Transcript No Slide Title

Chapter 10 Forecasting
• Overview of Forecasting Techniques
• The Time-Series Forecasting Methods in Perspective
• Case Study: Applying Time-Series Forecasting to The
Computer Club Warehouse Problem
1 - Chap 10
Problem 1
• You are working for Fortress,
an electronic outlet.
• Your assignment:
– Determine the number of units of a new heater to
stock for the coming winter.
• How would you approach this problem?
2 - Chap 10
Problem 2
• You are working for Hoixe Cake Shop
• Your assignment:
– Determine the number of loaves of bread to
produce for tomorrow’s sales
• How would you approach this problem?
3 - Chap 10
Problem 3
• You are working for a large production firm
• Your assignment:
– Forecast the employee turnover rate
• How would you approach this problem?
4 - Chap 10
Problem 4
• You are working for an investment firm
• Your assignment:
– forecast the interest rate movement
• How would you approach this problem?
5 - Chap 10
Forecasting Issues
• What is forecasting?
• Why do we forecast?
• How do we forecast?
• What is a good forecast?
6 - Chap 10
What is a forecast?
• A statement about the future value of a variable of interest such as
interest rate, unemployment rate, demand, supply, cost, rainfall,
etc.
• Observed measurement
= systematic part + random part
• Forecasting tries to isolate the systematic part
• The random part determines the forecast accuracy
7 - Chap 10
Characteristics of forecasts
• Forecasts rarely perfect because of randomness (natural or
assignable)
• Forecasts more accurate for groups vs. individuals
• Forecast accuracy decreases as time horizon increases
8 - Chap 10
Forecasting is hard:
Some famous forecasts
• This 'telephone' has too many shortcomings to be
seriously considered as a means of communication.
The device is inherently of no value to us.
– Western Union internal memo, 1876
• 640K memory ought to be enough for anybody.
– Bill Gates, 1981
9 - Chap 10
Forecasting is hard:
Some famous forecasts
• I think there is a world market for may be five
computers.
– Thomas Watson, chairman of IBM, 1943
• There is no reason anyone would want a computer in
their home.
– Ken Olson, president, chairman and founder of
DEC, 1977
10 - Chap 10
Why do we forecast?
• To make better decisions
• Forecasting is vital to every
functional area
– Finance and accounting:
budgetary planning and cost
control
– Marketing: new product demand
– Human resources: recruiting
– Production and operations:
capacity planning, process
selection, inventory control.
11 - Chap 10
Steps in the forecasting process
12 - Chap 10
How do we forecast
Types of forecasts
• Qualitative (Judgmental)- uses subjective inputs
• Time Series Analysis - uses historical data
assuming the future will be like the past
• Causal Relationship - uses explanatory variables
to predict the future (Covered in BUS102)
13 - Chap 10
How do we forecast?
Forecasting
Methods
Qualitative
methods
Manager’s
judgement
Jury of
Executive Opinion
Salesforce
Composite
Consumer Market
Survey
Delphi
Method
Time series
analysis
Last value
Causal
Relationship
Regression
analysis
Averaging
Simple moving
average
Exponential
smoothing
14 - Chap 10
Qualitative Forecasting Methods
• Manager’s Opinion: A single manager uses his or her best judgment.
• Jury of Executive Opinion: A small group of high-level managers
pool their best judgment to collectively make the forecast.
• Salesforce Composite: A bottom-up approach where each
salesperson provides an estimate of what sales will be in his or her
region. These estimates are then aggregated into a corporate sales
forecast.
• Consumer Market Survey: A grass-roots approach that surveys
customers and potential customers regarding their future purchasing
plans and how they would respond to various new features in
products.
• Delphi Method: A panel of experts in different locations who
independently fill out a series of questionnaires. The results from
each questionnaire are provided with the next one, so each expert
can evaluate the group information in adjusting his or her responses
next time.
15 - Chap 10
Time Series Analysis
Time series data: data collected over different time periods
(Hourly, Daily, Weekly, Monthly, or Annually).
