FinalLandingCargos'+days[t]+airport_names[i]+airport_names[j])\n",
    "'''\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1727,
   "id": "fcdc4b90",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"\\n# sum delivered equals sum need to be delivered \\nfor i in range(num_airports):\\n    for j in range(num_airports):\\n        if i != j:\\n            constExpr = LinExpr()\\n            for t in range(num_days):\\n                # out of node\\n                curVar = myVars[t][i][j]\\n                constExpr += 1*curVar\\n                curVar1 = cargo_lst[t][i][j]\\n                constExpr -= 1*curVar1\\n\\n            myModel.addConstr(lhs = constExpr, sense = GRB.EQUAL, rhs = 0, name = 'cargo' + airport_names[i]+airport_names[j])\\n\\nmyModel.update()\\n\""
      ]
     },
     "execution_count": 1727,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''\n",
    "# sum delivered equals sum need to be delivered \n",
    "for i in range(num_airports):\n",
    "    for j in range(num_airports):\n",
    "        if i != j:\n",
    "            constExpr = LinExpr()\n",
    "            for t in range(num_days):\n",
    "                # out of node\n",
    "                curVar = myVars[t][i][j]\n",
    "                constExpr += 1*curVar\n",
    "                curVar1 = cargo_lst[t][i][j]\n",
    "                constExpr -= 1*curVar1\n",
    "\n",
    "            myModel.addConstr(lhs = constExpr, sense = GRB.EQUAL, rhs = 0, name = 'cargo' + airport_names[i]+airport_names[j])\n",
    "\n",
    "myModel.update()\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1728,
   "id": "509cb52f",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"\\n# each time delivered must be less than or equal to current amount of cargos\\nfor i in range(num_airports):\\n    for j in range(num_airports):\\n        if i != j:\\n            for t in range(1,num_days):\\n                constExpr1 = LinExpr()\\n                constExpr2 = LinExpr()\\n                # out of node\\n                curVar = myVars[t][i][j]\\n                constExpr1 += 1*curVar\\n                curVar1 = cargo_lst[t][i][j]\\n                constExpr2 += 1*curVar1\\n                curVar2 = L_Vars[t-1][i][j]\\n                constExpr2 += 1*curVar2\\n\\n                myModel.addConstr(lhs = constExpr1, sense = GRB.LESS_EQUAL, rhs = constExpr2, name = 'Capacity' + airport_names[i]+airport_names[j]+days[t])\\n\\nmyModel.update()\\n\""
      ]
     },
     "execution_count": 1728,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''\n",
    "# each time delivered must be less than or equal to current amount of cargos\n",
    "for i in range(num_airports):\n",
    "    for j in range(num_airports):\n",
    "        if i != j:\n",
    "            for t in range(1,num_days):\n",
    "                constExpr1 = LinExpr()\n",
    "                constExpr2 = LinExpr()\n",
    "                # out of node\n",
    "                curVar = myVars[t][i][j]\n",
    "                constExpr1 += 1*curVar\n",
    "                curVar1 = cargo_lst[t][i][j]\n",
    "                constExpr2 += 1*curVar1\n",
    "                curVar2 = L_Vars[t-1][i][j]\n",
    "                constExpr2 += 1*curVar2\n",
    "\n",
    "                myModel.addConstr(lhs = constExpr1, sense = GRB.LESS_EQUAL, rhs = constExpr2, name = 'Capacity' + airport_names[i]+airport_names[j]+days[t])\n",
    "\n",
    "myModel.update()\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1729,
   "id": "fdf2e153",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "200"
      ]
     },
     "execution_count": 1729,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cargo_lst[1][2][1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1730,
   "id": "21703d37",
   "metadata": {},
   "outputs": [],
   "source": [
    "# write the model in a file to make sure it is constructed correctly\n",
    "myModel.write(filename = \"Express_Air.lp\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1731,
   "id": "6551b2eb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (mac64[x86])\n",
      "Thread count: 8 physical cores, 16 logical processors, using up to 16 threads\n",
      "Optimize a model with 49 rows, 108 columns and 249 nonzeros\n",
      "Model fingerprint: 0xcedfc35f\n",
      "Variable types: 0 continuous, 108 integer (0 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [3e+00, 1e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [2e+01, 1e+03]\n",
      "Presolve removed 1 rows and 1 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 48 rows, 107 columns, 248 nonzeros\n",
      "Variable types: 0 continuous, 107 integer (0 binary)\n",
      "\n",
      "Root relaxation: objective 1.792500e+04, 25 iterations, 0.00 seconds (0.00 work units)\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    17925.000000 17925.0000  0.00%     -    0s\n",
