Forecasting demand planning

 Natural numbers
 1,2,3….∞
 whole numbers
 0,1,2,3….∞
 Integer
 Whole number+ their negatives
 Rational number
 Can be written as fractions
 All integers are rational. But not all rational are integers
 Irrational numbers
 Cannot be written as simple fraction
 Eg: π, Euler’s number
2

Data
Quantitative
Discrete Continuous
Interval
scale
Ratio scale
Qualitative
Nominal
Scale
Ordinal
Scale
3

 Nominal
 To describe characteristics. Eg: Happy/ Unhappy; Black/white;
 Dichotomous: Male/Female
 Nominal with order. Eg: Hot, Hotter, Hottest
 Nominal with out order: Yes/ No
 Can’t perform any meaningful calculations.
 Ordinal
 Ranking is the focus
 Difference between them is not easy to understand
 Eg: Likert’s scale; ranking in a class room
 Can use mode or median
4

 Interval
 Order and exact difference between values are known. Eg: temperature difference in degrees
 Can perform mean, median and mode
 No absolute zero
 Cant do multiplication or division. Addition & Subtraction allowed
 Eg: temperature in degree Celsius
 Ratio
 Has absolute zero
 Can do all statistical analysis
 Eg: Temperature in Kelvin
5

 Time series
 Cross sectional
 Panel data
6

 Uniform time interval
 Successive periods
 Pattern in historical data
 Eg:
Source: https://www.weather-ind.com/en/india/chennai-climate#temperature
7

 At a point in time- snapshot
 Multiple variables of interest
 Eg:
Amount spent on advert
(Rs)
Sales
(Rs)
1,000 12,000
1,200 17,000
800 11,000
2,000 27,000
6,000 45,000
8

 Multiple variables
 Multiple time
 Eg
 10 years annual Inflation data for G20 countries
9

 Forecast will never be accurate
 Difficult to predict when a product will be sold at what location and when
 Measure error and create forecast band.
 Aggregate forecast are better
 Reduces variability, so easy to forecast.
 Aggregate by SKU, location and time.
 Pooling
 Shorter the better
 Forecast for tomorrow will be better than 3 months in advance
 Modularity
10

 What is the forecast
 Shipment
 Order
 POS
 What is the unit of measurement
 Is it in units or value
 What is the horizon- How far
 What is the time bucket- weekly, monthly, quarterly
 How frequently do we update the forecast
11

 First plot the data.
 What patterns can you see
 Keep an eye for
 Missing data
 Outlier
 Trend
 One-offs
 Correct the data before forecasting
 Use 3 times standard deviation as a rule of thumb
12

𝐻𝑖𝑠𝑡𝑜𝑟𝑦 = 𝑃𝑎𝑡𝑡𝑒𝑟𝑛 + 𝐸𝑟𝑟𝑜𝑟
Pattern:
 Level
 Trend
 Seasonality
 Cyclicality
13

 “When a time series data displays a steady tendency of increase or decrease
through time. Such a tendency is called a trend.”1
 Trend could be temporary
 Understand the reason for the pattern
 Trend can also be damped.
 Parameter to damp the trend is ø- Phi
141. Complete Business Statistics, 7th Edition, Amir D Aczel et al..

“when a cyclical pattern in our data has a
period of 1 year, we usually call the pattern
seasonal variation. When a cyclical pattern
has a period other than 1 year, we refer to it
as cyclical variation”1
151. Complete Business Statistics, 7th Edition, Amir D Aczel et al..

Forecasting
Subjective
Experimental
(Extrapolating
test group)
Judgemental
•(Expert
opinion)
Objective
Time Series Causal models
16

 Purpose
 Data collection
 Summarise and plot
 Data management
 Test and hold out period
 Deploy model
 Metrics
 Prediction/ forecast
17

 Naïve forecast
 Average
 Simple
 weighted
 Simple exponential smoothing
 Linear regression
 Double exponential smoothing (Holts model)
 Triple exponential smoothing(Holts- winter model)
 Simple Linear Regression
18

 Last month actual will be forecast for next month.
 Advantages
 Easy to use
 Sometimes can be more accurate
 Can be used for benchmarking.
 Disadvantages
 Not using full history
 Cant be other than next month
 Can’t capture pattern.
19

 It can be simple average, moving average or weighted average
 Suitable for:
 Level
 Not Suitable for:
 Trend
 Seasonality
 Advantages
 Easy to use
 Smoothens the forecast
 Disadvantages
 What is the optimum weights
 Missing some history
20

 Suitable for:
 Level
 Trend
 Seasonality
 Concept:
 Weights for historical data
 parameter:
 Alpha (0 to 1)
21

 Yˆt+1= 𝛼*Yt +(1- 𝛼)*Ft
 Yˆt+1 = 𝛼*Yt + Ft - 𝛼*Ft
 Yˆt+1 = Ft + 𝛼*(Yt –Ft)
 Yˆt+1 = Ft + 𝛼*𝜀
 𝜀= Error= (Actual- Forecast)
22

