Chapter
3
Demand
Forecasting
Slides prepared by
Laurel Donaldson
Douglas College
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Learning Objectives
LO 1
Identify uses of demand forecasts, distinguish between forecasting
time frames, describe common features of forecasts, list the
elements of a good forecast and steps of forecasting process, and
contrast different forecasting approaches.
LO 2
Describe at least three judgmental forecasting methods.
LO 3
Describe the components of a time series model, and explain
averaging techniques and solve typical problems.
LO 4
Describe trend forecasting and solve typical problems.
LO 5
Describe seasonality forecasting and solve typical problems.
LO 6
Describe associative models and solve typical problems.
LO 7
Describe three measures of forecast accuracy, and two ways of
controlling forecasts, and solve typical problems.
LO 8
Identify the major factors to consider when choosing a forecasting
technique.
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2
Chapter Outline











What is forecasting?
Features common to all forecasts
Elements of a good forecast
Steps in the forecasting process
Approaches to forecasting
Judgmental methods
Time series models
Associative models
Accuracy and control of forecasts
Choosing a forecasting technique
Excel Templates
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
3
What is Forecasting?
A demand forecast is
an estimate of demand
expected over a future
time period
I see that you will
get a 100 in OM this semester.
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4
 How big a facility do I need to manufacture a new
videophone?
 How much
money
do I need to run
operations of my
Need
to FORECAST
demand!
accounting office?
 How many pairs of white shoes should I
order for the summer season in my store?
 How many operators should I schedule next month for my
call centre?
 How much lettuce should I buy for next week in my
restaurant?
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5
3 Uses for Forecasts:
Design the System
• long term
(annual)
• (types of products
& services to offer,
capacities,
equipment,
location)
Use of the System
• medium term
(monthly)
• (inventory,
workforce levels,
planning
production)
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Schedule the
System
• short term
(daily, weekly)
• (production,
purchasing, staff
scheduling)
6
Features of Forecasts
Assumes causal system
past ==> future
Forecasts rarely perfect because of
randomness
Forecasts more accurate for
groups vs. individuals
Forecast accuracy decreases
as time horizon increases
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7
Elements of a Good Forecast
Compatible
Useful time
horizon
Meaningful
Reliable
Accurate
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Easy to
understand
& use
8
Steps in the Forecasting Process
1 Determine
purpose of
forecast
2 Establish a
time horizon
3 Select a
forecasting
technique
4 Obtain,
clean and
analyze data
5 Make the
forecast
6 Monitor the
forecast
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9
Approaches to Forecasting
Judgmental
non-quantitative analysis of subjective inputs
considers “soft” information such as
human factors, experience, gut instinct
Quantitative
Time series models
 extends historical patterns of numerical data
Associative models
 create equations with explanatory variables
to predict the future
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10
Judgmental Methods
Executive opinions
pool opinions of high-level executives
long term strategic or new product development
Expert opinions
Delphi method: iterative questionnaires
circulated until consensus is reached.
 technological forecasting
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11
Judgmental Methods
Sales force opinions
based on direct customer contact
Consumer surveys
questionnaires or focus groups
Historical analogies
use demand for a similar product
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12
What is a Time Series?
Time series:
a time ordered sequence of observations
taken at regular intervals of time
The following 6 patterns could be identified in a time series:
 Level: (average) horizontal pattern
 Trend: steady upward or downward movement
 Seasonality: regular variations related to time of year or day
 Cycles: wavelike variations lasting more than one year
 Irregular variations: caused by unusual circumstances, not
reflective of typical behaviour
 Random variations: residual variations after all other
behaviours are accounted for (called noise)
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13
Patterns of a Time Series
Demand for snowboards
Seasonal peaks (winters)
Trend component
Actual
demand line
Random
variation
Year
1
Year
2
Year
3
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Year
4
14
Time series models
Naive methods
Averaging methods
Moving average
Weighted moving average
Exponential smoothing
Trend models
Linear and non-linear trend
Trend adjusted exponential smoothing
Techniques for seasonality
Techniques for cycles
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15
Naive Methods
 Next period = last period
 Simple to use and understand
 Very low cost
 Low accuracy
Stable time series data : Ft  At 1
Seasonal variation s : Ft  At  n
Data with tren d : Ft  At 1   At 1  At  2 
F = forecast
A = actual
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16
Naive Method - Example
Uh, give me a minute....
We sold 250 wheels last
week.... Now, next week
we should sell....
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17
Naive Method with Trend: Example
2 years ago we sold 50 memberships.
Last year we sold 75 memberships.
This year we expect to sell …
100
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18
Averaging Methods
Demand in previous n periods
Moving