      "\n",
      "Explored 1 nodes (25 simplex iterations) in 0.02 seconds (0.00 work units)\n",
      "Thread count was 16 (of 16 available processors)\n",
      "\n",
      "Solution count 1: 17925 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 1.792500000000e+04, best bound 1.792500000000e+04, gap 0.0000%\n"
     ]
    }
   ],
   "source": [
    "# optimize the model\n",
    "myModel.optimize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1732,
   "id": "8cd67ec9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Optimal Objective: 17925.0\n",
      "\n",
      "Optimal Solution:\n",
      "xAB1 200.0\n",
      "xAB2 290.0\n",
      "xAB3 100.0\n",
      "xAB4 400.0\n",
      "xAB5 110.0\n",
      "xAC1 50.0\n",
      "xAC2 50.0\n",
      "xAC3 50.0\n",
      "xAC4 50.0\n",
      "xAC5 50.0\n",
      "xBA1 25.0\n",
      "xBA2 25.0\n",
      "xBA3 25.0\n",
      "xBA4 25.0\n",
      "xBA5 25.0\n",
      "xBC1 25.0\n",
      "xBC2 25.0\n",
      "xBC3 25.0\n",
      "xBC4 25.0\n",
      "xBC5 25.0\n",
      "xCA1 40.0\n",
      "xCA2 40.0\n",
      "xCA3 40.0\n",
      "xCA4 40.0\n",
      "xCA5 40.0\n",
      "xCB1 400.0\n",
      "xCB2 200.0\n",
      "xCB3 300.0\n",
      "xCB4 200.0\n",
      "xCB5 400.0\n",
      "EAA1 -0.0\n",
      "EAA2 -0.0\n",
      "EAA3 220.0\n",
      "EAA4 -0.0\n",
      "EAA5 -0.0\n",
      "EAB1 -0.0\n",
      "EAB2 -0.0\n",
      "EAB3 -0.0\n",
      "EAB4 -0.0\n",
      "EAB5 -0.0\n",
      "EAC1 -0.0\n",
      "EAC2 -0.0\n",
      "EAC3 -0.0\n",
      "EAC4 -0.0\n",
      "EAC5 -0.0\n",
      "EBA1 275.0\n",
      "EBA2 305.0\n",
      "EBA3 165.0\n",
      "EBA4 95.0\n",
      "EBA5 185.0\n",
      "EBB1 -0.0\n",
      "EBB2 -0.0\n",
      "EBB3 -0.0\n",
      "EBB4 -0.0\n",
      "EBB5 -0.0\n",
      "EBC1 185.0\n",
      "EBC2 245.0\n",
      "EBC3 275.0\n",
      "EBC4 255.0\n",
      "EBC5 365.0\n",
      "ECA1 -0.0\n",
      "ECA2 -0.0\n",
      "ECA3 -0.0\n",
      "ECA4 -0.0\n",
      "ECA5 -0.0\n",
      "ECB1 -0.0\n",
      "ECB2 -0.0\n",
      "ECB3 -0.0\n",
      "ECB4 -0.0\n",
      "ECB5 -0.0\n",
      "ECC1 -0.0\n",
      "ECC2 20.0\n",
      "ECC3 -0.0\n",
      "ECC4 110.0\n",
      "ECC5 -0.0\n",
      "LAB1 90.0\n",
      "LAB2 -0.0\n",
      "LAB3 -0.0\n",
      "LAB4 -0.0\n",
      "LAB5 190.0\n",
      "LAC1 -0.0\n",
      "LAC2 -0.0\n",
      "LAC3 -0.0\n",
      "LAC4 -0.0\n",
      "LAC5 -0.0\n",
      "LBA1 -0.0\n",
      "LBA2 -0.0\n",
      "LBA3 -0.0\n",
      "LBA4 -0.0\n",
      "LBA5 -0.0\n",
      "LBC1 -0.0\n",
      "LBC2 -0.0\n",
      "LBC3 -0.0\n",
      "LBC4 -0.0\n",
      "LBC5 -0.0\n",
      "LCA1 -0.0\n",
      "LCA2 -0.0\n",
      "LCA3 -0.0\n",
      "LCA4 -0.0\n",
      "LCA5 -0.0\n",
      "LCB1 -0.0\n",
      "LCB2 -0.0\n",
      "LCB3 -0.0\n",
      "LCB4 -0.0\n",
      "LCB5 -0.0\n",
      "SA 250.0\n",
      "SB 510.0\n",
      "SC 440.0\n"
     ]
    }
   ],
   "source": [
    "# print optimal objective and optimal solution\n",
    "print(\"\\nOptimal Objective: \" + str(myModel.ObjVal))\n",
    "print(\"\\nOptimal Solution:\")\n",
    "allVars = myModel.getVars()\n",
    "for curVar in allVars:\n",
    "    print(curVar.varName + \" \" + str(curVar.x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1733,
   "id": "37f5d932",
   "metadata": {},
   "outputs": [],
   "source": [
    "decision_variables = [y.x for y in allVars]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1734,
   "id": "2b4920a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "Xijt = np.array(decision_variables[:30]).reshape(6,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1735,
   "id": "adedb9e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[200., 290., 100., 400., 110.],\n",
       "       [ 50.,  50.,  50.,  50.,  50.],\n",
       "       [ 25.,  25.,  25.,  25.,  25.],\n",
       "       [ 25.,  25.,  25.,  25.,  25.],\n",
       "       [ 40.,  40.,  40.,  40.,  40.],\n",
       "       [400., 200., 300., 200., 400.]])"
      ]
     },
     "execution_count": 1735,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xijt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1736,
   "id": "bcf736a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "Eijt = np.array(decision_variables[30:75]).reshape(9,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1737,
   "id": "92019047",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -0.,  -0., 220.,  -0.,  -0.],\n",
       "       [ -0.,  -0.,  -0.,  -0.,  -0.],\n",
       "       [ -0.,  -0.,  -0.,  -0.,  -0.],\n",
       "       [275., 305., 165.,  95., 185.],\n",
       "       [ -0.,  -0.,  -0.,  -0.,  -0.],\n",
       "       [185., 245., 275., 255., 365.],\n",
       "       [ -0.,  -0.,  -0.,  -0.,  -0.],\n",
       "       [ -0.,  -0.,  -0.,  -0.,  -0.],\n",
       "       [ -0.,  20.,  -0., 110.,  -0.]])"
