introduction to forecasting in operations management Chapter 3.ppt

3-1
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Chapter 3
Forecasting

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McGraw-Hill/Irwin
Forecasting
FORECAST:
• A statement about the future
• Used to help managers
– Plan the system
– Plan the use of the system

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McGraw-Hill/Irwin
Forecasting
Forecast Uses
• Plan the system
– Generally involves long-range plans related to:
• Types of products and services to offer
• Facility and equipment levels
• Facility location
• Plan the use of the system
– Generally involves short- and medium-range plans related to:
• Inventory management
• Workforce levels
• Purchasing
• Budgeting

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McGraw-Hill/Irwin
Forecasting
• 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
I see that you will
get an A this quarter.
Common Features

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McGraw-Hill/Irwin
Forecasting
Elements of a Good Forecast
Timely
Accurate
Reliable
Written

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McGraw-Hill/Irwin
Forecasting
Steps in the Forecasting Process
Step 1 Determine purpose of forecast
Step 2 Establish a time horizon
Step 3 Select a forecasting technique
Step 4 Gather and analyze data
Step 5 Make the forecast
Step 6 Monitor the forecast
“The forecast”

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McGraw-Hill/Irwin
Forecasting
Types of Forecasts
• Judgmental - uses subjective inputs (qualitative)
• Time series - uses historical data assuming the
future will be like the past (quantitative)
• Associative models - uses explanatory variables
to predict the future

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McGraw-Hill/Irwin
Forecasting
Judgmental Forecasts
(Qualitative)
•Consumer surveys
•Delphi method
•Executive opinions
– Opinions of managers and staff
•Sales force.

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McGraw-Hill/Irwin
Forecasting
Time Series Forecasts
(Quantitative)
• Trend - long-term movement in data
• Seasonality - short-term regular variations in
data
• Irregular variations - caused by unusual
circumstances
• Random variations - caused by chance
• CYCLE- wave like variations lasting more
than one year

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McGraw-Hill/Irwin
Forecasting
Forecast Variations
Trend
Irregular
variation
Cycles
Seasonal variations
90
89
88
Figure 3-1
cycle

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McGraw-Hill/Irwin
Forecasting
The Forecast of Forecasts
• Naïve
• Simple Moving Average
• Weighted Moving Average
• Exponential Smoothing
• ES with Trend and Seasonality

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McGraw-Hill/Irwin
Forecasting
• Simple to use
• Virtually no cost
• Data analysis is nonexistent
• Easily understandable
• Cannot provide high accuracy
Naïve Forecast

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McGraw-Hill/Irwin
Forecasting
NAÏVE METHOD
• No smoothing of data
Period 1 2 3 4 5 6 7 8 Average
Demand 74 86 88
Forecast 98 90
change 12 2

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McGraw-Hill/Irwin
Forecasting
Techniques for Averaging
• Moving average
• Weighted moving average
• Exponential smoothing

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McGraw-Hill/Irwin
Forecasting
Simple Moving Average
• Smoothes out randomness by averaging positive and
negative random elements over several periods
• n - number of periods (this example uses 4)
Period 1 2 3 4 5 6 7
Demand 74 90 100 60 80 90
Forecast 81 82.5 82.5

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McGraw-Hill/Irwin
Forecasting
Points to Know on Moving Averages
• Pro: Easy to compute and understand
• Con: All data points were created equal….
…. Weighted Moving Average

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McGraw-Hill/Irwin
Forecasting
Weighted Moving Average
• Similar to a moving average methods except that it
assigns more weight to the most recent values in a time
series.
• n -- number of periods
ai – weight applied to period t-i+1
1 2 3
Alpha
Demand 46 48 47 23 40
Forecast 32.70 35.60






 a

t
1
n
t
i
i
1
i
t
1
t A
F
0.6 0.3 0.1

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McGraw-Hill/Irwin
Forecasting
Exponential Smoothing
• Simpler equation, equivalent to WMA
a – exponential smoothing parameter (0< a<1)
• )
( 1
1
1 

