7_אלמוג_דניאל_ניר_שני.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Production Systems Analysis Project\n",
    "Owners: Almog Asraf, Daniel Pidtylok, Nir Levanon, Shani Yorav"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "J = 50 # Numbers of the orders"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating the amount of vegtables, fruits and others from poission destribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9</td>\n",
       "      <td>4</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10</td>\n",
       "      <td>3</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>9</td>\n",
       "      <td>7</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>13</td>\n",
       "      <td>1</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>11</td>\n",
       "      <td>5</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>11</td>\n",
       "      <td>12</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>6</td>\n",
       "      <td>9</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>13</td>\n",
       "      <td>6</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>9</td>\n",
       "      <td>4</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>9</td>\n",
       "      <td>4</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>13</td>\n",
       "      <td>5</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>10</td>\n",
       "      <td>4</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>12</td>\n",
       "      <td>8</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>12</td>\n",
       "      <td>6</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>9</td>\n",
       "      <td>4</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>10</td>\n",
       "      <td>6</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>6</td>\n",
       "      <td>9</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>11</td>\n",
       "      <td>6</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     1   2   3\n",
       "0    6   2  27\n",
       "1    9   4  23\n",
       "2    8   6  18\n",
       "3    9   9  21\n",
       "4   10   3  15\n",
       "5    7   5  16\n",
       "6    9   7  19\n",
       "7   13   1  22\n",
       "8    4   4  20\n",
       "9    3   6  16\n",
       "10   6   5  24\n",
       "11  11   5  19\n",
       "12   3   3  20\n",
       "13   6   4  21\n",
       "14   7   3  23\n",
       "15   4   5  20\n",
       "16   6   6  27\n",
       "17   6   1  18\n",
       "18  11  12  19\n",
       "19   6   7  26\n",
       "20  10   2  13\n",
       "21   7   2  18\n",
       "22   6   7  20\n",
       "23   8   3  14\n",
       "24   6   9  21\n",
       "25   8   0  10\n",
       "26   7   2  21\n",
       "27  13   6  23\n",
       "28   9   4  24\n",
       "29   9   4  27\n",
       "30  13   5  26\n",
       "31   9   2  19\n",
       "32   7   5  28\n",
       "33  10   4  21\n",
       "34   8   7  16\n",
       "35  12   8  19\n",
       "36   5   1  21\n",
       "37   6   7  21\n",
       "38  10   5  19\n",
       "39  12   6  16\n",
       "40   9   4  20\n",
       "41  10   6  19\n",
       "42   6   2  18\n",
       "43   8  10  27\n",
       "44   6   9  20\n",
       "45   5   4  28\n",
       "46   7   4  12\n",
       "47   5   3  14\n",
       "48   7   4  21\n",
       "49  11   6  26"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lamb = [7.5, 5.2, 20] # Lambdas for the poission destribution\n",
    "m = {1:[],2:[],3:[]} # 1: veggies, 2: fruits, 3: other\n",
    "for i in m.keys(): # For each type of order\n",
    "    for j in range(J): # For each order\n",
    "        m[i].append(np.random.poisson(lamb[i-1]))\n",
    "m_df = pd.DataFrame(m) # More easy to work with pandas df\n",
    "m_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating the velocity matrix for each order:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>veg</th>\n",
       "      <th>fru</th>\n",
       "      <th>oth</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.096802</td>\n",
       "      <td>0.260239</td>\n",
       "      <td>0.084746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.063096</td>\n",
       "      <td>0.144620</td>\n",
       "      <td>0.098039</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.071599</td>\n",
       "      <td>0.098811</td>\n",
       "      <td>0.121951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.063096</td>\n",
       "      <td>0.066211</td>\n",
       "      <td>0.106383</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.056277</td>\n",
       "      <td>0.186624</td>\n",
       "      <td>0.142857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.082469</td>\n",
       "      <td>0.117596</td>\n",
       "      <td>0.135135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.063096</td>\n",
       "      <td>0.085027</td>\n",
       "      <td>0.116279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.042135</td>\n",
       "      <td>0.420083</td>\n",
       "      <td>0.102041</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.144956</td>\n",
       "      <td>0.144620</td>\n",
       "      <td>0.111111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.189465</td>\n",
       "      <td>0.098811</td>\n",
       "      <td>0.135135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.096802</td>\n",
       "      <td>0.117596</td>\n",
       "      <td>0.094340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.050697</td>\n",
       "      <td>0.117596</td>\n",
       "      <td>0.116279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.189465</td>\n",
       "      <td>0.186624</td>\n",
       "      <td>0.111111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.096802</td>\n",
       "      <td>0.144620</td>\n",
       "      <td>0.106383</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.082469</td>\n",
       "      <td>0.186624</td>\n",
       "      <td>0.098039</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.144956</td>\n",
       "      <td>0.117596</td>\n",
       "      <td>0.111111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.096802</td>\n",
       "      <td>0.098811</td>\n",
       "      <td>0.084746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.096802</td>\n",
       "      <td>0.420083</td>\n",
       "      <td>0.121951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.050697</td>\n",
       "      <td>0.049400</td>\n",
       "      <td>0.116279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.096802</td>\n",
       "      <td>0.085027</td>\n",
       "      <td>0.087719</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.056277</td>\n",
       "      <td>0.260239</td>\n",
       "      <td>0.161290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.082469</td>\n",
       "      <td>0.260239</td>\n",
       "      <td>0.121951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.096802</td>\n",
       "      <td>0.085027</td>\n",
       "      <td>0.111111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.071599</td>\n",
       "      <td>0.186624</td>\n",
       "      <td>0.151515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.096802</td>\n",
       "      <td>0.066211</td>\n",
       "      <td>0.106383</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.071599</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.082469</td>\n",
       "      <td>0.260239</td>\n",
       "      <td>0.106383</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.042135</td>\n",
       "      <td>0.098811</td>\n",
       "      <td>0.098039</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.063096</td>\n",
       "      <td>0.144620</td>\n",
       "      <td>0.094340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.063096</td>\n",
       "      <td>0.144620</td>\n",
       "      <td>0.084746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>0.042135</td>\n",
       "      <td>0.117596</td>\n",
       "      <td>0.087719</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>0.063096</td>\n",
       "      <td>0.260239</td>\n",
       "      <td>0.116279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>0.082469</td>\n",
       "      <td>0.117596</td>\n",
       "      <td>0.081967</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>0.056277</td>\n",
       "      <td>0.144620</td>\n",
       "      <td>0.106383</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>0.071599</td>\n",
       "      <td>0.085027</td>\n",
       "      <td>0.135135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>0.046054</td>\n",
       "      <td>0.074501</td>\n",
       "      <td>0.116279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>0.116471</td>\n",
       "      <td>0.420083</td>\n",
       "      <td>0.106383</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>0.096802</td>\n",
       "      <td>0.085027</td>\n",
       "      <td>0.106383</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>0.056277</td>\n",
       "      <td>0.117596</td>\n",
       "      <td>0.116279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>0.046054</td>\n",
       "      <td>0.098811</td>\n",
       "      <td>0.135135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>0.063096</td>\n",
       "      <td>0.144620</td>\n",
       "      <td>0.111111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>0.056277</td>\n",
       "      <td>0.098811</td>\n",
       "      <td>0.116279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>0.096802</td>\n",
       "      <td>0.260239</td>\n",
       "      <td>0.121951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>0.071599</td>\n",
       "      <td>0.059520</td>\n",
       "      <td>0.084746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>0.096802</td>\n",
       "      <td>0.066211</td>\n",
       "      <td>0.111111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>0.116471</td>\n",
       "      <td>0.144620</td>\n",
       "      <td>0.081967</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>0.082469</td>\n",
       "      <td>0.144620</td>\n",
       "      <td>0.172414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>0.116471</td>\n",
       "      <td>0.186624</td>\n",
       "      <td>0.151515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>0.082469</td>\n",
       "      <td>0.144620</td>\n",
       "      <td>0.106383</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>0.050697</td>\n",
       "      <td>0.098811</td>\n",
       "      <td>0.087719</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         veg       fru       oth\n",
       "0   0.096802  0.260239  0.084746\n",
       "1   0.063096  0.144620  0.098039\n",
       "2   0.071599  0.098811  0.121951\n",
       "3   0.063096  0.066211  0.106383\n",
       "4   0.056277  0.186624  0.142857\n",
       "5   0.082469  0.117596  0.135135\n",
       "6   0.063096  0.085027  0.116279\n",
       "7   0.042135  0.420083  0.102041\n",
       "8   0.144956  0.144620  0.111111\n",
       "9   0.189465  0.098811  0.135135\n",
       "10  0.096802  0.117596  0.094340\n",
       "11  0.050697  0.117596  0.116279\n",
       "12  0.189465  0.186624  0.111111\n",
       "13  0.096802  0.144620  0.106383\n",
       "14  0.082469  0.186624  0.098039\n",
       "15  0.144956  0.117596  0.111111\n",
       "16  0.096802  0.098811  0.084746\n",
       "17  0.096802  0.420083  0.121951\n",
       "18  0.050697  0.049400  0.116279\n",
       "19  0.096802  0.085027  0.087719\n",
       "20  0.056277  0.260239  0.161290\n",
       "21  0.082469  0.260239  0.121951\n",
       "22  0.096802  0.085027  0.111111\n",
       "23  0.071599  0.186624  0.151515\n",
       "24  0.096802  0.066211  0.106383\n",
       "25  0.071599  1.000000  0.200000\n",
       "26  0.082469  0.260239  0.106383\n",
       "27  0.042135  0.098811  0.098039\n",
       "28  0.063096  0.144620  0.094340\n",
       "29  0.063096  0.144620  0.084746\n",
       "30  0.042135  0.117596  0.087719\n",
       "31  0.063096  0.260239  0.116279\n",
       "32  0.082469  0.117596  0.081967\n",
       "33  0.056277  0.144620  0.106383\n",
       "34  0.071599  0.085027  0.135135\n",
       "35  0.046054  0.074501  0.116279\n",
       "36  0.116471  0.420083  0.106383\n",
       "37  0.096802  0.085027  0.106383\n",
       "38  0.056277  0.117596  0.116279\n",
       "39  0.046054  0.098811  0.135135\n",
       "40  0.063096  0.144620  0.111111\n",
       "41  0.056277  0.098811  0.116279\n",
       "42  0.096802  0.260239  0.121951\n",
       "43  0.071599  0.059520  0.084746\n",