      ]
     },
     "execution_count": 1737,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eijt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1738,
   "id": "e50bae25",
   "metadata": {},
   "outputs": [],
   "source": [
    "Lijt = np.array(decision_variables[75:105]).reshape(6,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1739,
   "id": "fe955fcd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 90.,  -0.,  -0.,  -0., 190.],\n",
       "       [ -0.,  -0.,  -0.,  -0.,  -0.],\n",
       "       [ -0.,  -0.,  -0.,  -0.,  -0.],\n",
       "       [ -0.,  -0.,  -0.,  -0.,  -0.],\n",
       "       [ -0.,  -0.,  -0.,  -0.,  -0.],\n",
       "       [ -0.,  -0.,  -0.,  -0.,  -0.]])"
      ]
     },
     "execution_count": 1739,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Lijt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1740,
   "id": "71881fb1",
   "metadata": {},
   "outputs": [],
   "source": [
    "S_ = np.array(decision_variables[105:]).reshape(3,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1741,
   "id": "3d6a69ca",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[250.],\n",
       "       [510.],\n",
       "       [440.]])"
      ]
     },
     "execution_count": 1741,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1746,
   "id": "e9659e29",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17925.0"
      ]
     },
     "execution_count": 1746,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "myModel.ObjVal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1774,
   "id": "b407e34b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_optimal_value(fleet_size):\n",
    "    # create a new model\n",
    "    myModel = Model(\"Express_Air\")\n",
    "\n",
    "    # create decision variables and store them in the array myVars\n",
    "    # decision variables Xijt denote number of flights with cargos from airport i to airport j on day t\n",
    "    # Xijt is integer\n",
    "    myVars = [[[0 for j in range (num_airports)] for i in range (num_airports)] for t in range(num_days)]\n",
    "    for i in range(num_airports):\n",
    "        for j in range(num_airports):\n",
    "            for t in range(num_days):\n",
    "                if i != j:\n",
    "                    curVar = myModel.addVar(vtype = GRB.INTEGER,\n",
    "                                               name = \"x\" + airport_names[i] + airport_names[j] + str(t+1))\n",
    "                    myVars[t][i][j] = curVar\n",
    "\n",
    "    # integrate decision variables into the model\n",
    "    myModel.update()\n",
    "    \n",
    "    # create decision variables Eijt denote empty flights from airport i to airport j on day t\n",
    "    E_Vars = [[[0 for j in range (num_airports)] for i in range (num_airports)] for t in range(num_days)]\n",
    "    for i in range(num_airports):\n",
    "        for j in range(num_airports):\n",
    "            for t in range(num_days):\n",
    "                #if i != j:\n",
    "                    curVar = myModel.addVar(vtype = GRB.INTEGER,\n",
    "                                               name = \"E\" + airport_names[i] + airport_names[j] + str(t+1))\n",
    "                    E_Vars[t][i][j] = curVar\n",
    "\n",
    "    # integrate decision variables into the model\n",
    "    myModel.update()\n",
    "    \n",
    "    # create decisons variables Lijt denote unshipped cargo from airport i to airport j on day t\n",
    "    # create decision variables Eijt denote empty flights from airport i to airport j on day t\n",
    "    L_Vars = [[[0 for j in range (num_airports)] for i in range (num_airports)] for t in range(num_days)]\n",
    "    for i in range(num_airports):\n",
    "        for j in range(num_airports):\n",
    "            for t in range(num_days):\n",
    "                if i != j:\n",
    "                    curVar = myModel.addVar(vtype = GRB.INTEGER,\n",