 

 t
t
t
t F
A
F
F a
a 0.1
Demand 74 90 100 60
Forecast 72 72.2 73.98

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McGraw-Hill/Irwin
Forecasting
F2 = 37 + (0.30)(37-37)
= 37
F3 =37+ (0.30)(40-37)
= 37.9
Exponential Smoothing (α=0.30)
PERIOD MONTH DEMAND
1 Jan 37
2 Feb 40
3 Mar 41
4 Apr 37
5 May 45
6 Jun 50
7 Jul 43
8 Aug 47
9 Sep 56
10 Oct 52
11 Nov 55
12 Dec 54
)
( 1
1
1 

 

 t
t
t
t F
A
F
F a

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McGraw-Hill/Irwin
Forecasting
FORECAST, Ft + 1
PERIOD MONTH DEMAND (a = 0.3) (a = 0.5)
1 Jan 37 – –
2 Feb 40 37.00 37.00
3 Mar 41 37.90 38.50
4 Apr 37 38.83 39.75
5 May 45 38.28 38.37
6 Jun 50 40.29 41.68
7 Jul 43 43.20 45.84
8 Aug 47 43.14 44.42
9 Sep 56 44.30 45.71
10 Oct 52 47.81 50.85
11 Nov 55 49.06 51.42
12 Dec 54 50.84 53.21
13 Jan – 51.79 53.61
Exponential Smoothing (cont.)

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McGraw-Hill/Irwin
Forecasting
AFt +1 = Ft +1 + Tt +1
where
T = an exponentially smoothed trend factor
Tt +1 = (Ft +1 - Ft) + (1 - ) Tt
where
Tt = the last period trend factor
= a smoothing constant for trend
Adjusted Exponential Smoothing

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McGraw-Hill/Irwin
Forecasting
Adjusted Exponential Smoothing
(β=0.30)
PERIOD MONTH DEMAND
1 Jan 37
2 Feb 40
3 Mar 41
4 Apr 37
5 May 45
6 Jun 50
7 Jul 43
8 Aug 47
9 Sep 56
10 Oct 52
11 Nov 55
12 Dec 54
T3 = (F3 - F2) + (1 - ) T2
= (0.30)(38.5 - 37.0) + (0.70)(0)
= 0.45
AF3 = F3 + T3 = 38.5 + 0.45
= 38.95
T13 = (F13 - F12) + (1 - ) T12
= (0.30)(53.61 - 53.21) + (0.70)(1.77)
= 1.36
AF13 = F13 + T13 = 53.61 + 1.36 = 54.96

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McGraw-Hill/Irwin
Forecasting
Adjusted Exponential Smoothing:
Example
FORECAST TREND ADJUSTED
PERIOD MONTH DEMAND Ft +1 Tt +1 FORECAST AFt +1
1 Jan 37 37.00 – –
2 Feb 40 37.00 0.00 37.00
3 Mar 41 38.50 0.45 38.95
4 Apr 37 39.75 0.69 40.44
5 May 45 38.37 0.07 38.44
6 Jun 50 38.37 0.07 38.44
7 Jul 43 45.84 1.97 47.82
8 Aug 47 44.42 0.95 45.37
9 Sep 56 45.71 1.05 46.76
10 Oct 52 50.85 2.28 58.13
11 Nov 55 51.42 1.76 53.19
12 Dec 54 53.21 1.77 54.98
13 Jan – 53.61 1.36 54.96

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McGraw-Hill/Irwin
Forecasting
Linear Trend Equation
• b is the line slope.
Yt = a + bt
0 1 2 3 4 5 t
Y
a

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McGraw-Hill/Irwin
Forecasting
Calculating a and b
b =
n (ty) - t y
n t2 - ( t)2
a =
y - b t
n







Yes… Linear Regression!!