       "44  0.096802  0.066211  0.111111\n",
       "45  0.116471  0.144620  0.081967\n",
       "46  0.082469  0.144620  0.172414\n",
       "47  0.116471  0.186624  0.151515\n",
       "48  0.082469  0.144620  0.106383\n",
       "49  0.050697  0.098811  0.087719"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = {\"veg\":[],\"fru\":[], \"oth\":[]} # A dataframe of collector's velocity\n",
    "for i in v.keys(): # For each type of order\n",
    "    for j in range(J): # For each order\n",
    "        if i == \"veg\":\n",
    "            v[i].append((25/(25+25*m[1][j]))**1.2)\n",
    "        elif i == \"fru\":\n",
    "            v[i].append((25/(25+30*m[2][j]))**1.1)\n",
    "        else:\n",
    "            v[i].append(25/(25+10*m[3][j]))\n",
    "v_df = pd.DataFrame(v) # More easy to work with pandas\n",
    "v_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Definig the length of each shelf:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "len_shelf = 25\n",
    "len_pass = len_shelf*2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Definig the time metrix that takes to do each type of order, by using velpcity matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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>veg</th>\n",
       "      <th>fru</th>\n",
       "      <th>oth</th>\n",
       "      <th>Sum</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>96.065361</td>\n",
       "      <td>590.0</td>\n",
       "      <td>944.325664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>396.223298</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>510.0</td>\n",
       "      <td>1079.089783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>349.165254</td>\n",
       "      <td>253.008578</td>\n",
       "      <td>410.0</td>\n",
       "      <td>1012.173832</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>396.223298</td>\n",
       "      <td>377.581073</td>\n",
       "      <td>470.0</td>\n",
       "      <td>1243.804371</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>444.233423</td>\n",
       "      <td>133.959533</td>\n",
       "      <td>350.0</td>\n",
       "      <td>928.192956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>303.143313</td>\n",
       "      <td>212.592458</td>\n",
       "      <td>370.0</td>\n",
       "      <td>885.735771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>396.223298</td>\n",
       "      <td>294.022555</td>\n",
       "      <td>430.0</td>\n",
       "      <td>1120.245853</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>593.326371</td>\n",
       "      <td>59.512056</td>\n",
       "      <td>490.0</td>\n",
       "      <td>1142.838428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>172.466208</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>450.0</td>\n",
       "      <td>795.332693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>131.950791</td>\n",
       "      <td>253.008578</td>\n",
       "      <td>370.0</td>\n",
       "      <td>754.959369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>212.592458</td>\n",
       "      <td>530.0</td>\n",
       "      <td>1000.852761</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>493.125549</td>\n",
       "      <td>212.592458</td>\n",
       "      <td>430.0</td>\n",
       "      <td>1135.718007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>131.950791</td>\n",
       "      <td>133.959533</td>\n",
       "      <td>450.0</td>\n",
       "      <td>715.910324</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>470.0</td>\n",
       "      <td>901.126788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>303.143313</td>\n",
       "      <td>133.959533</td>\n",
       "      <td>510.0</td>\n",
       "      <td>947.102846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>172.466208</td>\n",
       "      <td>212.592458</td>\n",
       "      <td>450.0</td>\n",
       "      <td>835.058665</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>253.008578</td>\n",
       "      <td>590.0</td>\n",
       "      <td>1101.268882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>59.512056</td>\n",
       "      <td>410.0</td>\n",
       "      <td>727.772360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>493.125549</td>\n",
       "      <td>506.072574</td>\n",
       "      <td>430.0</td>\n",
       "      <td>1429.198123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>294.022555</td>\n",
       "      <td>570.0</td>\n",
       "      <td>1122.282859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>444.233423</td>\n",
       "      <td>96.065361</td>\n",
       "      <td>310.0</td>\n",
       "      <td>850.298784</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>303.143313</td>\n",
       "      <td>96.065361</td>\n",
       "      <td>410.0</td>\n",
       "      <td>809.208674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>294.022555</td>\n",
       "      <td>450.0</td>\n",
       "      <td>1002.282859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>349.165254</td>\n",
       "      <td>133.959533</td>\n",
       "      <td>330.0</td>\n",
       "      <td>813.124787</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>377.581073</td>\n",
       "      <td>470.0</td>\n",
       "      <td>1105.841377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>349.165254</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>250.0</td>\n",
       "      <td>624.165254</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>303.143313</td>\n",
       "      <td>96.065361</td>\n",
       "      <td>470.0</td>\n",
       "      <td>869.208674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>593.326371</td>\n",
       "      <td>253.008578</td>\n",
       "      <td>510.0</td>\n",
       "      <td>1356.334949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>396.223298</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>530.0</td>\n",
       "      <td>1099.089783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>396.223298</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>590.0</td>\n",
       "      <td>1159.089783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>593.326371</td>\n",
       "      <td>212.592458</td>\n",
       "      <td>570.0</td>\n",
       "      <td>1375.918829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>396.223298</td>\n",
       "      <td>96.065361</td>\n",
       "      <td>430.0</td>\n",
       "      <td>922.288659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>303.143313</td>\n",
       "      <td>212.592458</td>\n",
       "      <td>610.0</td>\n",
       "      <td>1125.735771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>444.233423</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>470.0</td>\n",
       "      <td>1087.099908</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>349.165254</td>\n",
       "      <td>294.022555</td>\n",
       "      <td>370.0</td>\n",
       "      <td>1013.187809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>542.840237</td>\n",
       "      <td>335.564848</td>\n",
       "      <td>430.0</td>\n",
       "      <td>1308.405085</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>214.645362</td>\n",
       "      <td>59.512056</td>\n",
       "      <td>470.0</td>\n",
       "      <td>744.157419</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>294.022555</td>\n",
       "      <td>470.0</td>\n",
       "      <td>1022.282859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>444.233423</td>\n",
       "      <td>212.592458</td>\n",
       "      <td>430.0</td>\n",
       "      <td>1086.825881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>542.840237</td>\n",
       "      <td>253.008578</td>\n",
       "      <td>370.0</td>\n",
       "      <td>1165.848815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>396.223298</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>450.0</td>\n",
       "      <td>1019.089783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>444.233423</td>\n",
       "      <td>253.008578</td>\n",
       "      <td>430.0</td>\n",
       "      <td>1127.242002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>96.065361</td>\n",
       "      <td>410.0</td>\n",
       "      <td>764.325664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>349.165254</td>\n",
       "      <td>420.027472</td>\n",
       "      <td>590.0</td>\n",
       "      <td>1359.192726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>377.581073</td>\n",
       "      <td>450.0</td>\n",
       "      <td>1085.841377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>214.645362</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>610.0</td>\n",
       "      <td>997.511847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>303.143313</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>290.0</td>\n",
       "      <td>766.009798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>214.645362</td>\n",
       "      <td>133.959533</td>\n",
       "      <td>330.0</td>\n",
       "      <td>678.604895</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>303.143313</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>470.0</td>\n",
       "      <td>946.009798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>493.125549</td>\n",
       "      <td>253.008578</td>\n",
       "      <td>570.0</td>\n",
       "      <td>1316.134127</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           veg         fru    oth          Sum\n",
       "0   258.260303   96.065361  590.0   944.325664\n",
       "1   396.223298  172.866485  510.0  1079.089783\n",
       "2   349.165254  253.008578  410.0  1012.173832\n",
       "3   396.223298  377.581073  470.0  1243.804371\n",
       "4   444.233423  133.959533  350.0   928.192956\n",
       "5   303.143313  212.592458  370.0   885.735771\n",
       "6   396.223298  294.022555  430.0  1120.245853\n",
       "7   593.326371   59.512056  490.0  1142.838428\n",
       "8   172.466208  172.866485  450.0   795.332693\n",
       "9   131.950791  253.008578  370.0   754.959369\n",
       "10  258.260303  212.592458  530.0  1000.852761\n",
       "11  493.125549  212.592458  430.0  1135.718007\n",
       "12  131.950791  133.959533  450.0   715.910324\n",
       "13  258.260303  172.866485  470.0   901.126788\n",
       "14  303.143313  133.959533  510.0   947.102846\n",
       "15  172.466208  212.592458  450.0   835.058665\n",
       "16  258.260303  253.008578  590.0  1101.268882\n",
       "17  258.260303   59.512056  410.0   727.772360\n",
       "18  493.125549  506.072574  430.0  1429.198123\n",
       "19  258.260303  294.022555  570.0  1122.282859\n",
       "20  444.233423   96.065361  310.0   850.298784\n",
       "21  303.143313   96.065361  410.0   809.208674\n",
       "22  258.260303  294.022555  450.0  1002.282859\n",
       "23  349.165254  133.959533  330.0   813.124787\n",
       "24  258.260303  377.581073  470.0  1105.841377\n",
       "25  349.165254   25.000000  250.0   624.165254\n",
       "26  303.143313   96.065361  470.0   869.208674\n",
       "27  593.326371  253.008578  510.0  1356.334949\n",
       "28  396.223298  172.866485  530.0  1099.089783\n",
       "29  396.223298  172.866485  590.0  1159.089783\n",
       "30  593.326371  212.592458  570.0  1375.918829\n",
       "31  396.223298   96.065361  430.0   922.288659\n",
       "32  303.143313  212.592458  610.0  1125.735771\n",
       "33  444.233423  172.866485  470.0  1087.099908\n",
       "34  349.165254  294.022555  370.0  1013.187809\n",
       "35  542.840237  335.564848  430.0  1308.405085\n",
       "36  214.645362   59.512056  470.0   744.157419\n",
       "37  258.260303  294.022555  470.0  1022.282859\n",
       "38  444.233423  212.592458  430.0  1086.825881\n",
       "39  542.840237  253.008578  370.0  1165.848815\n",
       "40  396.223298  172.866485  450.0  1019.089783\n",
       "41  444.233423  253.008578  430.0  1127.242002\n",
       "42  258.260303   96.065361  410.0   764.325664\n",
       "43  349.165254  420.027472  590.0  1359.192726\n",
       "44  258.260303  377.581073  450.0  1085.841377\n",
       "45  214.645362  172.866485  610.0   997.511847\n",
       "46  303.143313  172.866485  290.0   766.009798\n",
       "47  214.645362  133.959533  330.0   678.604895\n",
       "48  303.143313  172.866485  470.0   946.009798\n",
       "49  493.125549  253.008578  570.0  1316.134127"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = {\"veg\":[],\"fru\":[], \"oth\":[]} # A dataframe of collector's times\n",
