Supply Planning Problem.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from pulp import *\n",
    "import numpy as np\n",
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Parameters\n",
    "#### Inbound Costs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>FROM</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>P1</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>P2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>6.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  FROM   D1   D2\n",
       "0   P1  3.0  5.0\n",
       "1   P2  2.3  6.6"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Inbound Costs\n",
    "df_inbound = pd.read_csv('df_inprice.csv', index_col = 0)\n",
    "df_inbound"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Outbound Costs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\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>from</th>\n",
       "      <th>S1</th>\n",
       "      <th>S2</th>\n",
       "      <th>S3</th>\n",
       "      <th>S4</th>\n",
       "      <th>S5</th>\n",
       "      <th>S6</th>\n",
       "      <th>S7</th>\n",
       "      <th>S8</th>\n",
       "      <th>S9</th>\n",
       "      <th>...</th>\n",
       "      <th>S191</th>\n",
       "      <th>S192</th>\n",
       "      <th>S193</th>\n",
       "      <th>S194</th>\n",
       "      <th>S195</th>\n",
       "      <th>S196</th>\n",
       "      <th>S197</th>\n",
       "      <th>S198</th>\n",
       "      <th>S199</th>\n",
       "      <th>S200</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>D1</td>\n",
       "      <td>2.30</td>\n",
       "      <td>4.23</td>\n",
       "      <td>2.26</td>\n",
       "      <td>3.38</td>\n",
       "      <td>1.59</td>\n",
       "      <td>2.01</td>\n",
       "      <td>5.32</td>\n",
       "      <td>6.63</td>\n",
       "      <td>2.38</td>\n",
       "      <td>...</td>\n",
       "      <td>5.86</td>\n",
       "      <td>8.30</td>\n",
       "      <td>3.02</td>\n",
       "      <td>1.01</td>\n",
       "      <td>2.77</td>\n",
       "      <td>2.96</td>\n",
       "      <td>3.53</td>\n",
       "      <td>8.60</td>\n",
       "      <td>2.77</td>\n",
       "      <td>7.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>D2</td>\n",
       "      <td>5.31</td>\n",
       "      <td>2.18</td>\n",
       "      <td>8.52</td>\n",
       "      <td>8.34</td>\n",
       "      <td>4.59</td>\n",
       "      <td>1.04</td>\n",
       "      <td>1.89</td>\n",
       "      <td>6.45</td>\n",
       "      <td>8.35</td>\n",
       "      <td>...</td>\n",
       "      <td>7.54</td>\n",
       "      <td>2.11</td>\n",
       "      <td>4.33</td>\n",
       "      <td>1.54</td>\n",
       "      <td>4.75</td>\n",
       "      <td>7.84</td>\n",
       "      <td>8.21</td>\n",
       "      <td>4.51</td>\n",
       "      <td>3.27</td>\n",
       "      <td>3.13</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 201 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "  from    S1    S2    S3    S4    S5    S6    S7    S8    S9  ...  S191  S192  \\\n",
       "0   D1  2.30  4.23  2.26  3.38  1.59  2.01  5.32  6.63  2.38  ...  5.86  8.30   \n",
       "1   D2  5.31  2.18  8.52  8.34  4.59  1.04  1.89  6.45  8.35  ...  7.54  2.11   \n",
       "\n",
       "   S193  S194  S195  S196  S197  S198  S199  S200  \n",
       "0  3.02  1.01  2.77  2.96  3.53  8.60  2.77  7.06  \n",
       "1  4.33  1.54  4.75  7.84  8.21  4.51  3.27  3.13  \n",
       "\n",
       "[2 rows x 201 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Outbound Costs\n",
    "df_outbound = pd.read_csv('df_outprice.csv', index_col = 0)\n",
    "df_outbound"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "400 records\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\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>index</th>\n",
       "      <th>from</th>\n",
       "      <th>value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>S1</td>\n",
       "      <td>D1</td>\n",
       "      <td>2.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>S2</td>\n",
       "      <td>D1</td>\n",
       "      <td>4.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>S3</td>\n",
       "      <td>D1</td>\n",
       "      <td>2.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>S4</td>\n",
       "      <td>D1</td>\n",
       "      <td>3.38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>S5</td>\n",