23
-
200
400
600
800
1,000
1,200
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Time Y
1 866
2 468
3 502
4 584
5 875
6 247
7 772
8 415
9 958
10 964
11 359
12 817
13 450
14 963
15 876
16 460

24
Initialising forecast
Smoothing parameter (0 to 1)
Forecast

25
Installing data analysis tab
• Click file tab
• Click options
• Click Add-ins
• In the manage box, click go button
• Check Anlaysis ToolPak box

31
Click Exponential smoothing

32
• Input range is the actual historical sales data we have
• Damping factor is (1- 𝛼). So if 𝛼 is .30, then Damping factor is (1-.3)=.7
• For output range click a new column adjacent to first actual data point
• Click OK

34
Now, drag the formula from last column to next column for forecasting new period.

 Pattern suited:
 Level & trend
 Seasonality
 Concept:
 All data points
 Equal weightage to all data points
35

36
t Y
1 37
2 42
3 44
4 47
5 52
6 55
7 62
8 71
9 73
10 75

 Aim:
 To reduce the error sum of squares.
 ∑e^2
 Error= Actual- Forecast
 Et= Yt-a-bt
 ∑Et
2= ∑(Yt-a-bt) 2
 Partially differentiating with respect to a & b
 ∑y = n*a+b*∑t
 ∑yt = a*∑t+b*∑t2
37

t Y Y*t t^2
1 37 37 1
2 42 84 4
3 44 132 9
4 47 188 16
5 52 260 25
6 55 330 36
7 62 434 49
8 71 568 64
9 73 657 81
10 75 750 100
55 558 3440 385
38
∑y = n*a+b*∑t
∑yt = a*∑t+b*∑t2

 Solving a and b:
 Yˆ=31.06+4.496*t
 Forecast for period 11:
 Yˆ=31.06+4.496*11
 Yˆ=80.516
39

 Select actual sales (Y)
 Plot a line graph in Excel
 Click on the graph and right click
 Click add trend line
 Check the display equation on chart
 No we have a slope & intercept form
 Plug in the value for t and we will have the forecast
40

 Suitable for:
 Level & Trend
 Seasonality
 Concept:
 All data points
 Progressive Weights for historical data
 parameter:
 Alpha (0 to 1)- level
 Beta (0 to 1)-Trend
46

 Ft+1=Lt+ bt
 Lt is a representation of level
 Lt=𝛼 ∗ 𝑌t + (1 − 𝛼)*(Lt-1+ bt-1)
 Bt is a representation of trend
 Bt=𝛽 ∗ (Lt −Lt−1) + (1 − 𝛽)*bt-1
47

 Suitable for:
 Level, Trend & Seasonality
 Concept:
 All data points
 Progressive Weights for historical data
 parameter:
 Alpha (0 to 1)- level
 Beta (0 to 1)-Trend
 Gamma (0 to 1)- Seasonality
48

 Ft+k = (Lt + k*bt)* St-M+k
 Lt = Level
 M= Length of seasonality( number of weeks or month in a year)
 Bt = Trend
 St = Seasonal component
 F = Forecast for k periods ahead
49

 Level
 Lt =𝛼 ∗ (𝑌t/St−M) + (1 − 𝛼)*(Lt-1+ bt-1)
 Trend
 bt = 𝛽 ∗ (Lt −Lt−1) + (1 − 𝛽)*bt-1
 Seasonality
 St = 𝛾 ∗ (Yt/Lt) + (1 − 𝛾)* St-M
50

 Divide available data into
 Test period
 Validation period/ Hold out period
51
T-6 T-5 T-4 T-3 T-2 T-1 T
Test Validation

 To measure how well we have predicted the actual data
 To compare different statistical models that fits the data
 Necessary for improvement of the process
 Different industries will have different error drivers
 Try to segregate outliers like new launches etc.
52

 Error
 Et = At – Ft
 Et = Error
 At = Actual
 Ft = Forecast
53
Ft can be measured at a lag

 Mean Error
 At = Actual
 Ft = Forecast
 t= time periods
 n= number of time periods
54
ME =
1
𝑛 𝑡=1
𝑛
(𝐴 𝑡 − 𝐹𝑡)

 Mean Absolute Deviation
 At = Actual
 Ft = Forecast
 t= time periods
55
MAD =
1
𝑛 𝑡=1
𝑛
(|𝐴 𝑡 − 𝐹𝑡|)

 Mean Percent Error
 At = Actual
 Ft = Forecast
 t= time periods
56
MPE =
1
𝑛 𝑡=1
𝑛
(𝐴 𝑡 − 𝐹𝑡)
𝐴 𝑡
X 100

 Mean Absolute Percent Error
 At = Actual
 Ft = Forecast
 t= time periods
57
MAPE =
1
𝑛 𝑡=1
𝑛
(|𝐴 𝑡 − 𝐹𝑡|)
𝐴 𝑡
X 100