    "for i in t.keys(): # For each type of order\n",
    "    for j in range(J): # For each order\n",
    "        if i == \"veg\" or i == \"fru\": # Because veggies and fruits are in the same passage\n",
    "            t[i].append(len_shelf/v_df[i][j])\n",
    "        else: # Because others are in different passege\n",
    "            t[i].append(len_pass/v_df[i][j])\n",
    "t_df = pd.DataFrame(t)\n",
    "t_df['Sum'] = t_df.sum(axis=1) # We will use it later and we will fix it to the real amount of time that will take to do the order\n",
    "t_df       "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question no. 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For more info, look at the docs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "52898.348310016765"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def internal_arrangement(t_df, len_pass): # This function recives a time matrix, and we will use it for q2\n",
    "    c = [0 for i in range(J)] # Definig end time matrix\n",
    "    schedule = [0 for i in range(J)] # Defining the schedule for each order\n",
    "    # Defining clock of the simulation\n",
    "    t_now = 0 \n",
    "    t_prev = 0\n",
    "    for j in range(J): # For each order\n",
    "        if m_df[1][j] > 0 or m_df[2][j] > 0: # If there are fruits or veggies to collect\n",
    "            schedule[j] += t_now # Schedule the order for now\n",
    "            t_prev = t_now \n",
    "            #if m_df[1][j] > 0: # If there are veggies, collect them\n",
    "            t_now += t_df[\"veg\"][j]\n",
    "            #if m_df[2][j] > 0: # if ther are fruits, collect them\n",
    "            t_now += t_df[\"fru\"][j]\n",
    "            if m_df[3][j] > 0: # If there are others, return back and collect them\n",
    "                t_now += len_pass + t_df[\"oth\"][j]\n",
    "            t_df[\"Sum\"][j] = t_now - t_prev # Fixing the sum collumn\n",
    "            c[j] = t_now # Defining the end time of the order after all the collections\n",
    "        else: # There are only others to collect\n",
    "            t_now += t_df[\"oth\"][j]\n",
    "            c[j] = t_now # Defining the end time of the order after all the collections\n",
    "    return c, schedule\n",
    "c,schedule = internal_arrangement(t_df, len_pass)\n",
    "max(c) # The answer to the question"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Translating seconds to hours:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.693985641671324"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(c)/(60*60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The schedule of the orders:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0,\n",
       " 994.3256639047424,\n",
       " 2123.415447131726,\n",
       " 3185.5892795850996,\n",
       " 4479.3936510561525,\n",
       " 5457.586606847561,\n",
       " 6393.322377856478,\n",
       " 7563.568231262441,\n",
       " 8756.406658777803,\n",
       " 9601.739351572161,\n",
       " 10406.69872097187,\n",
       " 11457.551481957753,\n",
       " 12643.269488519756,\n",
       " 13409.179812182854,\n",
       " 14360.306600573607,\n",
       " 15357.409446461495,\n",
       " 16242.468111850983,\n",
       " 17393.736993452447,\n",
       " 18171.509353171503,\n",
       " 19650.70747569745,\n",
       " 20822.990334267182,\n",
       " 21723.289118098477,\n",
       " 22582.497792026254,\n",
       " 23634.780650595985,\n",
       " 24497.90543731275,\n",
       " 25653.74681394757,\n",
       " 26302.912068078527,\n",
       " 27222.120742006304,\n",
       " 28628.455691404073,\n",
       " 29777.545474631057,\n",
       " 30986.63525785804,\n",
       " 32412.55408664023,\n",
       " 33384.842745381204,\n",
       " 34560.57851639012,\n",
       " 35697.678424707425,\n",
       " 36760.86623412907,\n",
       " 38119.27131938403,\n",
       " 38913.42873798982,\n",
       " 39985.71159655955,\n",
       " 41122.53747747199,\n",
       " 42338.386292803225,\n",
       " 43407.47607603021,\n",
       " 44584.71807755823,\n",
       " 45399.04374146297,\n",
       " 46808.2364673477,\n",
       " 47944.07784398252,\n",
       " 48991.589691260015,\n",
       " 49807.5994896738,\n",
       " 50536.20438442539,\n",
       " 51532.214182839176]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "schedule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fixed time matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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>veg</th>\n",
       "      <th>fru</th>\n",
       "      <th>oth</th>\n",
       "      <th>Sum</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>96.065361</td>\n",
       "      <td>590.0</td>\n",
       "      <td>994.325664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>396.223298</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>510.0</td>\n",
       "      <td>1129.089783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>349.165254</td>\n",
       "      <td>253.008578</td>\n",
       "      <td>410.0</td>\n",
       "      <td>1062.173832</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>396.223298</td>\n",
       "      <td>377.581073</td>\n",
       "      <td>470.0</td>\n",
       "      <td>1293.804371</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>444.233423</td>\n",
       "      <td>133.959533</td>\n",
       "      <td>350.0</td>\n",
       "      <td>978.192956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>303.143313</td>\n",
       "      <td>212.592458</td>\n",
       "      <td>370.0</td>\n",
       "      <td>935.735771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>396.223298</td>\n",
       "      <td>294.022555</td>\n",
       "      <td>430.0</td>\n",
       "      <td>1170.245853</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>593.326371</td>\n",
       "      <td>59.512056</td>\n",
       "      <td>490.0</td>\n",
       "      <td>1192.838428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>172.466208</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>450.0</td>\n",
       "      <td>845.332693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>131.950791</td>\n",
       "      <td>253.008578</td>\n",
       "      <td>370.0</td>\n",
       "      <td>804.959369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>212.592458</td>\n",
       "      <td>530.0</td>\n",
       "      <td>1050.852761</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>493.125549</td>\n",
       "      <td>212.592458</td>\n",
       "      <td>430.0</td>\n",
       "      <td>1185.718007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>131.950791</td>\n",
       "      <td>133.959533</td>\n",
       "      <td>450.0</td>\n",
       "      <td>765.910324</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>470.0</td>\n",
       "      <td>951.126788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>303.143313</td>\n",
       "      <td>133.959533</td>\n",
       "      <td>510.0</td>\n",
       "      <td>997.102846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>172.466208</td>\n",
       "      <td>212.592458</td>\n",
       "      <td>450.0</td>\n",
       "      <td>885.058665</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>253.008578</td>\n",
       "      <td>590.0</td>\n",
       "      <td>1151.268882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>59.512056</td>\n",
       "      <td>410.0</td>\n",
       "      <td>777.772360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>493.125549</td>\n",
       "      <td>506.072574</td>\n",
       "      <td>430.0</td>\n",
       "      <td>1479.198123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>294.022555</td>\n",
       "      <td>570.0</td>\n",
       "      <td>1172.282859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>444.233423</td>\n",
       "      <td>96.065361</td>\n",
       "      <td>310.0</td>\n",
       "      <td>900.298784</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>303.143313</td>\n",
       "      <td>96.065361</td>\n",
       "      <td>410.0</td>\n",
       "      <td>859.208674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>294.022555</td>\n",
       "      <td>450.0</td>\n",
       "      <td>1052.282859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>349.165254</td>\n",
       "      <td>133.959533</td>\n",
       "      <td>330.0</td>\n",
       "      <td>863.124787</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>377.581073</td>\n",
       "      <td>470.0</td>\n",
       "      <td>1155.841377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>349.165254</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>250.0</td>\n",
       "      <td>649.165254</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>303.143313</td>\n",
       "      <td>96.065361</td>\n",
       "      <td>470.0</td>\n",
       "      <td>919.208674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>593.326371</td>\n",
       "      <td>253.008578</td>\n",
       "      <td>510.0</td>\n",
       "      <td>1406.334949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>396.223298</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>530.0</td>\n",
       "      <td>1149.089783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>396.223298</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>590.0</td>\n",
       "      <td>1209.089783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>593.326371</td>\n",
       "      <td>212.592458</td>\n",
       "      <td>570.0</td>\n",
       "      <td>1425.918829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>396.223298</td>\n",
       "      <td>96.065361</td>\n",
       "      <td>430.0</td>\n",
       "      <td>972.288659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>303.143313</td>\n",
       "      <td>212.592458</td>\n",
       "      <td>610.0</td>\n",
       "      <td>1175.735771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>444.233423</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>470.0</td>\n",
       "      <td>1137.099908</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>349.165254</td>\n",
       "      <td>294.022555</td>\n",
       "      <td>370.0</td>\n",
       "      <td>1063.187809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>542.840237</td>\n",
       "      <td>335.564848</td>\n",
       "      <td>430.0</td>\n",
       "      <td>1358.405085</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>214.645362</td>\n",
       "      <td>59.512056</td>\n",
       "      <td>470.0</td>\n",
       "      <td>794.157419</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>294.022555</td>\n",
       "      <td>470.0</td>\n",
       "      <td>1072.282859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>444.233423</td>\n",
       "      <td>212.592458</td>\n",
       "      <td>430.0</td>\n",
       "      <td>1136.825881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>542.840237</td>\n",
       "      <td>253.008578</td>\n",
       "      <td>370.0</td>\n",
       "      <td>1215.848815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>396.223298</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>450.0</td>\n",
       "      <td>1069.089783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>444.233423</td>\n",
       "      <td>253.008578</td>\n",
       "      <td>430.0</td>\n",
       "      <td>1177.242002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>96.065361</td>\n",
       "      <td>410.0</td>\n",
       "      <td>814.325664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>349.165254</td>\n",
       "      <td>420.027472</td>\n",
       "      <td>590.0</td>\n",
       "      <td>1409.192726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>258.260303</td>\n",
       "      <td>377.581073</td>\n",
       "      <td>450.0</td>\n",
       "      <td>1135.841377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>214.645362</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>610.0</td>\n",
       "      <td>1047.511847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>303.143313</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>290.0</td>\n",
       "      <td>816.009798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>214.645362</td>\n",
       "      <td>133.959533</td>\n",
       "      <td>330.0</td>\n",
       "      <td>728.604895</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>303.143313</td>\n",
       "      <td>172.866485</td>\n",
       "      <td>470.0</td>\n",
       "      <td>996.009798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>493.125549</td>\n",