       "      <td>D1</td>\n",
       "      <td>1.59</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  index from  value\n",
       "0    S1   D1   2.30\n",
       "1    S2   D1   4.23\n",
       "2    S3   D1   2.26\n",
       "3    S4   D1   3.38\n",
       "4    S5   D1   1.59"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Melting DataFrame\n",
    "df_melt = pd.melt(df_outbound.set_index('from').T.reset_index(), id_vars=['index'], value_vars=['D1', 'D2'])\n",
    "print(\"{:,} records\".format(len(df_melt)))\n",
    "df_melt.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot Outbound Transportation Costs BoxPlot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Td4yh2izldh9J5jHLUi1JkiRtDYbNOX7+FLsfDLwQ+HhniSRJW5WxsTE2zCv2P/KgvqNI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\n1Pj/M1/7MuRMkJMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "plt.figure(figsize=(12, 6))\n",
    "ax = sns.boxplot(x='from', y='value', data=df_melt, color='#99c2a2')\n",
    "# ax = sns.swarmplot(x=\"from\", y=\"value\", data=df_melt, color='#7d0013')\n",
    "plt.xlabel('Distribution Center')\n",
    "plt.ylabel('Outbound Transportation Unit Costs ($/Carton)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Production Plant Capacity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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>plant</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>P1</td>\n",
       "      <td>200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>P2</td>\n",
       "      <td>300</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  plant  max\n",
       "0    P1  200\n",
       "1    P2  300"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Production capacity\n",
    "df_prod = pd.DataFrame({\n",
    "    'plant': ['P1','P2'],\n",
    "    'max': [200, 300],\n",
    "})[['plant', 'max']]\n",
    "df_prod"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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>DC</th>\n",
       "      <th>CAPACITY</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>D1</td>\n",
       "      <td>450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>D2</td>\n",
       "      <td>300</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   DC  CAPACITY\n",
       "0  D1       450\n",
       "1  D2       300"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cross-Docking Capacity\n",
    "df_t = pd.DataFrame({\n",
    "    'DC': ['D1','D2'],\n",
    "    'CAPACITY': [450, 300]\n",
    "})[['DC', 'CAPACITY']]\n",
    "df_t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Demand Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "31,806 total demand\n"
     ]
    },
    {
     "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>STORE</th>\n",
       "      <th>DEMAND</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>D1</td>\n",
       "      <td>244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>D2</td>\n",
       "      <td>172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>D3</td>\n",
       "      <td>124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>D4</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>D5</td>\n",
       "      <td>158</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  STORE  DEMAND\n",
       "0    D1     244\n",
       "1    D2     172\n",
       "2    D3     124\n",
       "3    D4      90\n",
       "4    D5     158"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Demand\n",
    "df_demand = pd.read_csv('df_demand.csv', index_col = 0)\n",
    "print(\"{:,} total demand\".format(df_demand.DEMAND.sum()))\n",
    "df_demand.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Build the Optimization Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal\n",
      "Objective: z* = 217189.3199999999\n"
     ]
    }
   ],
   "source": [
    "# 1. Initiliaze Class\n",
    "model = LpProblem(\"Transhipment_Problem\", LpMinimize)\n",
    "\n",
    "# 2. Define Decision Variables\n",
    "# Inbound Flows\n",
    "I = LpVariable.dicts(\"I\", [(i+1,j+1) for i in range(2) for j in range(2)],\n",
    "                     lowBound=0, upBound=None, cat='Integer') # I(i,j) from plant i for platform j\n",
    "# Outbound Flows\n",
    "O = LpVariable.dicts(\"O\", [(i+1,j+1) for i in range(2) for j in range(200)],\n",
    "                     lowBound=0, upBound=None, cat='Integer') # O(i,j) from platform i for customer j\n",
    "\n",