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McGraw-Hill/Irwin
Forecasting
Linear Trend Equation Example
t y
Week t2
Sales ty
1 1 150 150
2 4 157 314
3 9 162 486
4 16 166 664
5 25 177 885
 t = 15 t2
= 55  y = 812  ty = 2499
(t)2
= 225

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McGraw-Hill/Irwin
Forecasting
Linear Trend Calculation
y = 143.5 + 6.3t
a =
812 - 6.3(15)
5
=
b =
5 (2499) - 15(812)
5(55) - 225
=
12495-12180
275-225
= 6.3
143.5
Look on page 85

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McGraw-Hill/Irwin
Forecasting
Disadvantage of simple linear regression
1-apply only to linear relationship with an
independent variable.
2-one needs a considerable amount of data to
establish the relationship ( at least 20).
3-all observations are weighted equally

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McGraw-Hill/Irwin
Forecasting
Forecast Accuracy
• Forecast error
– difference between forecast and actual demand
– MAD
• mean absolute deviation
– MAPD
• mean absolute percent deviation
– Cumulative error
– Average error or bias

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McGraw-Hill/Irwin
Forecasting
Mean Absolute Deviation (MAD)
where
t = period number
At = demand in period t
Ft = forecast for period t
n = total number of periods
 = absolute value
 At - Ft 
n
MAD =

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McGraw-Hill/Irwin
Forecasting
MAD Example
1 37 37.00 – –
2 40 37.00 3.00 3.00
3 41 37.90 3.10 3.10
4 37 38.83 -1.83 1.83
5 45 38.28 6.72 6.72
6 50 40.29 9.69 9.69
7 43 43.20 -0.20 0.20
8 47 43.14 3.86 3.86
9 56 44.30 11.70 11.70
10 52 47.81 4.19 4.19
11 55 49.06 5.94 5.94
12 54 50.84 3.15 3.15
557 49.31 53.39
PERIOD DEMAND, At Ft (a =0.3) (At - Ft) |At - Ft|
 At - Ft 
n
MAD =
=
= 4.85
53.39
11

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McGraw-Hill/Irwin
Forecasting
Other Accuracy Measures
Mean absolute percent deviation (MAPD)
MAPD =
|At - Ft|
At
Cumulative error
E = et
Average error
(E )=
et
n

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Forecasting
Comparison of Forecasts
FORECAST MAD MAPD E (E)
Exponential smoothing (a= 0.30) 4.85 9.6% 49.31 4.48
Exponential smoothing (a= 0.50) 4.04 8.5% 33.21 3.02
Adjusted exponential smoothing 3.81 7.5% 21.14 1.92
(a= 0.50, = 0.30)

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McGraw-Hill/Irwin
Forecasting
Forecast Control
• Tracking signal
– monitors the forecast to see if it is biased high
or low
Tracking signal = =
(At - Ft)
MAD
E
MAD

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McGraw-Hill/Irwin
Forecasting
Tracking Signal Values
1 37 37.00 – – –
2 40 37.00 3.00 3.00 3.00
3 41 37.90 3.10 6.10 3.05
4 37 38.83 -1.83 4.27 2.64
5 45 38.28 6.72 10.99 3.66
6 50 40.29 9.69 20.68 4.87
7 43 43.20 -0.20 20.48 4.09
8 47 43.14 3.86 24.34 4.06
9 56 44.30 11.70 36.04 5.01
10 52 47.81 4.19 40.23 4.92
11 55 49.06 5.94 46.17 5.02
12 54 50.84 3.15 49.32 4.85
DEMAND FORECAST, ERROR E =
PERIOD At Ft At - Ft (At - Ft) MAD
TS3 = = 2.00
6.10
3.05
Tracking signal for period 3
–
1.00
2.00
1.62
3.00
4.25
5.01
6.00
7.19
8.18
9.20
10.17
TRACKING
SIGNAL

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McGraw-Hill/Irwin
Forecasting
Sources of forecast errors
• The model may be inadequate.
• Irregular variation may be occur.
• The forecasting technique may be used
incorrectly or the results misinterpreted.
• There are always random variation in the
data.

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McGraw-Hill/Irwin
Forecasting
End Notes
• The two most important factors in choosing
a forecasting technique:
– Cost
– Accuracy
• Keep it SIMPLE!
• =FORECAST(70,{23,34,12},{67,76,56})
(if you can…let the computer do it)

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