國立臺北護理健康大學 NTUHS
Prediction of
inventory management
Orozco Hsu
2021-05-27
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About me
• Education
• NCU (MIS)、NCCU (CS)
• Work Experience
• Telecom big data Innovation
• AI projects
• Retail marketing technology
• User Group
• TW Spark User Group
• TW Hadoop User Group
• Taiwan Data Engineer Association Director
• Research
• Big Data/ ML/ AIOT/ AI Columnist
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「How can you not get romantic about baseball ? 」

Tutorial
Content
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Stationary of Time-Series
Forecasting with Seasonal or Periodic data
Homework
An accurate inventory prediction

Code
• Download code
• https://github.com/orozcohsu/ntunhs_2020/tree/master/alg_20210527
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An accurate inventory prediction
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An accurate inventory prediction
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The blocks of Inventory Management System

An accurate inventory prediction
• Inventory forecasting, also known as demand planning, is the practice
of using past data, trends and known upcoming events to predict
needed inventory levels for a future period.
• An accurate forecasting ensures businesses have enough product to
fulfill customer orders and do not spend too little or too much on
inventory.
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An accurate inventory prediction
• Data elements required for a success inventory forecasting include
• Current Inventory Levels
• OUTSTANDING purchase orders
• HISTORICAL TRENDLINES
• Forecasting period requirements
• Expected demand and SEASONALITY
• MAXIMUM possible stock levels
• Sales trends and velocity
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Accurate inventory prediction
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01 Future forecast period
02 Base demand
03 Variables and trends
04 Build model
05 Model tuning

Accurate inventory prediction
• Demand Factors (Base, trends, seasonality, qualitative…)
• An example of other demand factors that can impact or inflate your normal
base demand.
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Accurate inventory prediction
• Demand types
• Demand of Product X, Y, Z varies considerably.
• Some will have consistently high demand over time, for others there could be
sporadic or low demand.
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Quiz: What is the importance of demand forecasting?
Hint: Watch the video from https://youtu.be/DKJfForHw-w
What is demand forecasting?

Stationary of Time-Series
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Stationary of Time-Series
• Introduction to Stationarity
• Stationarity is one of the most important concepts you will come across when
working with time series data. A stationary series is one in which the
properties – mean, variance and covariance, do not vary with time.
(a) The mean varies (increases) with time which results in an upward trend
(b) We do not see a trend in the series. A stationary series must have a constant variance
(c) The spread becomes closer as the time increases, which implies that the covariance is a function of time.
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(a) (b) (c)

Stationary of Time-Series
• Stationary
• The mean, variance and covariance are constant with time.
• Most statistical models require the series to be stationary to make effective
and precise predictions.
• A stationary time series is the one for which the properties (namely mean,
variance and covariance) do not depend on time.
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Stationary of Time-Series
• How to check the series is stationary?
• Use the ADF (Augmented Dickey Fuller) Test
• It helps us understand if the series is stationary or not
• Null hypothesis: The series has a unit root
• Alternate hypothesis: The series has no unit root.
check_stationary.ipynb
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Null and Alternative Hypotheses
https://opentextbc.ca/introstatopenstax/chapter/null-and-alternative-hypotheses/

Stationary of Time-Series
• How to make our series to stationary: Differencing
• Compute the difference of consecutive terms in the series.
• Differencing is typically performed to get rid of the varying mean.
• How to make our series to stationary: Seasonal Differencing
• Calculate the difference between an observation and a previous observation
from the same season.
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Stationary of Time-Series
• Time series data are expected to contain some white noise
component on top of the signal generated by the underlying process.
• When forecast ERRORS (y hat and y) are white noise, it means that all
of the signal information in the time series has been harnessed by the
model in order to make predictions.
y(t) = signal(t) + noise(t)
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White noise:
A time series is white noise if the variables are random and
identically distributed with a mean of zero, autocorrelation is closer to 0.

Stationary of Time-Series
• How to make our series to stationary: Transformation
• Used to stabilize the non-constant variance of a series.
• Common transformation methods include power transform, square root, and
log transform.
• Check Durbin_Watson, ACF, Ljung box test of series after we process
our series.
making_a_time_series_stationary.ipynb
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Stationary of Time-Series
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Start
Random
Stationary
Non-
Stationary
White noise
(no pattern) terminated
Stationary
(original series is stationary)
Differencing
stationary
ARIMA model (Autoregressive
Integrated Moving Average model)
ARMA model (Autoregressive
moving average model)
Yes
No
No
Differencing
Yes

Forecasting with Seasonal or Periodic data
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Forecasting with Seasonal or Periodic data
• Some useful tools
• Moving average forecasting (MA)
• Simple Exponential Smoothing forecasting(SES; holtwinters)
• Stepwise Autoregressive forecasting
• Autoregressive Integrated Moving Average model forecasting (ARIMA)
• A seasonal autoregressive integrated moving average (SARIMA)
• Autoregressive conditional heteroskedasticity forecasting (ARCH)
• Hidden Markov Model forecasting (HMM)
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Forecasting with Seasonal or Periodic data
• A time series analysis focuses on a series of
data points ordered in time.
• If you’re a retailer, a time series analysis
can help you forecast daily sales volumes
to guide decisions around inventory and
better timing for marketing efforts.
• If you’re in the financial industry, a time
series analysis can allow you to forecast
stock prices for more effective investment
decisions.
• If you’re an agricultural company, a time
series analysis can be used for weather
forecasting to guide planning decisions
around planting and harvesting.
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Forecasting with Seasonal or Periodic data
• Check any time series data for patterns that can affect the results, and
can inform which forecasting model to use.
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Type Description
Irregular
Fluctuation
No pattern
Trend Increases, decreases, or stays the same over time
Seasonal or
Periodic
Pattern repeats periodically over time
Cyclical
Pattern that increases and decreases but usually related to non-
seasonal activity, like business cycles
Level The average of value