: Ft 
Average
n
Weighted
Moving Average

Weight

:F 
t
period n
 Demand
 Weights
period n

Exponentia l
: Ft  Ft 1    At 1  Ft 1 
Smoothing
F = forecast
A = actual
 = smoothing
constant
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19
Moving Average
average of last few actual data values,
updated each period
easy to calculate and understand
smoothes bumps, lags behind changes
choose number of periods to include
fewer data points = more sensitive to changes
more data points = smoother, less responsive
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20
Moving Average - Example
Compute a three-period moving average forecast
for period 6, given the demand below
Period
1
2
3
4
5
Demand 
42 
40 
F3  F4  F5 43  40  41

 41.33
 F6 
43 
3
3
40 

41 
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21
Weighted Moving Average - Example
 Compute a 4-period weighted moving average forecast for
period 6 using a weight of 0.4 for the most recent period,
0.3 for the next, 0.2 for the next, and 0.1 for the next.
Period
Demand
1
42
2
3
40
43
4
40
5
41
Weight 


0.1 
0.1 F2  0.2  F3  0.3  F4  0.4  F5
 41
 F6 
0.2 
0.1  0.2  0.3  0.4
0.3 

0.4 
 The choice of weights may involve the use of trial and
error to find a suitable weighting scheme
 Weights must add up to 100%
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22
Moving Average Example
Period
1
2
3
4
5
6
7
Demand
Forecast
9
12
14
16
19
23
26
(9 + 12 + 14)/3 = 11 2/3
(12 + 14 + 16)/3 = 14
(14 + 16 + 19)/3 = 16 1/3
(16 + 19 + 23)/3 = 19 1/3
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23
Quantity
Graph of Moving Average
30
28
26
24
22
20
18
16
14
12
10
Moving
Average
Forecast
–
–
–
–
–
–
–
–
–
–
–
Actual
Sales
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
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|
|
|
10 11 12
24
Moving Average Example
Apply weights of .5 for most recent period, then .3, then .2
Period
1
2
3
4
5
6
7
Demand
9
12
14
16
19
23
26
Forecast
[(.5 x 14) + (.3 x 12) + (.2 x 9)] = 12.4
[(.5 x 16) + (.3 x 14) + (.2 x 12)] = 14.6
[(.5 x 19) + (.3 x 16) + (.2 x 14)] = 17.1
[(.5 x 23) + (.3 x 19) + (.2 x16)] = 20.4
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25
Moving Average And
Weighted Moving Average
Weighted
moving
average
30 –
25 –
Quantity
20 –
Actual
sales
15 –
Moving
average
10 –
5 –
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
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|
|
|
10 11 12
26
Exponential Smoothing
sophisticated weighted moving average
weights decline exponentially
most recent data weighted most
subjectively choose smoothing constant 
 ranges from 0 to 1 (commonly .05 to .5)
widely used
easy to use
easy to alter weighting
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27
Exponential Smoothing Formula
Forecast = previous forecast plus a
percentage of the forecast error
Actual - Forecast is the error term
 is the % feedback
Ft = Ft-1 + (At-1 - Ft-1)
F = forecast
A = actual
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28
Exponential Smoothing: Alternate Formula
Forecast = previous forecast plus a
percentage of the forecast error
 is the weight on actual demand
1  is the weight on previous forecast
Ft = (1 - Ft-1 + (At-1)
F = forecast
A = actual
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29
Exponential Smoothing: Example
Forecasted demand = 142 video games