 Root Mean Square Error
 At = Actual
 Ft = Forecast
 t= time periods
58
RMSE =Sqrt(
1
𝑛 𝑡=1
𝑛
(𝐴 𝑡 − 𝐹𝑡)^2)

 Choose initial values for parameters between 0 and 1 based on the model
 Use an error measure as a target to minimise
 Deploy Excel solver
 Choose the objective function
 Choose the variables to optimise
 Enter the constraints
 Solve
 Validate the results
59

“Demand Sensing utilizes downstream data to
communicate what products and services have
been sold, who is buying the products & services
and the impact of sales and marketing activities on
influencing consumer demand.”1
671. Demand-Driven Forecasting by Charles W. Chase, Jr.

 Correlation is a measure of how things are related1
 Correlation coefficient (r) is way to put a value to the relationship1
 r can take a value between -1 and 1.
 r is unitless
 +1 is called perfect positive correlation
 -1 is called perfect negative correlation
 0 means there is no linear correlation
 Correlation doesn’t mean causation.
68
1. (Source: https://www.statisticshowto.datasciencecentral.com/probability-and-
statistics/correlation-analysis/)

0
20
40
60
80
100
120
140
160
180
200
0 10 20 30 40 50 60 70 80 90
69
Eg: Sales of ice cream during hot weather
R value will be above 0.

0
20
40
60
80
100
120
140
160
180
200
0 10 20 30 40 50 60 70 80 90
70
Eg: Sales of blankets during hot weather
R value will be below 0.

71
R value will be close to 0.
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90

72
Including header
doesn’t matter

 It is a statistical method for understanding and quantifying relationship between two
continuous variable.
𝑦 = 𝛽0 + 𝛽1 𝑥
 X- predictor, explanatory or independent variable
 Y- Response, Outcome or dependent variable
 𝛽0- Intercept
 𝛽1- Slope
 Only one predictor variable.
75

 Assumptions
 The mean value of response (Yi ) for each value of predictor (Xi) is a linear function.
 Errors (Ei) are independent
 Errors (Ei) for each value of predictor (Xi) are normally distributed.
 Errors (Ei) for each value of predictor (Xi) ave equal variances
76

78
Click data tab
Click Data Analysis button
Click Regression

79
Y range is the outcome or dependent
variable
X range is the independent or predictor
variable
Labels box tells us if the column has a
title. If so, tick the box
Constant is Zero- means where you don’t
need an intercept. I.e. the line will pass
through the origin

80
Confidence level – Don’t go less than 90%
or more than 99%. Optimal value is
always 95%
These boxes when ticked displays the
error table and graphs.

83
• Multiple R is the correlation coefficient r.
• R Square tell us how much variability in Y is
explained by the model.
• Higher the R square value always the better.
• When you square Multiple R you get R square.
• Mathematically R square
• 𝑆𝑢𝑚 𝑜𝑓 𝑆𝑞𝑢𝑎𝑟𝑒 𝑅𝑒𝑔𝑟𝑒𝑠𝑠𝑖𝑜𝑛 𝑆𝑢𝑚 𝑜𝑓 𝑆𝑞𝑢𝑎𝑟𝑒𝑠 𝑡𝑜𝑡𝑎𝑙

84
• Adjusted R square is only used for multiple
regression. I.e only when we use more than 1 X
variable.
• Standard Error measures accuracy of the prediction
• 𝑥 =
𝛴(𝑦− 𝑦)
𝑁−2

85
• How to calculate Standard Error

86
• How to calculate Standard Error

87
• Total sum of square = 𝑖=1
𝑛
𝑦𝑖 − 𝑦 2
• Total sum of Residual = 𝑖=1
𝑛
𝑦𝑖 − 𝑦𝑖
2
• Total sum of Regression= 𝑖=1
𝑛
𝑦𝑖 − 𝑦 2
Sum of Square Total= Sum of Square Regression + Sum of Square Residual

91
• MS= SS/ df
• F= MSregression / Msresidual
• Significance is P value

92
• Coefficient is what we will use for forecasting
• Always make sure P value is less than the alpha value.
• We choose alpha value. It is mostly 5%. It can also between 1-
10%.

93
• Check the plot for error. It should not have a pattern

94
Curvilinear shape is visible in the residual

95
Variance is increasing around the mean line
Also keep look out of outlier in error

96
Error is increasing with time. Suggesting Time series
model to be included

97
Positive serial correlation: same sign and same magnitude

98
Negative serial correlation: Error follow alternate sign

99
Values should be close to the slanting line

100
Clearly not following the slanting line

 First plot the data
 Once you ran regression line, check
 R square value
 P value of model
 P value of coefficients
 Error plot
101

102
Forecasting is a journey.
Collaborate and follow on a path based on data.

Forecasting demand planning

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