Transcript Production and Operations Management: Manufacturing and

Chapter 15
Demand Management
and
Forecasting
15-2
OBJECTIVES
Focus on two short-range
forecasting techniques
– Moving Average
– Exponential Smoothing
15-3
Simple Moving Average Formula
• The simple moving average model assumes an
average is a good estimator of future behavior
• The formula for the simple moving average is:
A t-1 + A t-2 + A t-3 +...+A t- n
Ft =
n
Ft = Forecast for the coming period
N = Number of periods to be averaged
A t-1 = Actual occurrence in the past period for up to “n”
periods
15-4
Simple Moving Average Problem (1)
Week
1
2
3
4
5
6
7
8
9
10
11
12
Demand
650
678
720
785
859
920
850
758
892
920
789
844
A t-1 + A t-2 + A t-3 +...+A t- n
Ft =
n
Question: What are the 3week and 6-week moving
average forecasts for
demand?
Assume you only have 3
weeks and 6 weeks of
actual demand data for the
respective forecasts
15-5
Calculating the moving averages gives us:
Week
1
2
3
4
5
6
7
8
9
10
11
12
Demand 3-Week 6-Week
650 F4=(650+678+720)/3
678
=682.67
720
F7=(650+678+720
+785+859+920)/6
785
682.67
859
727.67
=768.67
920
788.00
850
854.67
768.67
758
876.33
802.00
892
842.67
815.33
920
833.33
844.00
789
856.67
866.50
844
867.00
854.83
©The McGraw-Hill Companies, Inc., 2004
15-6
Plotting the moving averages and comparing
them shows how the lines smooth out to reveal
the overall upward trend in this example
1000
Demand
900
Demand
800
3-Week
700
6-Week
600
500
1 2 3 4 5 6 7 8 9 10 11 12
Week
Note how the
3-Week is
smoother than
the Demand,
and 6-Week is
even smoother
15-7
Simple Moving Average Problem (2) Data
Week
1
2
3
4
5
6
7
Demand
820
775
680
655
620
600
575
Question: What is
the 3 week
moving average
forecast for this
data?
Assume you only
have 3 weeks and
5 weeks of actual
demand data for
the respective
forecasts
15-8
Simple Moving Average Problem (2) Solution
Week
1
2
3
4
5
6
7
Demand
820
775
680
655
620
600
575
3-Week
5-Week
F4=(820+775+680)/3
=758.33
758.33
703.33
651.67
625.00
F6=(820+775+680
+655+620)/5
=710.00
710.00
666.00
15-9
Exponential Smoothing Model
Ft = Ft-1 + a(At-1 - Ft-1)
Where:
Ft  Forcast value for thecomingt timeperiod
Ft - 1  Forecast value in 1 past timeperiod
At - 1  Actualoccurancein thepast t time period
a  Alphasmoothingconstant
• Premise: The most recent observations might
have the highest predictive value
• Therefore, we should give more weight to the
more recent time periods when forecasting
15-10
Exponential Smoothing Problem (1) Data
Week
1
2
3
4
5
6
7
8
9
10
Demand
820
775
680
655
750
802
798
689
775
Question: Given the
weekly demand
data, what are the
exponential
smoothing
forecasts for
periods 2-10 using
a=0.10 and
a=0.60?
Assume F1=D1
15-11
Answer: The respective alphas columns denote the forecast values. Note
that you can only forecast one time period into the future.
Week
1
2
3
4
5
6
7
8
9
10
Demand
820
775
680
655
750
802
798
689
775
0.1
820.00
820.00
815.50
801.95
787.26
783.53
785.38
786.64
776.88
776.69
0.6
820.00
820.00
793.00
725.20
683.08
723.23
770.49
787.00
728.20
756.28
15-12
Exponential Smoothing Problem (1) Plotting
Note how that the smaller alpha results in a smoother line in
this example
Demand
900
800
Demand
700
0.1
600
0.6
500
1
2
3
4
5
6
Week
7
8
9
10
15-13
Exponential Smoothing Problem (2) Data
Week Demand Question: What are
1
820 the exponential
2
775 smoothing forecasts
3
680 for periods 2-5 using
4
655 a =0.5?
5
Assume F1=D1
15-14
Exponential Smoothing Problem (2) Solution
F1=820+(0.5)(820-820)=820
Week
1
2
3
4
5
Demand
820
775
680
655
F3=820+(0.5)(775-820)=797.75
0.5
820.00
820.00
797.50
738.75
696.88
15-15
The MAD Statistic to Determine Forecasting Error
n
A
MAD =
t
t=1
- Ft
1 MAD  0.8 standard deviation
1 standard deviation  1.25 MAD
n
• The ideal MAD is zero which would mean
there is no forecasting error
• The larger the MAD, the less the
accurate the resulting model
15-16
MAD Problem Data
Question: What is the MAD value given
the forecast values in the table below?
Month
1
2
3
4
5
Sales Forecast
220
n/a
250
255
210
205
300
320
325
315
15-17
MAD Problem Solution
Month
1
2
3
4
5
Sales
220
250
210
300
325
Forecast Abs Error
n/a
255
5
205
5
20
320
315
10
40
n
A
MAD =
t
t=1
n
- Ft
40
=
= 10
4
Note that by itself, the MAD
only lets us know the mean
error in a set of forecasts
MAPE
• Mean Absolute Percentage Error
(MAPE) is another measure often
used to evaluate forecasting
accuracy
n
MAPE  100

i 1
actual i  forecast i
actual i
n
A MAPE of under 8% is acceptable for most
applications
Computing MAD and MAPE: Problem (1)
Time
1
2
3
4
5
6
7
8
9
10
ACTUAL FORECAST ERROR ABS ERROR APE
820
820.00 ------775
820.00
-45.00
45.00
5.81
680
815.50 -135.50
135.50 19.93
655
801.95 -146.95
146.95 22.44
750
787.26
-37.26
37.26
4.97
802
783.53
18.47
18.47
2.30
798
785.38
12.62
12.62
1.58
689
786.64
-97.64
97.64 14.17
775
776.88
-1.88
1.88
0.24
776.69
61.91
8.93
MAD MAPE
15-20
Question Bowl
Which of the following is an example
of a “Time Series Analysis” type
of forecasting technique or
model?
a. Simulation
b. Exponential smoothing
c. Panel consensus
d. All of the above
e. None of the above
Answer: b. Exponential smoothing (Also includes Simple Moving
Average, Weighted Moving Average, Regression Analysis, Box
Jenkins, Shiskin Time Series, and Trend Projections.)
15-21
Question Bowl
Which of the following are reasons
why the Exponential Smoothing
model has been a well accepted
forecasting methodology?
a. It is accurate
b. It is easy to use
c. Computer storage
requirements are small
d. All of the above
e. None of the above
Answer: d. All of the above
15-22
Question Bowl
The value for alpha or α must
be between which of the
following when used in an
Exponential Smoothing
model?
a. 1 to 10
b. 1 to 2
c. 0 to 1
d. -1 to 1
e. Any number at all
Answer: c. 0 to 1
15-23
Question Bowl
Which of the following are
sources of error in forecasts?
a. Bias
b. Random
c. Employing the wrong trend
line
d. All of the above
e. None of the above
Answer: d. All of the above
15-24
Question Bowl
Which of the following would be
the “best” MAD values in an
analysis of the accuracy of a
forecasting model?
a. 1000
b. 100
c. 10
d. 1
e. 0
Answer: e. 0
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End of Chapter 15
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