       "      <td>253.008578</td>\n",
       "      <td>570.0</td>\n",
       "      <td>1366.134127</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           veg         fru    oth          Sum\n",
       "0   258.260303   96.065361  590.0   994.325664\n",
       "1   396.223298  172.866485  510.0  1129.089783\n",
       "2   349.165254  253.008578  410.0  1062.173832\n",
       "3   396.223298  377.581073  470.0  1293.804371\n",
       "4   444.233423  133.959533  350.0   978.192956\n",
       "5   303.143313  212.592458  370.0   935.735771\n",
       "6   396.223298  294.022555  430.0  1170.245853\n",
       "7   593.326371   59.512056  490.0  1192.838428\n",
       "8   172.466208  172.866485  450.0   845.332693\n",
       "9   131.950791  253.008578  370.0   804.959369\n",
       "10  258.260303  212.592458  530.0  1050.852761\n",
       "11  493.125549  212.592458  430.0  1185.718007\n",
       "12  131.950791  133.959533  450.0   765.910324\n",
       "13  258.260303  172.866485  470.0   951.126788\n",
       "14  303.143313  133.959533  510.0   997.102846\n",
       "15  172.466208  212.592458  450.0   885.058665\n",
       "16  258.260303  253.008578  590.0  1151.268882\n",
       "17  258.260303   59.512056  410.0   777.772360\n",
       "18  493.125549  506.072574  430.0  1479.198123\n",
       "19  258.260303  294.022555  570.0  1172.282859\n",
       "20  444.233423   96.065361  310.0   900.298784\n",
       "21  303.143313   96.065361  410.0   859.208674\n",
       "22  258.260303  294.022555  450.0  1052.282859\n",
       "23  349.165254  133.959533  330.0   863.124787\n",
       "24  258.260303  377.581073  470.0  1155.841377\n",
       "25  349.165254   25.000000  250.0   649.165254\n",
       "26  303.143313   96.065361  470.0   919.208674\n",
       "27  593.326371  253.008578  510.0  1406.334949\n",
       "28  396.223298  172.866485  530.0  1149.089783\n",
       "29  396.223298  172.866485  590.0  1209.089783\n",
       "30  593.326371  212.592458  570.0  1425.918829\n",
       "31  396.223298   96.065361  430.0   972.288659\n",
       "32  303.143313  212.592458  610.0  1175.735771\n",
       "33  444.233423  172.866485  470.0  1137.099908\n",
       "34  349.165254  294.022555  370.0  1063.187809\n",
       "35  542.840237  335.564848  430.0  1358.405085\n",
       "36  214.645362   59.512056  470.0   794.157419\n",
       "37  258.260303  294.022555  470.0  1072.282859\n",
       "38  444.233423  212.592458  430.0  1136.825881\n",
       "39  542.840237  253.008578  370.0  1215.848815\n",
       "40  396.223298  172.866485  450.0  1069.089783\n",
       "41  444.233423  253.008578  430.0  1177.242002\n",
       "42  258.260303   96.065361  410.0   814.325664\n",
       "43  349.165254  420.027472  590.0  1409.192726\n",
       "44  258.260303  377.581073  450.0  1135.841377\n",
       "45  214.645362  172.866485  610.0  1047.511847\n",
       "46  303.143313  172.866485  290.0   816.009798\n",
       "47  214.645362  133.959533  330.0   728.604895\n",
       "48  303.143313  172.866485  470.0   996.009798\n",
       "49  493.125549  253.008578  570.0  1366.134127"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question no. 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For more info, look at the docs:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Definig the waiting time of all the orders:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = [0 for i in range(J)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Defining the spt algoritem function, we will use it also at question no. 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c[i]:  649.1652541309559\n",
      "t_df['Sum'][index]:  649.1652541309559\n",
      "c[i]:  1377.7701488825514\n",
      "t_df['Sum'][index]:  728.6048947515956\n",
      "c[i]:  2143.6804725456495\n",
      "t_df['Sum'][index]:  765.9103236630981\n",
      "c[i]:  2921.4528322647056\n",
      "t_df['Sum'][index]:  777.7723597190561\n",
      "c[i]:  3715.610250870497\n",
      "t_df['Sum'][index]:  794.1574186057915\n",
      "c[i]:  4520.569620270206\n",
      "t_df['Sum'][index]:  804.9593693997085\n",
      "c[i]:  5334.895284174945\n",
      "t_df['Sum'][index]:  814.3256639047395\n",
      "c[i]:  6150.905082588728\n",
      "t_df['Sum'][index]:  816.0097984137828\n",
      "c[i]:  6996.237775383086\n",
      "t_df['Sum'][index]:  845.3326927943581\n",
      "c[i]:  7855.446449310863\n",
      "t_df['Sum'][index]:  859.2086739277765\n",
      "c[i]:  8718.571236027628\n",
      "t_df['Sum'][index]:  863.1247867167658\n",
      "c[i]:  9603.629901417116\n",
      "t_df['Sum'][index]:  885.0586653894879\n",
      "c[i]:  10503.928685248411\n",
      "t_df['Sum'][index]:  900.2987838312947\n",
      "c[i]:  11423.137359176188\n",
      "t_df['Sum'][index]:  919.2086739277765\n",
      "c[i]:  12358.873130185104\n",
      "t_df['Sum'][index]:  935.7357710089173\n",
      "c[i]:  13309.999918575857\n",
      "t_df['Sum'][index]:  951.1267883907531\n",
      "c[i]:  14282.288577316831\n",
      "t_df['Sum'][index]:  972.2886587409739\n",
      "c[i]:  15260.48153310824\n",
      "t_df['Sum'][index]:  978.1929557914082\n",
      "c[i]:  16254.807197012982\n",
      "t_df['Sum'][index]:  994.3256639047424\n",
      "c[i]:  17250.816995426765\n",
      "t_df['Sum'][index]:  996.0097984137828\n",
      "c[i]:  18247.91984131465\n",
      "t_df['Sum'][index]:  997.1028458878882\n",
      "c[i]:  19295.431688592143\n",
      "t_df['Sum'][index]:  1047.511847277492\n",
      "c[i]:  20346.284449578026\n",
      "t_df['Sum'][index]:  1050.852760985883\n",
      "c[i]:  21398.567308147758\n",
      "t_df['Sum'][index]:  1052.2828585697316\n",
      "c[i]:  22460.74114060113\n",
      "t_df['Sum'][index]:  1062.1738324533735\n",
      "c[i]:  23523.928950022775\n",
      "t_df['Sum'][index]:  1063.1878094216445\n",
      "c[i]:  24593.01873324976\n",
      "t_df['Sum'][index]:  1069.0897832269839\n",
      "c[i]:  25665.301591819487\n",
      "t_df['Sum'][index]:  1072.282858569728\n",
      "c[i]:  26794.39137504647\n",
      "t_df['Sum'][index]:  1129.0897832269836\n",
      "c[i]:  27930.232751681295\n",
      "t_df['Sum'][index]:  1135.841376634824\n",
      "c[i]:  29067.058632593733\n",
      "t_df['Sum'][index]:  1136.8258809124382\n",
      "c[i]:  30204.15854091104\n",
      "t_df['Sum'][index]:  1137.0999083173083\n",
      "c[i]:  31353.248324138025\n",
      "t_df['Sum'][index]:  1149.0897832269839\n",
      "c[i]:  32504.51720573949\n",
      "t_df['Sum'][index]:  1151.2688816014634\n",
      "c[i]:  33660.358582374305\n",
      "t_df['Sum'][index]:  1155.8413766348203\n",
      "c[i]:  34830.60443578027\n",
      "t_df['Sum'][index]:  1170.2458534059633\n",
      "c[i]:  36002.88729435\n",
      "t_df['Sum'][index]:  1172.2828585697316\n",
      "c[i]:  37178.623065358915\n",
      "t_df['Sum'][index]:  1175.7357710089127\n",
      "c[i]:  38355.86506688694\n",
      "t_df['Sum'][index]:  1177.2420015280222\n",
      "c[i]:  39541.58307344894\n",
      "t_df['Sum'][index]:  1185.7180065620032\n",
      "c[i]:  40734.42150096431\n",
      "t_df['Sum'][index]:  1192.8384275153621\n",
      "c[i]:  41943.51128419129\n",
      "t_df['Sum'][index]:  1209.0897832269839\n",
      "c[i]:  43159.36009952253\n",
      "t_df['Sum'][index]:  1215.8488153312355\n",
      "c[i]:  44453.16447099358\n",
      "t_df['Sum'][index]:  1293.804371471053\n",
      "c[i]:  45811.56955624854\n",
      "t_df['Sum'][index]:  1358.4050852549626\n",
      "c[i]:  47177.70368342613\n",
      "t_df['Sum'][index]:  1366.134127177589\n",
      "c[i]:  48584.0386328239\n",
      "t_df['Sum'][index]:  1406.3349493977694\n",
      "c[i]:  49993.231358708625\n",
      "t_df['Sum'][index]:  1409.1927258847281\n",
      "c[i]:  51419.15018749081\n",
      "t_df['Sum'][index]:  1425.918828782189\n",
      "c[i]:  52898.348310016765\n",
      "t_df['Sum'][index]:  1479.1981225259478\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[15260.48153310824,\n",
       " 25665.301591819487,\n",
       " 21398.567308147758,\n",
       " 43159.36009952253,\n",
       " 14282.288577316831,\n",
       " 11423.137359176188,\n",
       " 33660.358582374305,\n",
       " 39541.58307344894,\n",
       " 6150.905082588728,\n",
       " 3715.610250870497,\n",
       " 19295.431688592143,\n",
       " 38355.86506688694,\n",
       " 1377.7701488825514,\n",
       " 12358.873130185104,\n",
       " 17250.816995426765,\n",
       " 8718.571236027628,\n",
       " 31353.248324138025,\n",
       " 2143.6804725456495,\n",
       " 51419.15018749081,\n",
       " 34830.60443578027,\n",
       " 9603.629901417116,\n",
       " 6996.237775383086,\n",
       " 20346.284449578026,\n",
       " 7855.446449310863,\n",
       " 32504.51720573949,\n",
       " 0,\n",
       " 10503.928685248411,\n",
       " 47177.70368342613,\n",
       " 30204.15854091104,\n",
       " 40734.42150096431,\n",
       " 49993.231358708625,\n",
       " 13309.999918575857,\n",
       " 36002.88729435,\n",
       " 29067.058632593733,\n",
       " 22460.74114060113,\n",
       " 44453.16447099358,\n",
       " 2921.4528322647056,\n",
       " 24593.01873324976,\n",
       " 27930.232751681295,\n",
       " 41943.51128419129,\n",
       " 23523.928950022775,\n",
       " 37178.623065358915,\n",
       " 4520.569620270206,\n",
       " 48584.0386328239,\n",
       " 26794.39137504647,\n",
       " 18247.91984131465,\n",
       " 5334.895284174945,\n",
       " 649.1652541309559,\n",
       " 16254.807197012982,\n",
       " 45811.56955624854]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def spt_algo(t_df):\n",
    "    t_now = 0\n",
    "    #t_prev = t_now\n",
    "    t_copy = t_df[\"Sum\"].copy() # Creating a copy of the fixed sum column, because we don't want to lose this info\n",
    "    schedule = [0 for i in range(J)] # Defining the schedule for each order\n",
    "    c = [0 for i in range(J)] # Definig end time matrix, only for proving a point\n",
    "    for i in range(J): # For each order\n",
    "        #t_prev = t_now\n",
    "        index = t_copy.idxmin() # Pull the id of the minimal processing time\n",
    "        schedule[index] += t_now # Scheduling the shortest order for current time\n",
    "        t_now += t_copy[index] # Moving the sim clock to the end of the order\n",
    "        c[i] = t_now # Definig the end time of the order\n",
    "        w[i] = c[i] - t_df[\"Sum\"][index] # Calculating the waiting time: end time - processing time\n",
    "        print(\"c[i]: \",c[i])\n",
    "        print(\"t_df['Sum'][index]: \", t_df[\"Sum\"][index])\n",
    "        t_copy[index] = None # \"Deleting\" the minimal processing time, so we can find the next minimal time\n",
    "    return schedule, c, w\n",
    "sche_spt,c_spt, w = spt_algo(t_df)\n",
    "sche_spt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: We will use sche_spt in question 3."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The waiting time matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.0,\n",
       " 649.1652541309559,\n",
       " 1377.7701488825514,\n",
       " 2143.6804725456495,\n",
       " 2921.4528322647056,\n",
       " 3715.610250870497,\n",
       " 4520.569620270206,\n",
       " 5334.895284174945,\n",
       " 6150.905082588728,\n",
       " 6996.237775383086,\n",
       " 7855.446449310863,\n",
       " 8718.571236027628,\n",
       " 9603.629901417116,\n",
       " 10503.928685248411,\n",
       " 11423.137359176188,\n",
       " 12358.873130185104,\n",
       " 13309.999918575857,\n",
       " 14282.288577316831,\n",
       " 15260.48153310824,\n",
       " 16254.807197012982,\n",
       " 17250.816995426765,\n",
       " 18247.91984131465,\n",
       " 19295.431688592143,\n",
       " 20346.284449578026,\n",
       " 21398.567308147758,\n",
       " 22460.74114060113,\n",
       " 23523.928950022775,\n",
       " 24593.01873324976,\n",
       " 25665.301591819487,\n",
       " 26794.39137504647,\n",
       " 27930.232751681295,\n",
       " 29067.058632593733,\n",
       " 30204.15854091104,\n",
       " 31353.248324138025,\n",
       " 32504.517205739485,\n",
       " 33660.358582374305,\n",
       " 34830.604435780275,\n",
       " 36002.88729435,\n",
       " 37178.623065358915,\n",
       " 38355.86506688694,\n",
       " 39541.58307344894,\n",
       " 40734.42150096431,\n",
       " 41943.51128419129,\n",
       " 43159.36009952253,\n",
       " 44453.16447099358,\n",
       " 45811.56955624854,\n",
       " 47177.70368342612,\n",
       " 48584.0386328239,\n",