Actual demand = 153
Smoothing constant  = .20
New forecast = .2 (153) + (1 - .2)(142)
= 30.6 + 113.6
= 144.2 ≈ 144 games
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30
Exponential Smoothing: Example
Forecasted demand = 142 video games
Actual demand = 153
Smoothing constant  = .20
New forecast = 142 + .2 (153 - 142)
= 30.6 + 113.6
= 144.2 ≈ 144 games
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31
Exponential Smoothing: Example
 Prepare a forecast using smoothing constant  = 0.40.
 What is the starting point?
 average of several periods of actual data
 subjective estimate (for this example, use 60)
 first actual value (naïve approach)
Period
1
Actual
65
2
3
55
58
4
64
Forecast
60
F2  F1  0.4A1  F1 
F3  F2  0.4A 2  F2 
Calculatio ns
60  0.465 - 60   62
62  0.455 - 62  59.2
F4  F3  0.4A 3  F3  59.2  0.458 - 59.2   58.72
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32
Exponential Smoothing: Your Turn!
What are the exponential smoothing
forecasts for periods 2-5 using  =0.5?
Use naïve approach for 1st week
Week
1
2
3
4
5
Demand
820
775
680
655
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33
Exponential Smoothing: Your Turn!
F2=(.5)(820)+(1 - .5)(820) =820
F3=(.5)(775)+(1 - 0.5)(820)=797.5
Week
1
2
3
4
5
Demand
820
775
680
655
0.5
820.00
820.00
797.50
738.75
696.88
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34
Selecting a Smoothing Constant 
Demand
225 –
Actual
demand
200 –
a = .5
175 –
150 – |
1
|
2
|
3
|
4
|
|
5
6
Period
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a = .1
|
|
7
8
|
9
35
Choosing 
 When demand is fairly stable, use a lower value
for 
 smoothes out random fluctuations
 When demand increasing or decreasing, use a
higher value for 
 more responsive to real changes
 Try to find balance
 trial and error
 can change over time.
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36
True or False?
A moving average forecast tends to be more responsive to
changes in the data series when more data points are
included in the average.
False
As compared to a simple moving average, the weighted
moving average is more reflective of the recent changes.
True
A smoothing constant of .1 will cause an exponential
smoothing forecast to react more quickly to a sudden
change than a value of .3 will.
False
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37
Excel:
Exponential
Smoothing
Solved Problem 1: Excel Template
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38
Techniques for Trend
–
Develop an equation
that describes the trend
–
Look at historical data
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39
Nonlinear Trends
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40
Linear Trend Equation
–
–
Fit a trend line to a series of historical data
Use regression to find the equation of the line
(called the Least Squares Line)

Equation : yt  a  bt
Slope : b 
n ty   t  y
n t   t 
2
2
y  b t

y - intercept : a 
n
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41
Linear Trend
Demand
Actual
observation
Deviation
Deviation
Deviation
Deviation
Deviation
Deviation
Deviation
Points on the line

yt  a  bt
Time
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42
Linear Trend: Example
week t 
1
Sales  y 
150
t2
1
ty
150
2
3
4
157
162
166
4
9
16
314
486
664
5
 t  15
177
 y  812
25
 t 2  55
885
 ty  2,499
 t 
2
 225
5  2,499  15  812 12,495  12,180

