Gamma Distribution Calculation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import glob, os\n",
    "from scipy.stats import norm, gamma, stats, skew\n",
    "import statistics\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.style as style"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--- **Data Aggregation and Cleaning were here** ---\n",
    "\n",
    "Initially this script included lines meant for data aggregation and cleaning. As the process is going to be the same for all upcoming scripts, these lines are deleted. However, they can be found in the first script related to Safety and Cycle Stock calculation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--- **Gamma Distribution Calculation script starts here** ---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In case of Gamma Distribution Simulation we will not use the data for a specific product, but for the whole product range shipped from Supplier to Retailer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data sample is displayed below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Line_ID Movement_Week Movement_Date       EAN_Code Base_Unit_Code  Stock  Transit  Shipped  OOS  Demand\n",
      "34               cw06    2021-02-11  4000000000001     1000000001    408        0      408    0     408\n",
      "5840             cw36    2020-09-06  4000000000002     1000000002   3273     1728      648    0     648\n",
      "763              cw03    2021-01-22  4000000000003     1000000003   4806        0     2832   24    2856\n",
      "2164             cw51    2020-12-14  4000000000004     1000000004   5222        0       54    0      54\n",
      "5914             cw36    2020-09-04  4000000000005     1000000005  27964        0      864    0     864\n"
     ]
    }
   ],
   "source": [
    "print(dfPivot.sample(5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This line is kept in order to quickly switch from full products' range analysis to one product's only. The mentioned product is one of supplier's bestsellers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# dfPivot = dfPivot[dfPivot['Base_Unit_Code'] == '1000000006']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We choose calendar day as a period. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "dfGamma = dfPivot.groupby('Movement_Date',as_index=False)[['Stock','Shipped','OOS','Demand']].sum()\n",
    "dfGamma = dfGamma[['Movement_Date','Demand']].set_index('Movement_Date')\n",
    "dfGamma.index.name = None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aggregated quantities can be observed in the following chart."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dfGamma.plot(figsize=(8,4),legend=None)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the plot we can see extremely low value around early October'20. In order to prevent rough outliers from affecting our analysis, we will additionally check the minimum values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Line_ID     Demand\n",
      "2020-10-09    1280\n",
      "2020-10-08    1297\n",
      "2020-12-17    9432\n",
      "2020-12-16   11181\n",
      "2020-12-18   11619\n",
      "2021-01-05   12249\n",
      "2021-01-04   12508\n"
     ]
    }
   ],
   "source": [
    "print(dfGamma.sort_values(by='Demand').head(7))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above we see that the demand was extremely low within two days in October'20. It may have been the day of warehouse partial closure or the day the inventory checks were carried out. For that reason I decide to ignore the actual minimum in the datased and choose the third value in a row - 9432.\n",
    "\n",
    "However, the new adequate minimum may appear, that's why I will set a certain threshold for this value and next value above this border will be used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "dfGamma = dfGamma[dfGamma['Demand'] > 4000]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will find and display some values that would be used in further analytics and simulation.\n",
    "\n",
    "*Sigma (std)* is standard deviation value for products' demand."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "std = int(np.std(dfGamma['Demand'],ddof=1)) # standard deviation or std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we find and display the *mu (mean)*, *median*, *mode*, *minimum* and *maximum* for demand data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "mu = int(dfGamma['Demand'].mean())       # mu corresponds to the mean value\n",
    "median = int(dfGamma['Demand'].median())\n",
    "mode = statistics.mode(dfGamma['Demand'])\n",
    "d_min = int(dfGamma['Demand'].min())\n",
    "d_max = int(dfGamma['Demand'].max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " std: 14188 \n",
      " mu: 33632 \n",
      " median: 31108 \n",
      " mode: 41236 \n",
      " \n",
      " minimum: 9432 \n",
      " maximum: 94405\n"
     ]
    }
   ],
   "source": [
    "print('\\n','std:',std,'\\n','mu:',mu,'\\n','median:',median,\n",
    "      '\\n','mode:',mode,'\\n','\\n','minimum:',d_min,'\\n','maximum:',d_max)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will get a number of available data points. As we receive new data daily, this value will increase over time.\n",
    "\n",
    "For that reason we calculate a number of bins as 1/3 of all data points available. It's likely to provide the more precise overview of the available data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "All data points: 179\n",
      "Number of bins: 59\n"
     ]
    }