       " 49993.231358708625,\n",
       " 51419.15018749081]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The proof that c isn't dependent on the scheduling of the order:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "52898.348310016765"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(c_spt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The average waiting time for order:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23137.262810598444"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(w)/J"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question no. 3\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we will calculate v and t for the new collector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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>veg</th>\n",
       "      <th>fru</th>\n",
       "      <th>oth</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.111322</td>\n",
       "      <td>0.299275</td>\n",
       "      <td>0.097458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.072560</td>\n",
       "      <td>0.166313</td>\n",
       "      <td>0.112745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.082339</td>\n",
       "      <td>0.113633</td>\n",
       "      <td>0.140244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.072560</td>\n",
       "      <td>0.076143</td>\n",
       "      <td>0.122340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.064718</td>\n",
       "      <td>0.214617</td>\n",
       "      <td>0.164286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.094840</td>\n",
       "      <td>0.135235</td>\n",
       "      <td>0.155405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.072560</td>\n",
       "      <td>0.097782</td>\n",
       "      <td>0.133721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.048456</td>\n",
       "      <td>0.483095</td>\n",
       "      <td>0.117347</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.166699</td>\n",
       "      <td>0.166313</td>\n",
       "      <td>0.127778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.217884</td>\n",
       "      <td>0.113633</td>\n",
       "      <td>0.155405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.111322</td>\n",
       "      <td>0.135235</td>\n",
       "      <td>0.108491</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.058302</td>\n",
       "      <td>0.135235</td>\n",
       "      <td>0.133721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.217884</td>\n",
       "      <td>0.214617</td>\n",
       "      <td>0.127778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.111322</td>\n",
       "      <td>0.166313</td>\n",
       "      <td>0.122340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.094840</td>\n",
       "      <td>0.214617</td>\n",
       "      <td>0.112745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.166699</td>\n",
       "      <td>0.135235</td>\n",
       "      <td>0.127778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.111322</td>\n",
       "      <td>0.113633</td>\n",
       "      <td>0.097458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.111322</td>\n",
       "      <td>0.483095</td>\n",
       "      <td>0.140244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.058302</td>\n",
       "      <td>0.056810</td>\n",
       "      <td>0.133721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.111322</td>\n",
       "      <td>0.097782</td>\n",
       "      <td>0.100877</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.064718</td>\n",
       "      <td>0.299275</td>\n",
       "      <td>0.185484</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.094840</td>\n",
       "      <td>0.299275</td>\n",
       "      <td>0.140244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.111322</td>\n",
       "      <td>0.097782</td>\n",
       "      <td>0.127778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.082339</td>\n",
       "      <td>0.214617</td>\n",
       "      <td>0.174242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.111322</td>\n",
       "      <td>0.076143</td>\n",
       "      <td>0.122340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.082339</td>\n",
       "      <td>1.150000</td>\n",
       "      <td>0.230000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.094840</td>\n",
       "      <td>0.299275</td>\n",
       "      <td>0.122340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.048456</td>\n",
       "      <td>0.113633</td>\n",
       "      <td>0.112745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.072560</td>\n",
       "      <td>0.166313</td>\n",
       "      <td>0.108491</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.072560</td>\n",
       "      <td>0.166313</td>\n",
       "      <td>0.097458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>0.048456</td>\n",
       "      <td>0.135235</td>\n",
       "      <td>0.100877</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>0.072560</td>\n",
       "      <td>0.299275</td>\n",
       "      <td>0.133721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>0.094840</td>\n",
       "      <td>0.135235</td>\n",
       "      <td>0.094262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>0.064718</td>\n",
       "      <td>0.166313</td>\n",
       "      <td>0.122340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>0.082339</td>\n",
       "      <td>0.097782</td>\n",
       "      <td>0.155405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>0.052962</td>\n",
       "      <td>0.085676</td>\n",
       "      <td>0.133721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>0.133942</td>\n",
       "      <td>0.483095</td>\n",
       "      <td>0.122340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>0.111322</td>\n",
       "      <td>0.097782</td>\n",
       "      <td>0.122340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>0.064718</td>\n",
       "      <td>0.135235</td>\n",
       "      <td>0.133721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>0.052962</td>\n",
       "      <td>0.113633</td>\n",
       "      <td>0.155405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>0.072560</td>\n",
       "      <td>0.166313</td>\n",
       "      <td>0.127778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>0.064718</td>\n",
       "      <td>0.113633</td>\n",
       "      <td>0.133721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>0.111322</td>\n",
       "      <td>0.299275</td>\n",
       "      <td>0.140244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>0.082339</td>\n",
       "      <td>0.068448</td>\n",
       "      <td>0.097458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>0.111322</td>\n",
       "      <td>0.076143</td>\n",
       "      <td>0.127778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>0.133942</td>\n",
       "      <td>0.166313</td>\n",
       "      <td>0.094262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>0.094840</td>\n",
       "      <td>0.166313</td>\n",
       "      <td>0.198276</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>0.133942</td>\n",
       "      <td>0.214617</td>\n",
       "      <td>0.174242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>0.094840</td>\n",
       "      <td>0.166313</td>\n",
       "      <td>0.122340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>0.058302</td>\n",
       "      <td>0.113633</td>\n",
       "      <td>0.100877</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         veg       fru       oth\n",
       "0   0.111322  0.299275  0.097458\n",
       "1   0.072560  0.166313  0.112745\n",
       "2   0.082339  0.113633  0.140244\n",
       "3   0.072560  0.076143  0.122340\n",
       "4   0.064718  0.214617  0.164286\n",
       "5   0.094840  0.135235  0.155405\n",
       "6   0.072560  0.097782  0.133721\n",
       "7   0.048456  0.483095  0.117347\n",
       "8   0.166699  0.166313  0.127778\n",
       "9   0.217884  0.113633  0.155405\n",
       "10  0.111322  0.135235  0.108491\n",
       "11  0.058302  0.135235  0.133721\n",
       "12  0.217884  0.214617  0.127778\n",
       "13  0.111322  0.166313  0.122340\n",
       "14  0.094840  0.214617  0.112745\n",
       "15  0.166699  0.135235  0.127778\n",
       "16  0.111322  0.113633  0.097458\n",
       "17  0.111322  0.483095  0.140244\n",
       "18  0.058302  0.056810  0.133721\n",
       "19  0.111322  0.097782  0.100877\n",
       "20  0.064718  0.299275  0.185484\n",
       "21  0.094840  0.299275  0.140244\n",
       "22  0.111322  0.097782  0.127778\n",
       "23  0.082339  0.214617  0.174242\n",
       "24  0.111322  0.076143  0.122340\n",
       "25  0.082339  1.150000  0.230000\n",
       "26  0.094840  0.299275  0.122340\n",
       "27  0.048456  0.113633  0.112745\n",
       "28  0.072560  0.166313  0.108491\n",
       "29  0.072560  0.166313  0.097458\n",
       "30  0.048456  0.135235  0.100877\n",
       "31  0.072560  0.299275  0.133721\n",
       "32  0.094840  0.135235  0.094262\n",
       "33  0.064718  0.166313  0.122340\n",
       "34  0.082339  0.097782  0.155405\n",
       "35  0.052962  0.085676  0.133721\n",
       "36  0.133942  0.483095  0.122340\n",
       "37  0.111322  0.097782  0.122340\n",
       "38  0.064718  0.135235  0.133721\n",
       "39  0.052962  0.113633  0.155405\n",
       "40  0.072560  0.166313  0.127778\n",
       "41  0.064718  0.113633  0.133721\n",
       "42  0.111322  0.299275  0.140244\n",
       "43  0.082339  0.068448  0.097458\n",
       "44  0.111322  0.076143  0.127778\n",
       "45  0.133942  0.166313  0.094262\n",
       "46  0.094840  0.166313  0.198276\n",
       "47  0.133942  0.214617  0.174242\n",
       "48  0.094840  0.166313  0.122340\n",
       "49  0.058302  0.113633  0.100877"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v2_df = v_df.copy()\n",
    "v2_df = v2_df*1.15\n",
    "v2_df"
   ]
  },
  {
   "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>veg</th>\n",
       "      <th>fru</th>\n",
       "      <th>oth</th>\n",
       "      <th>Sum</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>83.535096</td>\n",
       "      <td>513.043478</td>\n",
       "      <td>821.152751</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>344.541998</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>443.478261</td>\n",
       "      <td>938.338942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>303.621960</td>\n",
       "      <td>220.007459</td>\n",
       "      <td>356.521739</td>\n",
       "      <td>880.151159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>344.541998</td>\n",
       "      <td>328.331368</td>\n",
       "      <td>408.695652</td>\n",
       "      <td>1081.569019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>386.289933</td>\n",
       "      <td>116.486550</td>\n",
       "      <td>304.347826</td>\n",
       "      <td>807.124309</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>263.602881</td>\n",
       "      <td>184.863007</td>\n",
       "      <td>321.739130</td>\n",
       "      <td>770.205018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>344.541998</td>\n",
       "      <td>255.671787</td>\n",
       "      <td>373.913043</td>\n",
       "      <td>974.126829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>515.935975</td>\n",
       "      <td>51.749614</td>\n",
       "      <td>426.086957</td>\n",
       "      <td>993.772546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>149.970615</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>391.304348</td>\n",
       "      <td>691.593646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>114.739818</td>\n",
       "      <td>220.007459</td>\n",
       "      <td>321.739130</td>\n",
       "      <td>656.486408</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>184.863007</td>\n",
       "      <td>460.869565</td>\n",
       "      <td>870.306749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>428.804825</td>\n",
       "      <td>184.863007</td>\n",
       "      <td>373.913043</td>\n",
       "      <td>987.580875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>114.739818</td>\n",
       "      <td>116.486550</td>\n",
       "      <td>391.304348</td>\n",
       "      <td>622.530716</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>408.695652</td>\n",
       "      <td>783.588512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>263.602881</td>\n",
       "      <td>116.486550</td>\n",
       "      <td>443.478261</td>\n",
       "      <td>823.567692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>149.970615</td>\n",