Forecasting with Seasonal or Periodic data
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Forecasting with Seasonal or Periodic data
• Use my code and present those models
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time_series_forecasting.ipynb

Forecasting with Seasonal or Periodic data
• Parameters: Additive model
• Usually represents a linear time series with fixed fluctuations and a fixed
period pattern.
• y(t) = Level + Trend + Seasonality + Cyclical/Noise/Random
• Parameters: Multiplicative model
• The fluctuations and cycles of the time series will change with time. It is a
non-linear time series, and most of the time series data of stocks fall into this
category.
• y(t) = Level * Trend * Seasonality * Cyclical/Noise/Random
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We will use it for seasonal_decompose, check my code

Forecasting with Seasonal or Periodic data
• Simple Exponential Smoothing (SES)
• Suitable for time series data without trend or seasonal components.
• This model is using weighted averages of past observations to forecast new
values.
• Parameters:
• Determine the smoothing level α: Between 0 and 1 (Level equation)
• When α = 0, the forecasts are equal to the average of the historical data.
• When α = 1, the forecasts will be equal to the value of the last observation.
• Write the model RMSE in P33 table
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Forecasting with Seasonal or Periodic data
• Holts Linear Trend Method
• Suitable for time series data with a trend component but without a seasonal
component.
• Expanding the SES method, the Holt method helps you forecast time series
data that HAS a trend.
• Parameters:
• Level smoothing parameter α: Between 0 and 1 (Level equation)
• Trend smoothing parameter β*: Between 0 and 1 (Trend equation)
• Write the model RMSE in P33 table
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Forecasting with Seasonal or Periodic data
• Holt-Winters Seasonal Method
• Suitable for time series data with trend and/or seasonal components.
• Parameters:
• Seasonality smoothing parameter: γ
• Two general types of seasonality: Additive and Multiplicative (Check Page 26)
• Identify the frequency of seasonality m: m=4 (Quarterly seasonal pattern)
m=12 (Yearly seasonal pattern)
• Box-Cox transformations for data normalization
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https://www.statisticshowto.com/box-cox-transformation
https://www.statsmodels.org/dev/generated/statsmodels.tsa.holtwinter
s.ExponentialSmoothing.fit.html
Homework2: Set use_boxcox to False, log, float to compare the result.

Forecasting with Seasonal or Periodic data
• SARIMA (Seasonal autoregressive integrated moving average)
• Suitable for time series data with trend and/or seasonal components
• ARIMA model looks at autocorrelations or serial correlations in the data, and
it looks at differences between values in the time series.
• SARIMA builds upon the concept of ARIMA but extends it to model the
seasonal elements in your data.
• Parameters (we need to find those SEVEN parameters):
• Trend elements:
• p: Trend autoregression order
• d: Trend difference order
• q: Trend moving average order
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• Seasonal elements:
• P: Seasonal autoregression order
• D: Seasonal difference order
• Q: Seasonal moving average order
• m: The number of time steps for a single seasonal period

Forecasting with Seasonal or Periodic data
• Grid search
• A python package.
• It is a tuning technique that attempts to compute the optimum values of
hyperparameters.
• Find out the best value of (p, d, q, P, D, Q, m)
• Evaluation metric
• AIC (Akaike Information Criterion)
• The AIC measures how well a model fits the data while taking into account
the overall complexity of the model.
• Pick the combination with the LOWEST AIC value.
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Forecasting with Seasonal or Periodic data
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Check model’s residuals are near normally distributed.
This indicates we have found a WELL-FIT model suitable for our dataset.
Symmetry KDE line follow closely with N(0,1)
N(0,1) => mean =0, variance =1
If residuals are normally distributed, the
points will fall on the 45-degree
https://desktop.arcgis.com/en/arcmap/10.3/guide-
books/extensions/geostatistical-analyst/normal-qq-plot-and-
general-qq-plot.htm
Residuals have a low autocorrelation with the
lagged versions of itself, the majority of dots
fall into the blue shaded area

Forecasting with Seasonal or Periodic data
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Algorithm RMSE
Simple Exponential Smoothing 108.63
Holts Linear Trend Method 305.25
Holt-Winters Seasonal Method
(multiplicative)
25.78
SARIMA (dynamic=False) 17.9
Homework3: Try to use Holt-Winters Seasonal Method to predict future sales value

Forecasting with Seasonal or Periodic data
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Prediction: 1961-01-01 -> 1965-04-01

Homework
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Homework
• Continue to use square root or power transformation on
Making_a_Time_Series_Stationary.ipynb series and compare with
better results.
• Set use_boxcox to False, log, float to compare the result.
• Try to use Holt-Winters Seasonal Method to predict future sales value
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