    "                                               name = \"L\" + airport_names[i] + airport_names[j] + str(t+1))\n",
    "                    L_Vars[t][i][j] = curVar\n",
    "\n",
    "    # integrate decision variables into the model\n",
    "    myModel.update()\n",
    "    \n",
    "    # create decison variables Si denote starting number of aircrafts at airport i on day 1\n",
    "    S_Vars = [0 for i in range (num_airports)]\n",
    "    for i in range(num_airports):\n",
    "        curVar = myModel.addVar(vtype = GRB.INTEGER,\n",
    "                                   name = \"S\" + airport_names[i])\n",
    "        S_Vars[i] = curVar\n",
    "\n",
    "    # integrate decision variables into the model\n",
    "    myModel.update()\n",
    "    \n",
    "    # create a linear expression for the objective\n",
    "    objExpr = LinExpr()\n",
    "\n",
    "    # add all repositioning cost\n",
    "    for i in range(num_airports):\n",
    "        for j in range(num_airports):\n",
    "            for t in range(num_days):\n",
    "                #if i != j:\n",
    "                    curVar = E_Vars[t][i][j]\n",
    "                    objExpr += repositioning_cost[i][j] * curVar\n",
    "\n",
    "    # add all landing cargo cost:\n",
    "    for i in range(num_airports):\n",
    "        for j in range(num_airports):\n",
    "            for t in range(num_days):\n",
    "                if i != j:\n",
    "                    curVar = L_Vars[t][i][j]\n",
    "                    objExpr += 10 * curVar\n",
    "\n",
    "    myModel.setObjective(objExpr, GRB.MINIMIZE)\n",
    "    \n",
    "    # create constraint so that total number of outflow for airport i at time 1 is equal to starting number Si \n",
    "    for i in range(num_airports):\n",
    "        constExpr = LinExpr()\n",
    "        for j in range(num_airports):\n",
    "            # out of node\n",
    "            curVar = myVars[0][i][j]\n",
    "            constExpr += 1*curVar\n",
    "            #if i != j:\n",
    "            curVar1 = E_Vars[0][i][j]\n",
    "            constExpr += 1*curVar1\n",
    "\n",
    "        myModel.addConstr(lhs = constExpr, sense = GRB.EQUAL, rhs = S_Vars[i], name = \"Monday\"+ 'airport'+ airport_names[i])\n",
    "\n",
    "    myModel.update()\n",
    "    \n",
    "    # create constraint so that total number of outflow for airport i at time t is equal to inflow for airport i at time t \n",
    "    for i in range(num_airports):\n",
    "        for t in range(1,num_days):\n",
    "            constExpr = LinExpr()\n",
    "            for j in range(num_airports):\n",
    "                # out of node\n",
    "                curVar = myVars[t][i][j]\n",
    "                constExpr += 1*curVar\n",
    "                #if i != j:\n",
    "                curVar1 = E_Vars[t][i][j]\n",
    "                constExpr += 1*curVar1\n",
    "                curVar2 = myVars[t-1][j][i]\n",
    "                constExpr -= curVar2\n",
    "                #if i != j:\n",
    "                curVar3 = E_Vars[t-1][j][i]\n",
    "                constExpr -= curVar3\n",
    "\n",
    "            myModel.addConstr(lhs = constExpr, sense = GRB.EQUAL, rhs = 0, name = days[t] + 'airport' + airport_names[i])\n",
    "\n",
    "    myModel.update()\n",
    "    \n",
    "    # create constraint so that total number of inflow for airport i at time 5 is equal to starting number Si \n",
    "    for i in range(num_airports):\n",
    "        constExpr = LinExpr()\n",
    "        for j in range(num_airports):\n",
    "            # out of node\n",
    "            curVar = myVars[4][j][i]\n",
    "            constExpr += 1*curVar\n",
    "            #if i != j:\n",
    "            curVar1 = E_Vars[4][j][i]\n",
    "            constExpr += 1*curVar1\n",
    "\n",
    "        myModel.addConstr(lhs = constExpr, sense = GRB.EQUAL, rhs = S_Vars[i], name = \"EndofWeek\"+ 'airport'+ airport_names[i])\n",