       "      <td>184.863007</td>\n",
       "      <td>391.304348</td>\n",
       "      <td>726.137970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>220.007459</td>\n",
       "      <td>513.043478</td>\n",
       "      <td>957.625114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>51.749614</td>\n",
       "      <td>356.521739</td>\n",
       "      <td>632.845530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>428.804825</td>\n",
       "      <td>440.063108</td>\n",
       "      <td>373.913043</td>\n",
       "      <td>1242.780976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>255.671787</td>\n",
       "      <td>495.652174</td>\n",
       "      <td>975.898138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>386.289933</td>\n",
       "      <td>83.535096</td>\n",
       "      <td>269.565217</td>\n",
       "      <td>739.390247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>263.602881</td>\n",
       "      <td>83.535096</td>\n",
       "      <td>356.521739</td>\n",
       "      <td>703.659716</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>255.671787</td>\n",
       "      <td>391.304348</td>\n",
       "      <td>871.550312</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>303.621960</td>\n",
       "      <td>116.486550</td>\n",
       "      <td>286.956522</td>\n",
       "      <td>707.065032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>328.331368</td>\n",
       "      <td>408.695652</td>\n",
       "      <td>961.601197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>303.621960</td>\n",
       "      <td>21.739130</td>\n",
       "      <td>217.391304</td>\n",
       "      <td>542.752395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>263.602881</td>\n",
       "      <td>83.535096</td>\n",
       "      <td>408.695652</td>\n",
       "      <td>755.833630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>515.935975</td>\n",
       "      <td>220.007459</td>\n",
       "      <td>443.478261</td>\n",
       "      <td>1179.421695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>344.541998</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>460.869565</td>\n",
       "      <td>955.730246</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>344.541998</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>513.043478</td>\n",
       "      <td>1007.904159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>515.935975</td>\n",
       "      <td>184.863007</td>\n",
       "      <td>495.652174</td>\n",
       "      <td>1196.451155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>344.541998</td>\n",
       "      <td>83.535096</td>\n",
       "      <td>373.913043</td>\n",
       "      <td>801.990138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>263.602881</td>\n",
       "      <td>184.863007</td>\n",
       "      <td>530.434783</td>\n",
       "      <td>978.900670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>386.289933</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>408.695652</td>\n",
       "      <td>945.304268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>303.621960</td>\n",
       "      <td>255.671787</td>\n",
       "      <td>321.739130</td>\n",
       "      <td>881.032878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>472.034989</td>\n",
       "      <td>291.795520</td>\n",
       "      <td>373.913043</td>\n",
       "      <td>1137.743552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>186.648141</td>\n",
       "      <td>51.749614</td>\n",
       "      <td>408.695652</td>\n",
       "      <td>647.093407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>255.671787</td>\n",
       "      <td>408.695652</td>\n",
       "      <td>888.941616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>386.289933</td>\n",
       "      <td>184.863007</td>\n",
       "      <td>373.913043</td>\n",
       "      <td>945.065983</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>472.034989</td>\n",
       "      <td>220.007459</td>\n",
       "      <td>321.739130</td>\n",
       "      <td>1013.781579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>344.541998</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>391.304348</td>\n",
       "      <td>886.165029</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>386.289933</td>\n",
       "      <td>220.007459</td>\n",
       "      <td>373.913043</td>\n",
       "      <td>980.210436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>83.535096</td>\n",
       "      <td>356.521739</td>\n",
       "      <td>664.631012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>303.621960</td>\n",
       "      <td>365.241280</td>\n",
       "      <td>513.043478</td>\n",
       "      <td>1181.906718</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>328.331368</td>\n",
       "      <td>391.304348</td>\n",
       "      <td>944.209893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>186.648141</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>530.434783</td>\n",
       "      <td>867.401606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>263.602881</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>252.173913</td>\n",
       "      <td>666.095477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>186.648141</td>\n",
       "      <td>116.486550</td>\n",
       "      <td>286.956522</td>\n",
       "      <td>590.091213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>263.602881</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>408.695652</td>\n",
       "      <td>822.617216</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>428.804825</td>\n",
       "      <td>220.007459</td>\n",
       "      <td>495.652174</td>\n",
       "      <td>1144.464458</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           veg         fru         oth          Sum\n",
       "0   224.574177   83.535096  513.043478   821.152751\n",
       "1   344.541998  150.318683  443.478261   938.338942\n",
       "2   303.621960  220.007459  356.521739   880.151159\n",
       "3   344.541998  328.331368  408.695652  1081.569019\n",
       "4   386.289933  116.486550  304.347826   807.124309\n",
       "5   263.602881  184.863007  321.739130   770.205018\n",
       "6   344.541998  255.671787  373.913043   974.126829\n",
       "7   515.935975   51.749614  426.086957   993.772546\n",
       "8   149.970615  150.318683  391.304348   691.593646\n",
       "9   114.739818  220.007459  321.739130   656.486408\n",
       "10  224.574177  184.863007  460.869565   870.306749\n",
       "11  428.804825  184.863007  373.913043   987.580875\n",
       "12  114.739818  116.486550  391.304348   622.530716\n",
       "13  224.574177  150.318683  408.695652   783.588512\n",
       "14  263.602881  116.486550  443.478261   823.567692\n",
       "15  149.970615  184.863007  391.304348   726.137970\n",
       "16  224.574177  220.007459  513.043478   957.625114\n",
       "17  224.574177   51.749614  356.521739   632.845530\n",
       "18  428.804825  440.063108  373.913043  1242.780976\n",
       "19  224.574177  255.671787  495.652174   975.898138\n",
       "20  386.289933   83.535096  269.565217   739.390247\n",
       "21  263.602881   83.535096  356.521739   703.659716\n",
       "22  224.574177  255.671787  391.304348   871.550312\n",
       "23  303.621960  116.486550  286.956522   707.065032\n",
       "24  224.574177  328.331368  408.695652   961.601197\n",
       "25  303.621960   21.739130  217.391304   542.752395\n",
       "26  263.602881   83.535096  408.695652   755.833630\n",
       "27  515.935975  220.007459  443.478261  1179.421695\n",
       "28  344.541998  150.318683  460.869565   955.730246\n",
       "29  344.541998  150.318683  513.043478  1007.904159\n",
       "30  515.935975  184.863007  495.652174  1196.451155\n",
       "31  344.541998   83.535096  373.913043   801.990138\n",
       "32  263.602881  184.863007  530.434783   978.900670\n",
       "33  386.289933  150.318683  408.695652   945.304268\n",
       "34  303.621960  255.671787  321.739130   881.032878\n",
       "35  472.034989  291.795520  373.913043  1137.743552\n",
       "36  186.648141   51.749614  408.695652   647.093407\n",
       "37  224.574177  255.671787  408.695652   888.941616\n",
       "38  386.289933  184.863007  373.913043   945.065983\n",
       "39  472.034989  220.007459  321.739130  1013.781579\n",
       "40  344.541998  150.318683  391.304348   886.165029\n",
       "41  386.289933  220.007459  373.913043   980.210436\n",
       "42  224.574177   83.535096  356.521739   664.631012\n",
       "43  303.621960  365.241280  513.043478  1181.906718\n",
       "44  224.574177  328.331368  391.304348   944.209893\n",
       "45  186.648141  150.318683  530.434783   867.401606\n",
       "46  263.602881  150.318683  252.173913   666.095477\n",
       "47  186.648141  116.486550  286.956522   590.091213\n",
       "48  263.602881  150.318683  408.695652   822.617216\n",
       "49  428.804825  220.007459  495.652174  1144.464458"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t2 = {\"veg\":[],\"fru\":[], \"oth\":[]}\n",
    "for i in t2.keys():\n",
    "    for j in range(J):\n",
    "        if i == \"veg\" or i == \"fru\":\n",
    "            t2[i].append(len_shelf/v2_df[i][j])\n",
    "        else:\n",
    "            t2[i].append(len_pass/v2_df[i][j])\n",
    "t2_df = pd.DataFrame(t2)\n",
    "t2_df['Sum'] = t2_df.sum(axis=1)\n",
    "t2_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c[i]:  564.4915253312683\n",
      "t_df['Sum'][index]:  564.4915253312683\n",
      "c[i]:  1198.0609990283083\n",
      "t_df['Sum'][index]:  633.5694736970399\n",
      "c[i]:  1864.069976126655\n",
      "t_df['Sum'][index]:  666.0089770983468\n",
      "c[i]:  2540.3937671867043\n",
      "t_df['Sum'][index]:  676.3237910600492\n",
      "c[i]:  3230.9654355395705\n",
      "t_df['Sum'][index]:  690.5716683528663\n",
      "c[i]:  3930.9301045827942\n",
      "t_df['Sum'][index]:  699.9646690432237\n",
      "c[i]:  4639.039377543433\n",
      "t_df['Sum'][index]:  708.1092729606389\n",
      "c[i]:  5348.613115294551\n",
      "t_df['Sum'][index]:  709.5737377511177\n",
      "c[i]:  6083.685022072253\n",
      "t_df['Sum'][index]:  735.0719067777018\n",
      "c[i]:  6830.822999400753\n",
      "t_df['Sum'][index]:  747.1379773285007\n",
      "c[i]:  7581.366292197942\n",
      "t_df['Sum'][index]:  750.5432927971888\n",
      "c[i]:  8350.982522971408\n",
      "t_df['Sum'][index]:  769.6162307734667\n",
      "c[i]:  9133.851030650792\n",
      "t_df['Sum'][index]:  782.8685076793845\n",
      "c[i]:  9933.162921022773\n",
      "t_df['Sum'][index]:  799.3118903719806\n",
      "c[i]:  10746.846200160962\n",
      "t_df['Sum'][index]:  813.6832791381885\n",
      "c[i]:  11573.91297267466\n",
      "t_df['Sum'][index]:  827.0667725136973\n",
      "c[i]:  12419.381371579855\n",
      "t_df['Sum'][index]:  845.4683989051955\n",
      "c[i]:  13269.983941833252\n",
      "t_df['Sum'][index]:  850.602570253398\n",
      "c[i]:  14134.614953924332\n",
      "t_df['Sum'][index]:  864.6310120910805\n",
      "c[i]:  15000.71043080589\n",
      "t_df['Sum'][index]:  866.0954768815573\n",
      "c[i]:  15867.75638375188\n",
      "t_df['Sum'][index]:  867.0459529459895\n",
      "c[i]:  16778.6362509497\n",
      "t_df['Sum'][index]:  910.879867197822\n",
      "c[i]:  17692.42126050264\n",
      "t_df['Sum'][index]:  913.7850095529411\n",
      "c[i]:  18607.449833171973\n",
      "t_df['Sum'][index]:  915.0285726693328\n",
      "c[i]:  19531.079252696647\n",
      "t_df['Sum'][index]:  923.629419524673\n",
      "c[i]:  20455.590391324164\n",
      "t_df['Sum'][index]:  924.5111386275166\n",
      "c[i]:  21385.233681086764\n",
      "t_df['Sum'][index]:  929.6432897626\n",
      "c[i]:  22317.65355810392\n",
      "t_df['Sum'][index]:  932.419877017157\n",
      "c[i]:  23299.470760909993\n",
      "t_df['Sum'][index]:  981.817202806073\n",
      "c[i]:  24287.15891450549\n",
      "t_df['Sum'][index]:  987.6881535954963\n",
      "c[i]:  25275.70315877717\n",
      "t_df['Sum'][index]:  988.5442442716812\n",
      "c[i]:  26264.48568774874\n",
      "t_df['Sum'][index]:  988.7825289715693\n",
      "c[i]:  27263.694194902637\n",
      "t_df['Sum'][index]:  999.2085071538968\n",
      "c[i]:  28264.797570208255\n",
      "t_df['Sum'][index]:  1001.1033753056199\n",
      "c[i]:  29269.87702815158\n",
      "t_df['Sum'][index]:  1005.0794579433241\n",
      "c[i]:  30287.48211806981\n",