 6.3
5  55  225
275  225
812  6.3  15
a
 143.5
5

yt  a  bt  143.5  6.3t
b
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43
Excel - Linear Trend
Scatter with Trendline
Insert Chart
160
Scatter
140
y = 10.171x - 20242
120
Highlight data range
Sales
100
80
Right Click on a data
point
60
40
20
0
1996
1997
1998
1999
2000
2001
2002
2003
2004
Year
Add Trendline
Type: Linear
Options: Show equation
on chart
Or Insert Functions:
=SLOPE(Range of y's,Range of x's)
=INTERCEPT(Range of y's,Range of x's)
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44
Excel - Linear Trend
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45
Trend-Adjusted Exponential Smoothing
select values (usually through trial and error) for
  = smoothing constant for average
 b = smoothing constant for trend
estimate starting smoothed average and
smoothed trend
 use most recent data
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46
Trend-Adjusted Exponential Smoothing
TAFt+1 = St + Tt (3–6)
St = TAFt +α(At  TAFt)
(3–7)
Tt = Tt-1 + b( St  St-1 Tt-1)
where
St = smoothed average at the end of period t
Tt = smoothed trend at the end of period t
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47
Trend-Adjusted Forecast: Example
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48
Techniques for Seasonality
Additive or Multiplicative Model
quantity added to average or trend
or proportion x average or trend Additive Model
Demand
Demand = Trend +
Seasonality
Multiplicative Model
Demand = Trend x
Seasonality
time
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49
Using Seasonal Relatives
Seasonal Relative (or index)
 = proportion of average or trend for a season in the
multiplicative model
seasonal relative of 1.2 = 20% above average
Deseasonalize
remove seasonal component to more clearly see other
components
divide by seasonal relative
Reseasonalize
adjust the forecast for seasonal component
multiply by seasonal relative
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50
Times Series Decomposition
1. Compute the seasonal relatives.
2. De-seasonalize the demand data.
3. Fit a model to de-seasonalized demand
data, e.g., moving average or trend.
4. Forecast using this model and the
de-seasonalized demand data.
5. Re-seasonalize the deseasonalized
forecasts.
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51
Techniques for Seasonality - Example
Predict quarterly demand for a certain loveseat
The series has both trend and seasonality.
Quarterly relatives : Q1 = 1.20, Q2 = 1.10, Q3 = 0.75, Q4 =
0.95.
Trend equation yt=124+7.5t (t = 1 in first quarter of 2003)
Predict demand for quarter 3 of 2006
for quarter 3 of 2006  t  15

y15  124  7.5 15  236.5
F15  236.5  0.75  177.38
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52
Associative Forecasting
If I want to predict ridership originating from a
new train station, what data might I look at?
1. Find (predictor) variables that are associated with
ridership at other stations.
2. Associated = correlated = as one moves the other
moves
3. Create a model that shows the relationship between
the predictor variables and the predicted variable (e.g.
ridership)
4. Technique is regression analysis
•
•
Simple linear regression with one variable
Multiple regression (can be non-linear)
5. Test the model to see which variables most useful in
predicting ridership (look at r2)
6. Use the model to predict ridership, given values of the
predictor variables.
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53
Associative Models
Predictor variables (x): used to predict values of
the variable of interest (y)
(also called independent variables)
Linear regression: process of finding a straight line
that best fits a set of points on a graph
(use the Least Squares Equation)
Multiple regression: models with more than one
predictor variable
(computations complex, created with computer)
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54
Simple Linear Regression
X
7
2
6
4
14
15
16
12
14
20
15
7
Y
15
10
13
15
25
27
24
20
27
44
34
17
Computed relationship
50
40
30
20
10
0
0
5
10
15
20
25
would a linear model be reasonable?
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55
Excel: Simple Linear Regression
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56
Correlation and Excel
Correlation coefficient (r): measure of the strength
of relationship between two variables
ranges from -1 to +1
-1 = two variables move together in same direction
+1 = two variables move together in opposite direction
=CORREL(Range of y values, Range of x values)
r2 measures proportion of variation in the values of
y that is “explained” by the predictor variables in
the regression model
ranges from 0 to 1
higher values = more useful predictors
=RSQ(Range of y values, Range of x values)
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57
Linear Regression Assumptions
Predictions are being made only within the range
of observed values
relationship may be non-linear outside that range
y-intercept often not meaningful
Variations around the line are random and
normally distributed
For best results:
Always plot the data to verify linearity
Small correlation may imply that
other variables are important
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58
Accuracy and Control of Forecasts
Error = Actual value - Forecast value
+ve = forecast too low, -ve = too high
Three measures of forecasts are used:
Mean absolute deviation (MAD)
Mean squared error (MSE)
Mean absolute percent error (MAPE)
Control charts
plot errors to see if within pre-set control limits
Tracking signal
Ratio of cumulative error and MAD
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59
Error, MAD, MSE and MAPE
Error  e  Actual  Forecast  At  Ft
Actual  Forecast