    "\n",
    "    myModel.update()\n",
    "    \n",
    "    # create constraint so that total number of flights is 1200\n",
    "    constExpr = LinExpr()\n",
    "    for i in range(num_airports):\n",
    "        curVar = S_Vars[i]\n",
    "        constExpr += 1*curVar\n",
    "\n",
    "    myModel.addConstr(lhs = constExpr, sense = GRB.EQUAL, rhs = fleet_size, name = \"NumberofAircrafts\")\n",
    "\n",
    "    myModel.update()\n",
    "    \n",
    "    # Create constraint so that number of landing cargos equals amount need to be shipped minus amount really shipped\n",
    "    # for Monday\n",
    "    for i in range(num_airports):\n",
    "        for j in range(num_airports):\n",
    "            if i != j:\n",
    "                constExpr1 = LinExpr()\n",
    "                constExpr2 = LinExpr()\n",
    "                curVar = L_Vars[0][i][j]\n",
    "                curVar0 = L_Vars[4][i][j]\n",
    "                curVar1 = cargo_lst[0][i][j]\n",
    "                curVar2 = myVars[0][i][j]\n",
    "                constExpr1 += 1*curVar - 1*curVar0 + 1*curVar2\n",
    "                constExpr2 += 1*curVar1\n",
    "                myModel.addConstr(lhs = constExpr1, sense = GRB.EQUAL, rhs = constExpr2, name = 'StartLandingCargos'+'Monday'+airport_names[i]+airport_names[j])\n",
    "    \n",
    "    # for Tues,Weds,Thurs\n",
    "    for i in range(num_airports):\n",
    "        for j in range(num_airports):\n",
    "            for t in range(1, num_days):\n",
    "                if i != j:\n",
    "                    constExpr1 = LinExpr()\n",
    "                    constExpr2 = LinExpr()\n",
    "                    curVar = L_Vars[t][i][j]\n",
    "                    curVar0 = L_Vars[t-1][i][j]\n",
    "                    curVar1 = cargo_lst[t][i][j]\n",
    "                    curVar2 = myVars[t][i][j]\n",
    "                    constExpr1 += 1*curVar - 1*curVar0 + 1*curVar2\n",
    "                    constExpr2 += 1*curVar1\n",
    "                    myModel.addConstr(lhs = constExpr1, sense = GRB.EQUAL, rhs = constExpr2, name = 'LandingCargos'+days[t]+airport_names[i]+airport_names[j])\n",
    "    \n",
    "    # optimize the model\n",
    "    myModel.optimize()\n",
    "    \n",
    "    if myModel.status == GRB.OPTIMAL:\n",
    "        return myModel.ObjVal\n",
    "    else:\n",
    "        return 20000\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1775,
   "id": "16b8923c",
   "metadata": {},
   "outputs": [],
   "source": [
    "fleet_size = range(1100,1500,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0a2d05b0",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "all_optimal_soln = []\n",
    "\n",
    "for n in fleet_size:\n",
    "    all_optimal_soln.append(get_optimal_value(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1792,
   "id": "541fe094",
   "metadata": {},
   "outputs": [],
   "source": [
    "my_df = pd.DataFrame({\"fleet_size\":fleet_size,\"all_optimal_soln\":all_optimal_soln})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1814,
   "id": "1bc21798",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fleet_size</th>\n",
       "      <th>all_optimal_soln</th>\n",
       "      <th>optimal_1st_diff</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1100</td>\n",
       "      <td>20000.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1101</td>\n",
       "      <td>20000.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1102</td>\n",
       "      <td>20000.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1103</td>\n",
       "      <td>20000.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1104</td>\n",
       "      <td>20000.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fleet_size  all_optimal_soln  optimal_1st_diff\n",
       "0        1100           20000.0               NaN\n",
       "1        1101           20000.0               0.0\n",