      "t_df['Sum'][index]:  1017.6050899182292\n",
      "c[i]:  31306.858516826098\n",
      "t_df['Sum'][index]:  1019.3763987562888\n",
      "c[i]:  32329.2374481382\n",
      "t_df['Sum'][index]:  1022.3789313121015\n",
      "c[i]:  33352.92614511908\n",
      "t_df['Sum'][index]:  1023.6886969808838\n",
      "c[i]:  34383.98528125996\n",
      "t_df['Sum'][index]:  1031.0591361408733\n",
      "c[i]:  35421.236087795056\n",
      "t_df['Sum'][index]:  1037.2508065350967\n",
      "c[i]:  36472.61850799243\n",
      "t_df['Sum'][index]:  1051.3824201973766\n",
      "c[i]:  37529.87834741089\n",
      "t_df['Sum'][index]:  1057.2598394184606\n",
      "c[i]:  38654.92562695094\n",
      "t_df['Sum'][index]:  1125.0472795400465\n",
      "c[i]:  39836.147440216126\n",
      "t_df['Sum'][index]:  1181.2218132651797\n",
      "c[i]:  41024.090159500985\n",
      "t_df['Sum'][index]:  1187.9427192848598\n",
      "c[i]:  42246.99011549905\n",
      "t_df['Sum'][index]:  1222.899955998062\n",
      "c[i]:  43472.37509452924\n",
      "t_df['Sum'][index]:  1225.3849790301902\n",
      "c[i]:  44712.30451086158\n",
      "t_df['Sum'][index]:  1239.9294163323393\n",
      "c[i]:  45998.563747840664\n",
      "t_df['Sum'][index]:  1286.2592369790855\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>veg</th>\n",
       "      <th>fru</th>\n",
       "      <th>oth</th>\n",
       "      <th>Sum</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>83.535096</td>\n",
       "      <td>513.043478</td>\n",
       "      <td>864.631012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>344.541998</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>443.478261</td>\n",
       "      <td>981.817203</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>303.621960</td>\n",
       "      <td>220.007459</td>\n",
       "      <td>356.521739</td>\n",
       "      <td>923.629420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>344.541998</td>\n",
       "      <td>328.331368</td>\n",
       "      <td>408.695652</td>\n",
       "      <td>1125.047280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>386.289933</td>\n",
       "      <td>116.486550</td>\n",
       "      <td>304.347826</td>\n",
       "      <td>850.602570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>263.602881</td>\n",
       "      <td>184.863007</td>\n",
       "      <td>321.739130</td>\n",
       "      <td>813.683279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>344.541998</td>\n",
       "      <td>255.671787</td>\n",
       "      <td>373.913043</td>\n",
       "      <td>1017.605090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>515.935975</td>\n",
       "      <td>51.749614</td>\n",
       "      <td>426.086957</td>\n",
       "      <td>1037.250807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>149.970615</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>391.304348</td>\n",
       "      <td>735.071907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>114.739818</td>\n",
       "      <td>220.007459</td>\n",
       "      <td>321.739130</td>\n",
       "      <td>699.964669</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>184.863007</td>\n",
       "      <td>460.869565</td>\n",
       "      <td>913.785010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>428.804825</td>\n",
       "      <td>184.863007</td>\n",
       "      <td>373.913043</td>\n",
       "      <td>1031.059136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>114.739818</td>\n",
       "      <td>116.486550</td>\n",
       "      <td>391.304348</td>\n",
       "      <td>666.008977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>408.695652</td>\n",
       "      <td>827.066773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>263.602881</td>\n",
       "      <td>116.486550</td>\n",
       "      <td>443.478261</td>\n",
       "      <td>867.045953</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>149.970615</td>\n",
       "      <td>184.863007</td>\n",
       "      <td>391.304348</td>\n",
       "      <td>769.616231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>220.007459</td>\n",
       "      <td>513.043478</td>\n",
       "      <td>1001.103375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>51.749614</td>\n",
       "      <td>356.521739</td>\n",
       "      <td>676.323791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>428.804825</td>\n",
       "      <td>440.063108</td>\n",
       "      <td>373.913043</td>\n",
       "      <td>1286.259237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>255.671787</td>\n",
       "      <td>495.652174</td>\n",
       "      <td>1019.376399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>386.289933</td>\n",
       "      <td>83.535096</td>\n",
       "      <td>269.565217</td>\n",
       "      <td>782.868508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>263.602881</td>\n",
       "      <td>83.535096</td>\n",
       "      <td>356.521739</td>\n",
       "      <td>747.137977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>255.671787</td>\n",
       "      <td>391.304348</td>\n",
       "      <td>915.028573</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>303.621960</td>\n",
       "      <td>116.486550</td>\n",
       "      <td>286.956522</td>\n",
       "      <td>750.543293</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>328.331368</td>\n",
       "      <td>408.695652</td>\n",
       "      <td>1005.079458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>303.621960</td>\n",
       "      <td>21.739130</td>\n",
       "      <td>217.391304</td>\n",
       "      <td>564.491525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>263.602881</td>\n",
       "      <td>83.535096</td>\n",
       "      <td>408.695652</td>\n",
       "      <td>799.311890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>515.935975</td>\n",
       "      <td>220.007459</td>\n",
       "      <td>443.478261</td>\n",
       "      <td>1222.899956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>344.541998</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>460.869565</td>\n",
       "      <td>999.208507</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>344.541998</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>513.043478</td>\n",
       "      <td>1051.382420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>515.935975</td>\n",
       "      <td>184.863007</td>\n",
       "      <td>495.652174</td>\n",
       "      <td>1239.929416</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>344.541998</td>\n",
       "      <td>83.535096</td>\n",
       "      <td>373.913043</td>\n",
       "      <td>845.468399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>263.602881</td>\n",
       "      <td>184.863007</td>\n",
       "      <td>530.434783</td>\n",
       "      <td>1022.378931</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>386.289933</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>408.695652</td>\n",
       "      <td>988.782529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>303.621960</td>\n",
       "      <td>255.671787</td>\n",
       "      <td>321.739130</td>\n",
       "      <td>924.511139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>472.034989</td>\n",
       "      <td>291.795520</td>\n",
       "      <td>373.913043</td>\n",
       "      <td>1181.221813</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>186.648141</td>\n",
       "      <td>51.749614</td>\n",
       "      <td>408.695652</td>\n",
       "      <td>690.571668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>255.671787</td>\n",
       "      <td>408.695652</td>\n",
       "      <td>932.419877</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>386.289933</td>\n",
       "      <td>184.863007</td>\n",
       "      <td>373.913043</td>\n",
       "      <td>988.544244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>472.034989</td>\n",
       "      <td>220.007459</td>\n",
       "      <td>321.739130</td>\n",
       "      <td>1057.259839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>344.541998</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>391.304348</td>\n",
       "      <td>929.643290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>386.289933</td>\n",
       "      <td>220.007459</td>\n",
       "      <td>373.913043</td>\n",
       "      <td>1023.688697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>83.535096</td>\n",
       "      <td>356.521739</td>\n",
       "      <td>708.109273</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>303.621960</td>\n",
       "      <td>365.241280</td>\n",
       "      <td>513.043478</td>\n",
       "      <td>1225.384979</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>224.574177</td>\n",
       "      <td>328.331368</td>\n",
       "      <td>391.304348</td>\n",
       "      <td>987.688154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>186.648141</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>530.434783</td>\n",
       "      <td>910.879867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>263.602881</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>252.173913</td>\n",
       "      <td>709.573738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>186.648141</td>\n",
       "      <td>116.486550</td>\n",
       "      <td>286.956522</td>\n",
       "      <td>633.569474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>263.602881</td>\n",
       "      <td>150.318683</td>\n",
       "      <td>408.695652</td>\n",
       "      <td>866.095477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>428.804825</td>\n",
       "      <td>220.007459</td>\n",
       "      <td>495.652174</td>\n",
       "      <td>1187.942719</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           veg         fru         oth          Sum\n",
       "0   224.574177   83.535096  513.043478   864.631012\n",
       "1   344.541998  150.318683  443.478261   981.817203\n",
       "2   303.621960  220.007459  356.521739   923.629420\n",
       "3   344.541998  328.331368  408.695652  1125.047280\n",
       "4   386.289933  116.486550  304.347826   850.602570\n",
       "5   263.602881  184.863007  321.739130   813.683279\n",
       "6   344.541998  255.671787  373.913043  1017.605090\n",
       "7   515.935975   51.749614  426.086957  1037.250807\n",
       "8   149.970615  150.318683  391.304348   735.071907\n",
       "9   114.739818  220.007459  321.739130   699.964669\n",
       "10  224.574177  184.863007  460.869565   913.785010\n",
       "11  428.804825  184.863007  373.913043  1031.059136\n",
       "12  114.739818  116.486550  391.304348   666.008977\n",
       "13  224.574177  150.318683  408.695652   827.066773\n",
       "14  263.602881  116.486550  443.478261   867.045953\n",
       "15  149.970615  184.863007  391.304348   769.616231\n",
       "16  224.574177  220.007459  513.043478  1001.103375\n",
       "17  224.574177   51.749614  356.521739   676.323791\n",
       "18  428.804825  440.063108  373.913043  1286.259237\n",
       "19  224.574177  255.671787  495.652174  1019.376399\n",
       "20  386.289933   83.535096  269.565217   782.868508\n",
       "21  263.602881   83.535096  356.521739   747.137977\n",
       "22  224.574177  255.671787  391.304348   915.028573\n",
       "23  303.621960  116.486550  286.956522   750.543293\n",
       "24  224.574177  328.331368  408.695652  1005.079458\n",
       "25  303.621960   21.739130  217.391304   564.491525\n",
       "26  263.602881   83.535096  408.695652   799.311890\n",
       "27  515.935975  220.007459  443.478261  1222.899956\n",
       "28  344.541998  150.318683  460.869565   999.208507\n",
       "29  344.541998  150.318683  513.043478  1051.382420\n",
       "30  515.935975  184.863007  495.652174  1239.929416\n",
       "31  344.541998   83.535096  373.913043   845.468399\n",
       "32  263.602881  184.863007  530.434783  1022.378931\n",
       "33  386.289933  150.318683  408.695652   988.782529\n",
       "34  303.621960  255.671787  321.739130   924.511139\n",
       "35  472.034989  291.795520  373.913043  1181.221813\n",
       "36  186.648141   51.749614  408.695652   690.571668\n",
       "37  224.574177  255.671787  408.695652   932.419877\n",
       "38  386.289933  184.863007  373.913043   988.544244\n",
       "39  472.034989  220.007459  321.739130  1057.259839\n",
       "40  344.541998  150.318683  391.304348   929.643290\n",
       "41  386.289933  220.007459  373.913043  1023.688697\n",
       "42  224.574177   83.535096  356.521739   708.109273\n",