MAD 
n
MSE 
2


Actual

Forecast

n
 Actual  Forecast

Actual

MAPE  100
n
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

%
60
MAD, MSE and MAPE
MAD
• Easy to
compute
• Weights
errors
linearly
MSE
MAPE
• Squares
error
• More
weight to
large errors
• Puts errors in
perspective
• above 70%
satisfactory
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61
Error, MAD, MSE and MAPE: Example
Compute MAD, MSE, and MAPE for the following data.
 100
Actual
Forecast
e
e
e
1
2
217
213
215
216
2
3
2
3
4
9
A
0.92%
1.41%
3
4
216
210
215
214
1
4
1
4
 10
1
16
  30
0.46%
1.90%
  4.69%
n
2
e

n
e
Period
e

MAD 
 2.5
MSE 
2
 7.5
e


100
 A


  1.17%
MAPE 
n
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
62
Forecast Errors
bias = the sum of the forecast errors
+ve bias = frequent underestimation
-ve bias = frequent overestimation
possible sources of error include:
Model may be inadequate (things have
changed)
Incorrect use of forecasting technique
Irregular variations
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
63
Controlling the Forecasting Process
Control chart
A visual tool for monitoring forecast errors
Used to detect non-randomness in errors
Set limits that are multiples of the √MSE
Forecasting errors are “in control” when only
random errors, no errors from identifiable causes
“in control” if
All errors are within control limits
No patterns (e.g. trends or cycles) are present
errors outside limit = need corrective action
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
64
Control Chart
Error

Upper limit
Range of
acceptable
variation
0

Lower limit
Time
Need for
corrective
action
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
65
Controlling Forecasts: Control Limits
Standard
deviation =
of error
s
Control
Limits
MSE 
2
e

n
= 0 ± 2 (or 3) s
95% of all errors should be within 2s
97.7% of all errors should be within 3s
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
66
Control Chart Example
A
F
A-F
Month (Sales) (Forecast) Error
1
2
3
4
5
6
s
90
95
115
100
125
140
100
100
100
110
110
110
1575

6
-10
-5
+15
-10
+15
+30
MSE
100
25
225
100
225
900
1575
262.5  16.2
Errors should be within ± 2(16.2).
Lower limit = -32.4 Upper limit = 32.4
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
67
Control Chart Example
32
24
16
8
0
-8 0
1
2
3
4
5
6
7
-16
-24
-32
All the errors are within the control limits
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
68
Pharmacy Forecast Control: Your Turn!
Below is a pharmacy’s actual sales and forecasted
demand for a certain prescription drug for 5 months.
How accurate is their forecast? Calculate MAD and
MSE and create a control chart.
Month
1
2
3
4
5
Sales Forecast
220
n/a
250
255
210
205
300
320
325
315
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
69
Pharmacy Forecast Control: Your Turn!
Sales
220
250
210
300
325
Month
1
2
3
4
5
A
MAD =
t
n
- Ft
Forecast
n/a
255
205
320
315
40
=
= 10 MSE =
4
Sq. Error
Abs Error
 A
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
t
n
5
5
20
10
25
25
400
100
40
550
- Ft
2

