Demand forecasting

1. Demand Forecasting
Professor & Lawyer.
Puttu Guru Prasad,
M.Com. M.B.A., L.L.B., M.Phil, PGDFTM, APSET. ICFAI TMF,
(PhD) at JNTUK,
Expert Resource person at APHRDI, Bapatla,
Senior Faculty for Management Studies,
Certified NSS Program Officer,
Coordinator – College Beautification
S&H Department, VVIT, Nambur,
93 94 96 98 98, 807 444 95 39,

2. Demand Forecasting
Planning
Forecast
Customer
Production
Process
Finished
Goods
Inputs

3. Forecasting
 Marketing: forecasts sales for new and
existing products.
 Production: uses sales forecasts to plan
production and operations; sometimes
involved in generating sales forecasts.

4. Characteristics of Forecasts
 They are usually wrong
 A good forecast is usually more than a
single number
 Aggregate forecast are more accurate
 The longer the forecasting horizon, the
less accurate the forecasts will be
 Forecasts should not be used to the
exclusion of known information

5. Forecasting Horizon
 Short term
(inventory management, production plans..)
 Intermediate term
(sales patterns for product families..)
 Long term
(long term planning of capacity needs)

6. Forecasting Techniques
Judgmental
Models
Time Series
Methods
Causal Methods
Forecasting
Technique
Delphi
Method
Moving
Average
Exponential
Smoothing
Regression
Analysis
Seasonality
Models

7. Types of forecasting Methods
 Subjective methods
Sales force composites
Customer survey
Jury of executive opinion
The Delphi method
 Objective methods
Causal methods
Time series methods

8. Qualitative Methods
 Don’t have data
 Don’t have time to develop a forecast
 Often used in practice
 “Close enough”
 Depend on expert opinions
 Market surveys
 More appropriate for long term forecasts

9. Delphi Technique
 A method to obtain a consensus forecast
by using opinions from a group of
“experts”
expert opinion
consulting salespersons
consulting consumers

10. Causal Methods
 Causal methods use data from sources other than the
series being predicted.
 If Y is the phenomenon to be forecast and X1 , X2 , . .., Xn are
the n variables we believe to be related to Y, then a causal
model is one in which the forecast for Y is some function of
these variables:
Y = f (X1 , X2 , . .., Xn )
 Econometric models are causal models in which the
relationship between Y and (X1 , X2 , . .., Xn ) is linear.
That is
Y = ao + a1 X1 + a2 X2 + … an Xn
for some constants a1 , a2 , . . . , an

11. Forecasting Steps for
Quantitative Methods
 Collect data
 Reduce/clean data
 Build and evaluate model(s)
 Forecast (model extrapolation)
 Track the forecast

12. Identify the correct pattern
• Collect data. Look for possible cause/effect
relationships
• Determine which form can be used to
generate the pattern
• Determine specific values of the parameters

13. 0
200
400
600
800
1000
1200
1400
1600
Jan
Apr
Jul
O
ct
Jan
Apr
Jul
O
ct
Jan
Apr
Jul
O
ct
Period
Salesinthousandsofcases

14. Building Models
 Plot data over time. (remove outliers & get right
scale).
 Using part of the data, estimate model parameters.
 Forecast the rest of the data with the model.
 Evaluate accuracy of the model.
 Use judgment to modify.
 Keep track of model accuracy over time (redo, if
needed).

15. Forecasting Stationary
Series

16. Time series Analysis
Patterns that arise most often
 Trend
 Seasonality
 Cycles
 Randomness

17. Time Series Patterns
Fig. 2-2

18. Notation
: Observed value of the demand during period t
time series we would like to predict
forecast made for period t in period t-1
forecast made at the end of t-1 after having
observed , , …1−tD
:
:}1,{
t
t
t
F
tD
D
≥
2−tD

19. Time Series Forecast
For some set of weights
,...., 10
0
aa
DaF
n
ntnt ∑
∞
=
−=

20. Evaluating forecasts
 Forecast error in period t
 For multiple-step-ahead
ttt DFe −=
ttt DFe −= −τ

21. Evaluating Forecasts
 Mean Absolute Deviation
 Mean Square Error
n
e
MAD
n
i
i∑=
= 1
||
n
e
MSE
n
i
i∑=
= 1
2

22. Forecast Errors Over Time
Fig. 2-3

23. TIME SERIES METHODS
Stationary Series
 A stationary time series is represented by a
constant plus a random fluctuation:
Dt = µ+ εt
where µ is an unknown constant corresponding to
the mean of the series and εt is a random error
with mean 0 and variance σ2
.
 The methods described for stationary series are:
 Moving Averages
 Exponential Smoothing

24. Methods of Forecasting
Stationary Series
 Moving Averages
 Exponential Smoothing
N
DDD
N
D
F Nttt
t
Nti
i
t
−−−
−
−= +++
==
∑ ...21
1
11 )1( −− −+= ttt FDF αα

25. Moving Average
N
DDD
F Nttt
t
−−− +++
=
...21

26. Month Deliveries
Jan 120
Feb 90
Mar 100
Apr 75
May 110
Jun 50
Jul 75
Aug 130
Sep 110
Oct 90
0
20
40
60
80
100
120
140
Jan Feb Mar Apr May Jun Jul Aug Sep Oct
Mont h

27. Month Deliveries MA(3) MA(6)
Jan 120
Feb 90
Mar 100
Apr 75 103
May 110 88
Jun 50 95
Jul 75 78 91
Aug 130 78 83
Sep 110 85 90
Oct 90 105 92
110 94

28. 0
20
40
60
80
100
120
140
1 2 3 4 5 6 7 8 9 10 11

29. Month Deliveries MA(3) MA(6)
1 2
2 4
3 6
4 8 4
5 10 6
6 12 8
7 14 10 7
8 16 12 9
9 18 14 11
10 20 16 13
11 22 18 15
12 24 20 17
22 19

30. Moving-Average Forecasts
Lag Behind a Trend
Fig. 2-4

31. EXPONENTIAL SMOOTHING
 Current forecast is a weighted average of the
last forecast and the current value of demand
New forecast = α (current observation of demand)
+ (1- α ) (last forecast)

32. Exponential Smoothing
11
111
11
)(
)1(
−−
−−−
−−
−=
−−=
−+=
ttt
tttt
ttt
eFF
DFFF
FDF
α
α
αα
Ft = Ft-1 – (fraction of the observed forecast error in t-1)
If we forecast high in period t-1  error is positive  adjustment
to decrease current forecast
If we forecast low in period t-1  error is negative  adjustment
to increase current forecast

33. ( ) 1
2
2
21
221
11
1
)1()1(
)1(
)1(
−−
∞
=
−−−
−−−
−−
∑ −=
−+−+=
−+=
−+=
it
oi
i
t
tttt
ttt
ttt
DF
FDDF
FDF
FDF
αα
αααα
αα
αα

34. Example
Quarter Failures Forecast
1 200 200
2 250 200
3 175 205
4 186 202
5 225 201
6 285 203
7 305 211
8 190 220

35. 0
50
100
150
200
250
300
350
1 2 3 4 5 6 7 8

36. Weights in Exponential
Smoothing
Fig. 2-5

37. Exponential Smoothing for
Different Values of Alpha
Fig. 2-6

38. Smaller values of α produce more stable forecasts,
whereas larger values of α will produce forecasts
which react more quickly to changes in the demand
pattern.

39. Comparison
2
1)1(
)...321(
1 +
=
+
=++++
N
N
NN
N
N
( )
α
αα
1
1
1
1
=−
−
∞
=
∑
i
i
i
2
11 +
=
N
α

40. Similarities & Differences
 Stationary series
 Single parameter
 Lag behind a trend
 When α=2/(N+1)
Same distribution of
forecast error
 ES weighted average
of all past data
 MA only last N periods
 MA : save past N data
 ES : only last forecast

41. Multiple-Step-Ahead Forecasts
Same as one-step-ahead-forecast

42. Trend Based Methods
 Regression Analysis
 Double Exponential
Smoothing
btaFt +=
tttt GSF ττ +=+,

43. Double Exponential Smoothing
Intercept at time t
and slope at time t
))(1( 11 −− +−+= tttt GSDS αα
11 )1()( −− −+−= tttt GSSG ββ
tttt GSF ττ +=+,