       "43  303.621960  365.241280  513.043478  1225.384979\n",
       "44  224.574177  328.331368  391.304348   987.688154\n",
       "45  186.648141  150.318683  530.434783   910.879867\n",
       "46  263.602881  150.318683  252.173913   709.573738\n",
       "47  186.648141  116.486550  286.956522   633.569474\n",
       "48  263.602881  150.318683  408.695652   866.095477\n",
       "49  428.804825  220.007459  495.652174  1187.942719"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "internal_arrangement(t2_df, len_pass = len_pass/1.15)\n",
    "spt_algo(t2_df)\n",
    "t2_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "prep for Q//c_max - for more info go to doc:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "calc the ratio of the task index (K) to the working rate of the gatherer (s_j: s1 = 1, s2 = 1.15): K/s_j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "K_S1 = [i for i in range(1, J+1)]\n",
    "\n",
    "K_S2 = [0 for i in range(1, J+1)]\n",
    "for i in range(1, 51):\n",
    "    K_S2[i-1] = i/1.15"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we do in Q//sigma(C_i): take the task with the longest time and match it to the min ratio of both gatherers.\n",
    "\n",
    "* The heuristics will be to place the tasks from the beginning and not the end (as we do in P//c_max). \n",
    "\n",
    "* Note the longest task will be the same for the both gatherers since the ratio is permanent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time_finish:  24825.50236809726\n",
      "sch for regular gather:  [30, 27, 35, 39, 7, 41, 6, 16, 33, 44, 37, 34, 22, 14, 0, 31, 5, 20, 23, 46, 9, 17, 47]\n",
      "sch for fast gather:  [18, 43, 49, 3, 29, 11, 32, 19, 24, 28, 38, 1, 40, 2, 10, 45, 48, 4, 13, 26, 15, 21, 8, 42, 36, 12, 25]\n"
     ]
    }
   ],
   "source": [
    "#initializing schedules: 1 for the regular, 2 for the faster one\n",
    "sch_1_Q3 = []\n",
    "sch_2_Q3 = []\n",
    "\n",
    "#initializing time counters\n",
    "time_1 = 0\n",
    "time_2 = 0\n",
    "\n",
    "# to compare with Q4 - initializing dictionaries for waiting time to each task in specific gather. \n",
    "waiting_time_1 = {}\n",
    "waiting_time_2 = {}\n",
    "\n",
    "#copy for processing times\n",
    "t_df_copy = t_df.copy()\n",
    "\n",
    "\n",
    "for i in range(J):\n",
    "    task_idx = t_df_copy['Sum'].idxmax() # task index with max time\n",
    "    task_time_1 = t_df_copy['Sum'][task_idx] # time processing for the regular\n",
    "    task_time_2 = t2_df['Sum'][task_idx] ## time processing for the fast gather\n",
    "\n",
    "    \n",
    "    t_df_copy['Sum'][task_idx] = None # for not using it again\n",
    "    \n",
    "    # taking min ratio\n",
    "    min_K_S1 = min(K_S1)\n",
    "    min_K_S2 = min(K_S2)\n",
    "    \n",
    "    min_tot = 0\n",
    "    \n",
    "    #case the min ratio is for the regular gather\n",
    "    if min_K_S1 < min_K_S2:\n",
    "        waiting_time_1[task_idx] = time_1 # waiting time until now, not including the process time for this task\n",
    "        min_tot = min_K_S1\n",
    "        idx = K_S1.index(min_tot)\n",
    "        K_S1.pop(idx)\n",
    "            \n",
    "        sch_1_Q3.append(task_idx) # add the task to regular gather schedule\n",
    "            \n",
    "        time_1 += task_time_1 # update time\n",
    "    \n",
    "    #case the min ratio is for the fast gather    \n",
    "    else:\n",
    "        waiting_time_2[task_idx] = time_2 # waiting time until now, not including the process time for this task\n",
    "        min_tot = min_K_S2\n",
    "        idx = K_S2.index(min_tot)\n",
    "        K_S2.pop(idx)\n",
    "            \n",
    "        sch_2_Q3.append(task_idx) # add the task to faster gather schedule\n",
    "            \n",
    "        time_2 += task_time_2 # update time\n",
    "\n",
    "\n",
    "time_finish = max(time_2, time_1) # C_MAX\n",
    "\n",
    "print('time_finish: ',time_finish)\n",
    "print('sch for regular gather: ', sch_1_Q3)\n",
    "print('sch for fast gather: ', sch_2_Q3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "#to compare woth Q4\n",
    "total_wt_1 = sum(list(waiting_time_1.values()))\n",
    "avg_wt_1 = total_wt_1/len(list(waiting_time_1.values()))\n",
    "\n",
    "total_wt_2 = sum(list(waiting_time_2.values()))\n",
    "avg_wt_2 = total_wt_2/len(list(waiting_time_2.values()))\n",
    "\n",
    "total_wt_both = total_wt_1 + total_wt_2\n",
    "avg_wt__both = total_wt_both/J"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question no. 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "re-calc the ratio of the task index (K) to the working rate of the gatherer (s_j: s1 = 1, s2 = 1.15): K/s_j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "#prep for the ratios \n",
    "K_S1_Q4 = [i for i in range(1, J+1)]\n",
    "\n",
    "K_S2_Q4 = [0 for i in range(1, J+1)]\n",
    "for i in range(1, 51):\n",
    "    K_S2_Q4[i-1] = i/1.15"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we do in Q//sigma(C_i): take the task with the longest time and match it to the min ratio of both gatherers. \n",
    "\n",
    "* Will place the tasks from end to beginning as should do in Q//sigma(C_i). \n",
    "\n",
    "* Note the longest task will be the same for the both gatherers since the ratio is permanent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time_finish Q4:  24825.50236809725\n",
      "sch for regular gather:  [47, 17, 9, 46, 23, 20, 5, 31, 0, 14, 22, 34, 37, 44, 33, 16, 6, 41, 7, 39, 35, 27, 30]\n",
      "sch for fast gather:  [25, 12, 36, 42, 8, 21, 15, 26, 13, 4, 48, 45, 10, 2, 40, 1, 38, 28, 24, 19, 32, 11, 29, 3, 49, 43, 18]\n"
     ]
    }
   ],
   "source": [
    "#initializing schedules: 1 for the regular, 2 for the faster one\n",
    "sch_1_Q4 = []\n",
    "sch_2_Q4 = []\n",
    "\n",
    "#initializing time counters\n",
    "time_1_Q4 = 0\n",
    "time_2_Q4 = 0\n",
    "\n",
    "# initializing dictionaries for waiting time to each task in specific gather. \n",
    "waiting_time_1_Q4 = {}\n",
    "waiting_time_2_Q4 = {}\n",
    "\n",
    "#copy for processing times\n",
    "t_Q4_copy = t_df.copy()\n",
    "\n",
    "### same algo as Q3 - no time clculations\n",
    "for i in range(J):\n",
    "    task_idx = t_Q4_copy['Sum'].idxmax() # task index with max time\n",
    "    task_time_1 = t_Q4_copy['Sum'][task_idx] # time processing for the regular\n",
    "    task_time_2 = t2_df['Sum'][task_idx] ## time processing for the fast gather\n",
    "    \n",
    "    t_Q4_copy['Sum'][task_idx] = None # for not using it again\n",
    "    \n",
    "    # taking min ratio\n",
    "    min_K_S1 = min(K_S1_Q4)\n",
    "    min_K_S2 = min(K_S2_Q4)\n",
    "    \n",
    "    min_tot = 0\n",
    "    \n",
    "    #case the min ratio is for the regular gather\n",
    "    if min_K_S1 < min_K_S2:\n",
    "        min_tot = min_K_S1\n",
    "        idx = K_S1_Q4.index(min_tot)\n",
    "        K_S1_Q4.pop(idx)\n",
    "            \n",
    "        sch_1_Q4.append([task_idx, task_time_1]) # add the task to regular gather schedule\n",
    "    \n",
    "    #case the min ratio is for the fast gather    \n",
    "    else:\n",
    "        min_tot = min_K_S2\n",
    "        idx = K_S2_Q4.index(min_tot)\n",
    "        K_S2_Q4.pop(idx)\n",
    "            \n",
    "        sch_2_Q4.append([task_idx,task_time_2]) # add the task to faster gather schedule\n",
    "###\n",
    "\n",
    "### New - Assign tasks from end to beginning\n",
    "t1=0 # time (regular gather) counter\n",
    "agg_time_1 = [0] # Auxiliary variable in order to calculate waiting time \n",
    "sch_1_rev = [] # Auxiliary variable to reverse scheduale\n",
    "sch_1_final = []\n",
    "\n",
    "for i in range(len(sch_1_Q4)):\n",
    "    sch_1_rev.append(sch_1_Q4[-1])\n",
    "    t1 += sch_1_Q4[-1][1]  # accumulation\n",
    "    sch_1_Q4.pop(-1)\n",
    "    \n",
    "    agg_time_1.append(t1) # list of waiting time - no task index\n",
    "    \n",
    "    waiting_time_1_Q4[sch_1_rev[i][0]] = agg_time_1[i] # dict of waiting time- k= task, v= waiting time (reg gather)\n",
    "    \n",
    "    sch_1_final.append(sch_1_rev[i][0])\n",
    "\n",
    "\n",
    "t2=0 # time (fast gather) counter\n",
    "agg_time_2 = [0] # Auxiliary variable in order to calculate waiting time\n",
    "sch_2_rev = [] # Auxiliary variable to reverse scheduale\n",
    "sch_2_final = []\n",
    "\n",
    "for i in range(len(sch_2_Q4)):\n",
    "    sch_2_rev.append(sch_2_Q4[-1]) \n",
    "    t2 += sch_2_Q4[-1][1] # accumulation\n",
    "    sch_2_Q4.pop(-1)\n",
    "    \n",
    "    agg_time_2.append(t2) # list of waiting time - no task index\n",
    "    \n",
    "    waiting_time_2_Q4[sch_2_rev[i][0]] = agg_time_2[i] # dict of waiting time- k= task, v= waiting time (fast gather)\n",
    "    \n",
    "    sch_2_final.append(sch_2_rev[i][0])\n",
    "\n",
    "\n",
    "time_finish_Q4 = max(agg_time_1[-1], agg_time_2[-1]) # C_MAX\n",
    "\n",
    "print('time_finish Q4: ', time_finish_Q4)\n",
    "print('sch for regular gather: ', sch_1_final)\n",
    "print('sch for fast gather: ', sch_2_final)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we expected all schedules are reversed (Q3 vs Q4). \n",
    "\n",
    "Now will compare waiting time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Regular worker:\n",
      "-----------------------------------------------------\n",
      "The total waiting time in Q3:  296558.95509284403 and the avg waiting time:  12893.867612732349\n",
      "Total waiting time Q4:  239119.49781466433  and avg waiting time Q4:  10396.499904985405\n",
      "-----------------------------------------------------\n",
      "-----------------------------------------------------\n",
      "Fast worker:\n",
      "-----------------------------------------------------\n",
      "The total waiting time in Q3:  358684.9409596131 and the avg waiting time in Q3:  13284.627442948633\n",
      "Total waiting time Q4:  286778.1206109156 and avg waiting tine Q4:  10621.411874478355\n",
      "-----------------------------------------------------\n",
      "-----------------------------------------------------\n",
      "Both workers:\n",
      "-----------------------------------------------------\n",
      "The total waiting time in Q3:  655243.8960524572  and The avg waiting time in Q3:  13104.877921049143\n",
      "Total waiting time Q4:  525897.61842558  and avg waiting time Q4:  10517.9523685116\n"
     ]
    }
   ],
   "source": [
    "#print('waiting_time for 1: ', waiting_time_1_Q4.items())\n",
    "total_wt_1_Q4 = sum(list(waiting_time_1_Q4.values()))\n",
    "avg_wt_1_Q4 = total_wt_1_Q4/len(list(waiting_time_1_Q4.values()))\n",
    "print('Regular worker:')\n",
    "print('-----------------------------------------------------')\n",
    "print('The total waiting time in Q3: ',total_wt_1, 'and the avg waiting time: ',avg_wt_1)\n",
    "print('Total waiting time Q4: ',total_wt_1_Q4, ' and avg waiting time Q4: ', avg_wt_1_Q4)\n",
    "\n",
    "print('-----------------------------------------------------')\n",
    "print('-----------------------------------------------------')\n",
    "\n",
    "\n",
    "total_wt_2_Q4 = sum(list(waiting_time_2_Q4.values()))\n",
    "avg_wt_2_Q4 = total_wt_2_Q4/len(list(waiting_time_2_Q4.values()))\n",
    "print('Fast worker:')\n",
    "print('-----------------------------------------------------')\n",
    "print('The total waiting time in Q3: ',total_wt_2, 'and the avg waiting time in Q3: ',avg_wt_2)\n",
    "print('Total waiting time Q4: ', total_wt_2_Q4,'and avg waiting tine Q4: ',avg_wt_2_Q4)\n",
    "\n",
    "print('-----------------------------------------------------')\n",
    "print('-----------------------------------------------------')\n",
    "\n",
    "total_wt_both_Q4 = total_wt_1_Q4 + total_wt_2_Q4\n",
    "avg_wt__both_Q4 = total_wt_both_Q4/J\n",
    "print('Both workers:')\n",
    "print('-----------------------------------------------------')\n",
    "print('The total waiting time in Q3: ',total_wt_both,' and The avg waiting time in Q3: ',avg_wt__both)\n",
    "print('Total waiting time Q4: ', total_wt_both_Q4, ' and avg waiting time Q4: ',avg_wt__both_Q4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question no. 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question no. 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "pass"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "ae5fc7badd896bf7d9607dde7e8d832035720849634606dbd24419cc840d7664"
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}