550
=
= 137.5
4
70
Pharmacy Forecast Control: Your Turn!
s
550
 137.5  11.7
4 Errors should be within ± 2(11.7).
Lower limit = -23.4 Upper limit = 23.4
23.4
15.6
7.8
0
0
1
2
3
4
5
-7.8
-15.6
-23.4
All the errors are within the control limits
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
71
Tracking Signal
Tracking signal
 ratio of cumulative error to MAD
 can be plotted on a control chart
 investigate if TS > 4
(Actual -forecast)

Tracking signal =
MAD
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
72
True or False?
When error values fall outside the limits of a control
chart, this signals a need for corrective action
Ans: True
When all errors plotted on a control chart are either
all positive, or all negative, this shows that the
forecasting technique is performing adequately.
Ans: False
A random pattern of errors within the limits of a
control chart signals a need for corrective action.
Ans: False
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
73
Choosing a Forecasting Technique
No single technique works in every situation
Two most important factors
Cost
Accuracy
Other factors include availability of:
Historical data
Computers
Time needed to gather and analyze the data
Forecast horizon
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
74
Choosing a Forecast Technique
Forecasting
Amount of
Historical Data
Method
Simple
exponential
smoothing
Trendadjusted
exponential
smoothing
Data Pattern
Forecast
Horizon
Preparation time
Complexity
5 to 10
observations
Data should be
stationary
Short
Short
Little
sophistication
10 to 15
observations
Trend
Short to
medium
Short
Moderate
sophistication
Trend
Short
Regression 10 to 20
Short,
Moderate
sophistication
medium,
Trend
long
models
Seasonal
Enough to see seasonal
Short to
Short to
Moderate
patterns
medium
moderate
sophistication
3 peaks and
troughs
Causal
10
Can handle
Medium or Long
Considerable
complex patterns long
sophistication
regression observations
development
models
per
time, short time
implementation
independent
variable
Source: J. Holton Wilson
and D. Allison-Koerber, “Combining Subjective and Objective Forecasts Improves Results,”
Journal of Business Forecasting Methods & Systems, 11(3) Fall 1992, p. 4.
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
75
Choosing a Forecast Technique
Factor
1. Frequency
Short Term
daily, weekly
Medium Term
monthly,
quarterly
Long Term
annual
2. Level of
aggregation
Item
Product family
Total output
3. Type of model
Smoothing
Trend
Trend
Seasonal
Regression
4. Degree of
management
involvement
Low
Moderate
Managerial
Judgment
Trend
Regression
High
5. Cost per
forecast
Low
Moderate
High
Source: C. L. Jain, “Benchmarking Forecasting Models,” Journal of Business Forecasting Methods & Systems, Fall 2002, pp. 18–20,
30.
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76
Which technique?
Sales for a product have been fairly consistent over several
years, although showing a steady upward trend. The
company wants to understand what drives sales. The best
forecasting technique would be:
A) trend models
B) judgmental methods
C) moving averages
D) regression models
E) exponential smoothing techniques
Ans: D
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77
Learning Checklist
 Describe at least three judgmental forecasting
methods.
 Describe the components of a time series
model, and explain averaging techniques and
solve typical problems.
 Describe trend forecasting and solve typical
problems.
 Describe seasonality forecasting and solve
typical problems.
 Describe associative models and solve typical
problems.
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78
Learning Checklist




Identify uses of demand forecasts
Distinguish between forecasting time frames
Describe common features of forecasts
List the elements of a good forecast and steps
of forecasting process,
 Contrast different forecasting approaches.
 Describe three measures of forecast
accuracy, and two ways of controlling
forecasts, and solve typical problems.
 Identify the major factors to consider when
choosing a forecasting technique.
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79