   ],
   "source": [
    "data_points = len(dfGamma.index)\n",
    "bins = int(data_points*0.33)\n",
    "\n",
    "print(\"All data points:\",data_points)\n",
    "print(\"Number of bins:\",bins)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will display the distribution on a histogram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "hist_range = (dfGamma.Demand.min()*0.8,dfGamma.Demand.max()*1.2)\n",
    "y_actuals, edges = np.histogram(dfGamma, bins=bins, density=True, range=hist_range)\n",
    "y_actuals = y_actuals/sum(y_actuals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dfGamma.plot(kind='hist',density=True,bins=bins,range=hist_range,legend=None)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we calculate skewness."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual skewness: 1.178\n"
     ]
    }
   ],
   "source": [
    "skewness = skew(dfGamma.Demand,bias=False)\n",
    "# skewness = dfGamma.Demand.skew() # another method for skewness calculation\n",
    "\n",
    "print('Actual skewness:',np.round(skewness,decimals=3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As our result is greather than 1, it means that we have the highly right-skewed distribution. In this case the skew - or tail - is located on the right."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we're going to calculate the PDF (probability density function) of a gamma distribution and its **fitted** version that is likely to display the distribution in a more precise way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "shape = mu**2/std**2 # k\n",
    "scale = std**2/mu      # theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_min = gamma.ppf(0.01, shape, scale=scale)\n",
    "x_max = gamma.ppf(0.99, shape, scale=scale)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(x_min, x_max, 200)\n",
    "y = gamma.pdf(x, shape, scale=scale)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to fit the density function we would use a modified value of the mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu_p = mu - d_min # mu\n",
    "shape_p = mu_p**2/std**2 # k\n",
    "scale_p = std**2/mu_p # theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_min = gamma.ppf(0.01, shape_p, loc=d_min, scale=scale_p)\n",
    "x_max = gamma.ppf(0.99, shape_p, loc=d_min, scale=scale_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "x1 = np.linspace(x_min,x_max, 200)\n",
    "y1 = gamma.pdf(x, shape_p, loc=d_min, scale=scale_p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will see the difference between 2 functions: standard and fitted (with offset)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "dfGamma.plot(figsize=(8,4),ax=ax,kind='hist',density=True,bins=bins,range=hist_range,color='darkgrey')\n",
    "ax.plot(x,y,label='Gamma - poor fit',color='navy',linewidth=2)\n",
    "ax.plot(x1,y1,label='Gamma - with offset',color='crimson',linewidth=2)\n",
    "\n",
    "ax.set_title(\"Gamma distributions for supplier's demand\")\n",
    "ax.set_xlabel('Daily demand')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make sure that our distribution is rather Gamma than Normal we need to observe its skewness values: for both actual and fitted versions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "skew_actual = skew(dfGamma.Demand,bias=False)\n",
    "skew_gamma = 2*std/mu\n",
    "skew_gamma_p = 2*std/(mu-d_min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Actual: 1.178 \n",
      " Gamma: 0.844 \n",
      " Gamma fitted: 1.173\n"
     ]
    }
   ],
   "source": [
    "print('\\n','Actual:',np.round(skew_actual,decimals=3),\n",
    "      '\\n','Gamma:',np.round(skew_gamma,decimals=3),\n",
    "      '\\n','Gamma fitted:',np.round(skew_gamma_p,decimals=3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gamma fitted value is slightly closer to gamma value than actual one. It adds some additional precision to distribution evaluation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With all the data we've found, now we'll calculate the recommended up-to and safety stock levels. We're working with a full products' range demand. This type of calculation may be useful for general tracking of total stock. \n",
    "\n",
    "If it exceeds the up-to level, it may become a sign to explore the reasons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.95 # target cycle service level\n",
    "L = 4        # lead time\n",
    "R = 7        # review period"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_min = (R+L)*d_min                         # minimum demand during replenishment cycle\n",
    "x_mu = (R+L)*mu                             # mean demand during replenishment cycle\n",
    "x_mu_p = x_mu - x_min                       # offset value of the mean\n",
    "x_std = np.sqrt(R+L)*std                    # offset standard deviation \n",
    "x_shape_p = x_mu_p**2/x_std**2              # offset shape of distribution\n",
    "x_scale_p = x_std**2/x_mu_p                 # offset scale of distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "S = round(gamma.ppf(alpha,x_shape_p,scale=x_scale_p),0) + x_min # up-to level\n",
    "Ss = S - x_mu                                                   # safety stock"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Up-to level: 451786.0\n",
      "Safety stock: 81834.0\n"
     ]
    }
   ],
   "source": [
    "print('Up-to level:',S)\n",
    "print('Safety stock:',Ss)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
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 },
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}