    "# 3. Define Objective Function\n",
    "# Total Transportation Cost\n",
    "model += lpSum([df_inbound.iloc[i,j+1] * I[i+1,j+1] for i in range(2) for j in range(2)]) + lpSum([df_outbound.iloc[i,j+1] * O[i+1,j+1] for i in range(2) for j in range(200)]) \n",
    "\n",
    "\n",
    "# 4. Define Constraints\n",
    "# Max capacity for plants\n",
    "# for i in range(5):\n",
    "#     model += lpSum([I[i+1, j+1] for j in range(2)]) <= df_prod.loc[i,'max']\n",
    "# Shipment from DCs higher than demand per store\n",
    "for j in range(200):\n",
    "    model += lpSum([O[i+1, j+1] for i in range(2)]) >= df_demand.loc[j,'DEMAND']\n",
    "# Conservation of the flow in the local DC (X-Docking Platform)\n",
    "for p in range(2):\n",
    "    model += lpSum([I[i+1, p+1] for i in range(2)]) == lpSum([O[p+1, j+1] for j in range(200)])\n",
    "# Maximum Inbound Capacity in Platform i\n",
    "# for p in range(2):\n",
    "#     model += lpSum([I[i+1, p+1] for i in range(5)]) <= df_t.loc[p,'capacity']\n",
    "\n",
    "# Solve Model\n",
    "status = model.solve()\n",
    "print(LpStatus[status])\n",
    "print(\"Objective: z* = {}\".format(\n",
    "    value(model.objective)))\n",
    "\n",
    "# Matrix result\n",
    "inbound, outbound = np.zeros([2,2]), np.zeros([2,200])\n",
    "for i in range(2):\n",
    "    for j in range(2):\n",
    "#         print(I[i+1, j+1].varValue, I[i+1, j+1].name)\n",
    "        inbound[i, j] = I[i+1, j+1].varValue\n",
    "for i in range(2):\n",
    "    for j in range(200):\n",
    "#         print(O[i+1, j+1].varValue, O[i+1, j+1].name)\n",
    "        outbound[i, j] = O[i+1, j+1].varValue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "\n",
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       "        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>D1</th>\n",
       "      <th>D2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>P1</th>\n",
       "      <td>0</td>\n",
       "      <td>6232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P2</th>\n",
       "      <td>25574</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       D1    D2\n",
       "P1      0  6232\n",
       "P2  25574     0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Inbound flow\n",
    "df_resin = pd.DataFrame(data = inbound, index =['P' + str(i+1) for i in range(2)], \n",
    "                        columns = ['D' + str(i+1) for i in range(2)]).astype(int)\n",
    "df_resin.to_csv('df_inbound_flow.csv')\n",
    "df_resin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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>D1</th>\n",
       "      <th>D2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>S1</th>\n",
       "      <td>244.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>S2</th>\n",
       "      <td>172.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>S3</th>\n",
       "      <td>124.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>S4</th>\n",
       "      <td>90.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>S5</th>\n",
       "      <td>158.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>S196</th>\n",
       "      <td>57.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>S197</th>\n",
       "      <td>52.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>S198</th>\n",
       "      <td>0.0</td>\n",
       "      <td>243.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>S199</th>\n",
       "      <td>70.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>S200</th>\n",
       "      <td>0.0</td>\n",
       "      <td>50.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>200 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         D1     D2\n",
       "S1    244.0    0.0\n",
       "S2    172.0    0.0\n",
       "S3    124.0    0.0\n",
       "S4     90.0    0.0\n",
       "S5    158.0    0.0\n",
       "...     ...    ...\n",
       "S196   57.0    0.0\n",
       "S197   52.0    0.0\n",
       "S198    0.0  243.0\n",
       "S199   70.0    0.0\n",
       "S200    0.0   50.0\n",
       "\n",
       "[200 rows x 2 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Outbound flow\n",
    "df_resout = pd.DataFrame(data = outbound, index =['D' + str(i+1) for i in range(2)], \n",
    "                        columns = ['S' + str(i+1) for i in range(200)])\n",
    "df_resout.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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