       "2        1102           20000.0               0.0\n",
       "3        1103           20000.0               0.0\n",
       "4        1104           20000.0               0.0"
      ]
     },
     "execution_count": 1814,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1800,
   "id": "e99cc513",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(x=\"fleet_size\", y=\"all_optimal_soln\", data=my_df)\n",
    "plt.xlabel('Number of aircrafts')\n",
    "plt.ylabel('Optimal cost')\n",
    "plt.title('Fleet size vs. Total cost')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1801,
   "id": "497f2b06",
   "metadata": {},
   "outputs": [],
   "source": [
    "my_df['optimal_1st_diff'] = my_df['all_optimal_soln'].diff()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1802,
   "id": "4fa1a0e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fleet_size</th>\n",
       "      <th>all_optimal_soln</th>\n",
       "      <th>optimal_1st_diff</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1100</td>\n",
       "      <td>20000.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1101</td>\n",
       "      <td>20000.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1102</td>\n",
       "      <td>20000.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1103</td>\n",
       "      <td>20000.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1104</td>\n",
       "      <td>20000.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fleet_size  all_optimal_soln  optimal_1st_diff\n",
       "0        1100           20000.0               NaN\n",
       "1        1101           20000.0               0.0\n",
       "2        1102           20000.0               0.0\n",
       "3        1103           20000.0               0.0\n",
       "4        1104           20000.0               0.0"
      ]
     },
     "execution_count": 1802,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1805,
   "id": "b0326f1e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/houruize/anaconda/lib/python3.8/site-packages/numpy/core/fromnumeric.py:57: FutureWarning: \n",
      "The current behaviour of 'Series.argmax' is deprecated, use 'idxmax'\n",
      "instead.\n",
      "The behavior of 'argmax' will be corrected to return the positional\n",
      "maximum in the future. For now, use 'series.values.argmax' or\n",
      "'np.argmax(np.array(values))' to get the position of the maximum\n",
      "row.\n",
      "  return bound(*args, **kwds)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "30"
      ]
     },
     "execution_count": 1805,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmax(my_df['optimal_1st_diff'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1809,
   "id": "33a3addb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fleet_size           1130.0\n",
       "all_optimal_soln    20525.0\n",
       "optimal_1st_diff      525.0\n",
       "Name: 30, dtype: float64"
      ]
     },
     "execution_count": 1809,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_df.loc[30]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1815,
   "id": "67bb22c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZbWe17Fa6TtI4AEnvk3SRpH3qHJeZmTVQLcnhP4EXJB0OfBx4HPheXaMyM7OGqiU59ER204eTgIsj4mJgfH3DMjOzRqrlqqzr0k143g8ck85WaqtvWGZm1ki1bDm8B+gCzoiIp8ju6XxhXaMyM7OG6jc5pIRwObCLpLcBGyNiUMccJJ0qaYmkkqSOXPl0SS9KWpQelw5mHDMzG5hafiH9brJbdZ4KvBv4X0nvGuS49wHvAG6vUrc0Io5Ij7MHOY6ZmQ1ALcccZgNHRcQqAEkTgQXAjwc6aETcn/oaaBdmZlZHtRxzaCknhuSZGtcbqH0l3S3pNknH9NZI0kxJnZI6V69eXcdwzMxGn1q2HP5b0o3AD9Pye4Ab+ltJ0gJgzypVsyOit8tvrACmRcQzko4ErpY0IyLWVjaMiHnAPICOjo6o4XWYmVmN+k0OEfGPkt4BvA4QMC8iflLDesdtazAR0UV2ZhQRsVDSUuAgoHNb+zIzs4HrNzlI2he4PiL+f1oeK2l6RDw21MGk4xnPRsRmSfsBBwLLhnocMzPrWy3HDv4LKOWWN6eyAZN0iqTlwGuAn6XdVgCvBxZLuofsgPfZEfHsYMYyM7NtV8sxh9aI2FReiIhNkl42mEHTbqnCrqmIuAq4ajB9m5nZ4NWy5bBa0onlBUknAU/XLyQzM2u0WrYczgYul3RJWl5Odp0lMzMboWo5W2kp8GpJOwGKiHX1D8vMzBqpli0HACJifT0DMTOz5lHPXzqbmdkw5eRgZmYFve5WSr+K7lX5R3FmZjby9HXM4e3p30nAa4FfpOU3ArcCTg5mZiNUr8khIv4KQNJ1wCERsSItTwa+tn3CMzOzRqjlmMP0cmJIVpJdDM/MzEaoWk5lvTV3ye4ATgNuqWtUZmbWULX8CO4cSaeQXRQParxkt5mZDV+1/gjuLmBdRCyQtKOk8f6ltJnZyNXvMQdJHyK7fPbXU9FU4Oo6xmRmZg1WywHpjwB/CqwFiIiHyU5vNTOzEaqW5NCVv5+DpFayA9NmZjZC1XLM4TZJ5wNjJb0Z+DDw08EMKulCsh/ZbQKWAn8VEc+nulnAmWR3nDs3Im7srR+DUin4/bMbeGb9JlAQAd2bS7RIIGht0YDKWscMbL3h3P/mEmzqKbHP7uPYd8I4WlrU6D+vWcPUkhw+SfZhfS9wFnA98M1BjvtzYFZE9Ej6EjAL+ISkQ8hOlZ0BTAEWSDooIjYPcrwRqVQKfvHgSv7w3Iu0t7XQ1jqGdS92b6kfaNlQ9jVc+t+waTMX3/wwG7tLtLe1cNG7j+CEGXs6QdioVcuprCXgG8A3JO0G7BURg9qtFBE35RbvAN6Vnp8EXBkRXcCjkh4BjgZ+M5jxRqrHntnA4uVrADho0ngeWrX1CWQDLRvKvoZL//NuX8bG7uxW6Ru7S3xs/iJece4x7DdxJ8xGo1rOVrpV0s4pMSwCvi3poiGM4QzghvR8KvBErm55KqsW10xJnZI6V69ePYThDB8r126kFFAK2NDVs+X5YMuGsq/h0n85MZRt7C6xat3GBv1lzRqvlt1Ku0TEWkl/DXw7Ij4jaXF/K0laAOxZpWp2RFyT2swGeoDLy6tVaV91KyUi5gHzADo6OkblAfI9dm5nTJqxce2tW56XDbRsKPsaLv23t7VslSDa21qYNL4ds9FK/e0hknQv8OfAd8k+2H8raXFEHDaogaUPkt2f+tiIeCGVzQKIiC+k5RuBORHR526ljo6O6OzsHEw4w5KPOQxd/z7mYKORpIUR0VGtrpYth88CNwK/TIlhP+DhQQZ0AvAJ4A3lxJBcC1yRdltNAQ4E7hzMWCNZS4t408F7VJytNLbK2TjbXpad7TM0fQ2X/r/5gQ6frWSW1HJA+r+A/8otLwPeOchxLwF2AH4uCeCOiDg7IpZImg/8jmx300d8plLfWlrE9Ak7MX1CoyMxs5Gk3+QgqZ3sVNYZwJadsBFxxkAHjYgD+qibC8wdaN9mZjZ4tfxC+vtkB5aPB24D9gJ80T0zsxGsluRwQER8GtgQEd8F/gL4o/qGZWZmjVRLciif3vG8pEOBXYDpdYvIzMwarpazleZJejnwabKziXYCLqhrVGZm1lC1nK1Uvo7SbcB+9Q3HzMyaQS2Xz9hD0rck3ZCWD5F0Zv1DMzOzRqnlmMN3yH4ENyUtPwR8tE7xmJlZE6glOUyIiPlACSAiesjutWBmZiNULclhg6TdSRfAk/RqYE1dozIzs4aq5Wylj5GdpbS/pF8BE3np/gtmZjYC9ZkcJI0B3pAeB5NdUvvBiOjuaz0zMxve+tytlC56d1JE9ETEkoi4z4nBzGzkq2W30q8kXQL8CNhQLoyIu+oWlZmZNVQtyeG16d/P5soCeNPQh2NmZs2gll9Iv3F7BGJmZs2jll9I/7OkXXPLL5f0+bpGZWZmDVXL7xzeEhHPlxci4jngrYMZVNKFkh6QtFjST8rJR9J0SS9KWpQelw5mHDMzG5haksMYSTuUFySNJbvF52D8HDg0Ig4juxzHrFzd0og4Ij3OHuQ4ZmY2ALUckP4BcLOkb5MdiD4D+O5gBo2Im3KLd+Af1ZmZNZVaDkh/WdJi4DiyH8F9LiJuHMIYziA7TbZsX0l3A2uBT0XE/1RbSdJMYCbAtGnThjAcMzOrZcsB4H6gJyIWSNpR0viI6PM+0pIWkN17utLsiLgmtZkN9ACXp7oVwLSIeEbSkcDVkmZExNrKTiJiHjAPoKOjI2p8HWZmVoN+k4OkD5F9Q98N2B+YClwKHNvXehFxXD/9fhB4G3BsRERapwvoSs8XSloKHAR09vtKzMxsyNRyQPojwJ+S7eYhIh4GJg1mUEknAJ8AToyIF3LlE9P1nJC0H3AgsGwwY5mZ2barZbdSV0RskgSApFbS5bsH4RKyM55+nvq9I52Z9Hrgs5LK94w4OyKeHeRYZma2jWpJDrdJOh8YK+nNwIeBnw5m0Ig4oJfyq4CrBtO3mZkNXi27lT4JrAbuBc4Crgc+Vc+gzMyssWo5lbUk6Wrg6ohYXf+QzMys0XrdclBmjqSngQeAByWtlnTB9gvPzMwaoa/dSh8lO0vpqIjYPSJ2A14F/Kmkv98ewZmZWWP0lRw+ALw3Ih4tF0TEMuB9qc7MzEaovpJDW0Q8XVmYjju01S8kMzNrtL6Sw6YB1pmZ2TDX19lKh0sqXNOI7OJ77XWKx8zMmkCvySEixmzPQMzMrHnU8iM4MzMbZZwczMyswMnBzMwKnBzMzKzAycHMzAqcHMzMrKAhyUHS5yQtlrRI0k2SpuTqZkl6RNKDko5vRHxmZqNdo7YcLoyIwyLiCOA64AIASYcApwEzgBOA/yjfNtTMzLafhiSHiMj/8nocL9129CTgyojoShf8ewQ4envHZ2Y22tVym9C6kDSX7Oqua4A3puKpwB25ZstTWbX1ZwIzAaZNm1a/QM3MRqG6bTlIWiDpviqPkwAiYnZE7A1cDpxTXq1KV1GljIiYFxEdEdExceLE+rwIM7NRqm5bDhFxXI1NrwB+BnyGbEth71zdXsAfhjg0MzPrR6POVjowt3gi2W1IAa4FTpO0g6R9gQOBO7d3fGZmo12jjjl8UdLBQAl4HDgbICKWSJoP/A7oAT4SEZsbFKOZ2ajVkOQQEe/so24uMHc7hmNmZhX8C2kzMytwcjAzswInBzMzK3ByMDOzAicHMzMrcHIwM7MCJwczMytwcjAzswInBzMzK3ByMDOzAicHMzMrcHIwM7MCJwczMytwcjAzswInBzMzK3ByMDOzgkbdJvRzkhZLWiTpJklTUvl0SS+m8kWSLm1EfGZmo12jthwujIjDIuII4Drgglzd0og4Ij3Obkx4ZmajW0OSQ0SszS2OA6IRcZiZWXUNO+Ygaa6kJ4DT2XrLYV9Jd0u6TdIxfaw/U1KnpM7Vq1fXPV4zs9FEEfX50i5pAbBnlarZEXFNrt0soD0iPiNpB2CniHhG0pHA1cCMii2Ngo6Ojujs7BzC6M3MRj5JCyOio1pda70GjYjjamx6BfAz4DMR0QV0pfUXSloKHAT4k9/MbDtq1NlKB+YWTwQeSOUTJY1Jz/cDDgSWbf8IzcxGt7ptOfTji5IOBkrA40D5rKTXA5+V1ANsBs6OiGcbFKOZ2ajVkOQQEe/spfwq4KrtHI6ZmVXwL6TNzKzAycHMzAqcHMzMrMDJwczMCpwczMyswMnBzMwKnBzMzKzAycHMzAqcHMzMrMDJwczMCpwczMyswMnBzMwKnBzMzKzAycHMzAqcHMzMrMDJwczMChp1JzgAJJ0HXAhMjIinU9ks4EyyO8GdGxE31mv8np4SD6xcy/quHgQgaG0REdC9uUSLROuYrZertam1bCj7Kpd1bw6eXb+JqS/fkRmTd6a11fnezAavYclB0t7Am4Hf58oOAU4DZgBTgAWSDoqIzUM9fk9PiRuWrOC5DZu2lLW3tdDWOoZ1L3ZXXR5M2VD2VS7bHOKffrqEjd0l2tta+PzJh3Ly4VOdIMxs0Bq55fBV4OPANbmyk4ArI6ILeFTSI8DRwG+GevAlK9bw8Kr1W5UdNGk8D61a1+vyYMqGsq9y2Xk/voeN3SUANnaX+NTV93HgpJ04fO+X9/q6zcxq0ZCvmJJOBJ6MiHsqqqYCT+SWl6eyan3MlNQpqXP16tXbHMOKNRspBVs9NnT19Lk8mLKh7KtcVk4MZRu7Szy1ZuM2z4WZWaW6bTlIWgDsWaVqNnA+8OfVVqtSFtX6j4h5wDyAjo6Oqm36MnmXsdy/Yu1WZePaWxmj3pcHUzaUfZXL2ttatkoQ7W0t7LlLO2Zmg1W35BARx1Url/RHwL7APZIA9gLuknQ02ZbC3rnmewF/qEd8MybvzO+f3bDVMYcXurqZPmHcln37lcuDKRvKvspln3n7jMIxhxmTdxmK6TGzUU4R2/yle2gDkB4DOiLiaUkzgCvIjjNMAW4GDuzvgHRHR0d0dnZu89gj5mylDZuYustYZkzZxQejzaxmkhZGREe1uoaeylopIpZImg/8DugBPlKPM5XKWltbOHTqrvXq3sxs2Gp4coiI6RXLc4G5jYnGzMzAv5A2M7MqnBzMzKzAycHMzAqcHMzMrKDhp7IOBUmrgccbNPwE4OkGjb0thkOcjnHoDIc4HePQGWic+0TExGoVIyI5NJKkzt7OE24mwyFOxzh0hkOcjnHo1CNO71YyM7MCJwczMytwchi8eY0OoEbDIU7HOHSGQ5yOcegMeZw+5mBmZgXecjAzswInBzMzK3ByqELSZZJWSbovV3aqpCWSSpI6cuXTJb0oaVF6XJqrO1LSvZIekfRvSjewqGOMF0p6QNJiST+RtGuublaK40FJxzdbjI2axz7i/FyKcZGkmyRNydU1y1xWjbGZ3pO5uvMkhaQJubLtPo/bGmczzaWkOZKezMXy1lzd0M9lRPhR8QBeD/wJcF+u7JXAwcCtZPefKJdPz7er6OdO4DVkd7i7AXhLnWP8c6A1Pf8S8KX0/BDgHmAHshstLQXGNFmMDZnHPuLcOff8XODSJpzL3mJsmvdkKt8buJHsh6oTGjmPA4izaeYSmAOcV6VtXebSWw5VRMTtwLMVZfdHxIO19iFpMtl/3t9E9lf6HnBynWO8KSJ60uIdZHfSAzgJuDIiuiLiUeAR4Ogmi7GqesfYR5z5e8iO46Xb1TbTXPYWY1WNiDH5KvDxivgaMo8DiLOqBs5lNXWZSyeHobGvpLsl3SbpmFQ2ley2p2XLU9n2cgbZN4VyLE9UiaWZYoQmm0dJcyU9AZwOXJCLp2nmspcYoUnmUtKJwJMRcU9FVbPNY29xQpPMZXJO2pV4maSX52IZ8rl0chi8FcC0iPhj4GPAFZJ2JtuMq7RdzhuWNJvsTnqXl4t6iaWZYmy6eYyI2RGxd4rxnFTcVHPZS4xNMZeSdgRms3XS2lLdSyzbfR77ibMp5jL5T2B/4IgU11dSeV3m0slhkNKm3DPp+UKy/X0HkWXp/C6TvYA/1DseSR8E3gacnjYlSbHsXSWWpomx2eaxwhXAO9PzpprLnC0xNtFc7k+2D/weZfeK3wu4S9KeNNc89hpnE80lEbEyIjZHRAn4BnB0qqrLXDo5DJKkiZLGpOf7AQcCyyJiBbBO0qvTGQIfAK6pcywnAJ8AToyIF3JV1wKnSdpB0r4pxjubKcZmmscUw4G5xROBB9LzZprLqjE2y1xGxL0RMSkipkd2O+DlwJ9ExFM00Tz2FWezzGUaf3Ju8RSgfCZTfeZyoEfTR/ID+CHZZls32RvlzPTHWA50ASuBG1PbdwJLyM4WuAt4e66fjvQHXApcQvpFeh1jfIRs3+Oi9Lg01352iuNBcmcsNEuMjZrHPuK8Ko25GPgpMLUJ57JqjM30nqyof4x0FlCj5nFb42ymuQS+D9yb/t7XApPrOZe+fIaZmRV4t5KZmRU4OZiZWYGTg5mZFTg5mJlZgZODmZkVODlY01N2lcyv5JbPkzRniPr+jqR3DUVf/YxzqqT7Jd2yDev8uk6xTJT0v+mSEMdI+nA9xrHhzcnBhoMu4B3KXe65GZR/HFWjM4EPR8Qba10hIl470DH7aXcs8EBkl4R4AnBysAInBxsOesjukfv3lRWV3/wlrU///lm6UNp8SQ9J+qKk0yXdqez69vvnujlO0v+kdm9L649Rdu+J36YLnZ2V6/cWSVeQ/SCpMp73pv7vk/SlVHYB8DrgUkkXVrTfSdLNku5K653Uy2vZMmaK7V9S+8WS/ja1e0zSBZJ+CZwq6UMp/nskXSVpR0lHAF8G3ippEdll0/dXdn+ACyVNlnR7Wr5PL11ozkaZ1kYHYFajrwGLJX15G9Y5nOw+HM8Cy4BvRsTRkv4O+Fvgo6nddOANZNfYuUXSAWSXGlgTEUdJ2gH4laSbUvujgUMjuzzyFsputvMl4EjgOeAmSSdHxGclvYnsWvydFTFuBE6JiLVpy+gOSddG8depW8aU9Ddk1wL644jokbRbvr+IeF2KZ/eI+EZ6/nmyXwL/e0pWHRFxjqTpwIyIOCK1+weyX//PTVsfO9Y00zbiODnYsJA+PL9HdlObF2tc7beRXV8GSUuB8of7vUB+9878yC5m9rCkZcAryG5KdFhuq2QXsmvWbCK7bs1WiSE5Crg1IlanMS8nu2nL1X3EKOCfJb0eKJFdUnkP4KmKdvkxjyO77EgPQETkr/v/o9zzQ1NS2BXYiexGNv35LXCZpDbg6ohYVMM6NgJ5t5INJ/9Ktu9+XK6sh/Q+ThcXe1muriv3vJRbLrH1F6PKb+nlyx3/bUQckR77RkQ5uWzoJb6B3CbydGAicGT69r4SaK/SLj+mqsRcrd13gHMi4o+Af+ql361EdpOZ1wNPAt+X9IH+1rGRycnBho30DXk+WYIoe4xsNw5kd8RqG0DXp0pqScch9iO7eNmNwN+kb9BIOkjSuL46Af4XeIOkCWmXzHuB2/pZZxdgVUR0S3ojsE8N8d4EnC2pNcW2Wy/txgMr0ms4vZc261I7Ul/7pHi+AXyL7FaVNgp5t5INN1/hpZvaQHZd+2sk3QncTO/f6vvyINmH+B7A2RGxUdI3yY5F3JW2SFbTzy0WI2KFpFnALWTf7q+PiP4ukXw58FNJnWRXqX2g7+YAfJPsngKLJXWTzcElVdp9mixhPU62K218ZYOIeEbSr5TdyP4Gsit4/mPqdz3ZsRcbhXxVVjMzK/BuJTMzK3ByMDOzAicHMzMrcHIwM7MCJwczMytwcjAzswInBzMzK/g/6R0BHYh4X6gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(x=\"fleet_size\", y=\"optimal_1st_diff\", data=my_df[31:])\n",
    "plt.xlabel('Number of aircrafts')\n",
    "plt.ylabel('Decreased cost')\n",
    "plt.title('Fleet size vs. 1-step decreased cost')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1779,
   "id": "e9aa1da8",
   "metadata": {},
   "outputs": [],
   "source": [
    "#dir(myModel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1762,
   "id": "0c32a5df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 1762,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "myModel.Status"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1763,
   "id": "ba1fdb7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 1763,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GRB.OPTIMAL"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}