Best Lending Rate of Last 37 Years
From
HKMA
23.00
21.00
19.00
15.00
13.00
11.00
9.00
7.00
5.00
3.00
2.
08
01
.0
9.
05
23
.0
1.
01
08
.1
5.
00
22
.0
0.
98
19
.1
1.
95
03
.0
9.
91
16
.0
7.
89
10
.0
5.
88
09
.0
6.
87
02
.0
6.
85
24
.0
8.
84
23
.0
1.
84
30
.0
2.
82
30
.1
0.
81
07
.1
6.
80
23
.0
1.
78
09
.1
2.
75
7.
74
22
.0
15
.0
5.
71
1.00
05
.0
Prime-Rate in %
17.00
From HSI
Company
16 - Chap 10
Time Series Analysis
• Four components of a time series
― Trend - long-term movement in data
― Seasonality - short-term regular variations in data
― Cycle – wavelike variations of more than one year’s
duration
― Irregular /Random variations - caused by unusual
circumstances/ chance
• Multiplicative model: Y = T * S * C * I
• Additive model: Y = T + S + C + I
17 - Chap 10
A typical time-series of past demands
Seasonal variation
x
x x
x
x
Sales
x
x
x x
xx
x
x xx
x
x x
x
x
x
x
x
x
x
x
x
x
x
x
xxxx
1
2
x x
x
x
3
Year
x
x
x
x
x
x
Linear
x
Trend
x
x
4
18 - Chap 10
Components of A Time Series
Irregular
variation
Random
variation
Trend
Cycles
90
89
88
Seasonal variations
19 - Chap 10
Forecasting at Fastchips
• Fastchips is a leading producer of microprocessors.
• Six months ago, it launched the sales of its latest
microprocessor.
• Month-by-month sales (in thousands) over the initial six
months have been
17
25
24
26
30
28
Question: What is the forecast for next month’s sales?
20 - Chap 10
The Last-Value (Naïve) Forecasting Method
The last-value forecasting method ignores all data points in a time
series except the last one.
Forecast = Last value
Fastchips: Month-by-month sales (in thousands) over the initial
six months:
17
25
24
26
30
28
Forecast = 28
21 - Chap 10
The Averaging Forecasting Method
The averaging forecasting method uses all the data points in the
time series and simply averages these points.
Forecast = Average of all data to date
Fastchips: Month-by-month sales (in thousands) over the initial
six months:
17
25
24
26
30
28
Forecast = (17+25+24+26+30+28) / 6 = 25
22 - Chap 10
The Moving-Average Forecasting Method
The moving-average forecasting method averages the data for
only the most recent time periods.
n = Number of recent periods to consider as relevant for
forecasting
Forecast = Average of last n values
Fastchips: Month-by-month sales (in thousands) over the initial
six months:
17
25
24
26
30
28
Forecast (n=3) = (26+30+28) / 3 = 28
23 - Chap 10
The Exponential Smoothing Forecasting Method
• The exponential smoothing forecasting method provides a
more sophisticated version of the moving-average method.
• It gives the greatest weight to the last month and then
progressively smaller weights to the older months.
Forecast = a (Last value) + (1 – a) (Last forecast)
a is the smoothing constant between 0 and 1.
24 - Chap 10
Measuring the Forecast Error
• The mean absolute deviation (called MAD) measures the
average absolute forecasting error.
MAD = (Sum of absolute forecasting errors) / (Number of
forecasts)
• The mean square error (often abbreviated MSE) measures the
average of the square of the forecasting error.
MSE = (Sum of square of forecasting errors) / (Number of
forecasts).
• The MSE increases the weight of large errors relative to the
weight of small errors.
25 - Chap 10
Case Study
The Computer Club Warehouse (CCW)
•
The Computer Club Warehouse (CCW) sells computer products at bargain
prices by taking telephone orders (as well as website and fax orders)
directly from customers.
•
Products include computers, peripherals, supplies, software, and computer
furniture.
•
The CCW call center is never closed. It is staffed by dozens of agents to
take and process customer orders.
•
A large number of telephone trunks are provided for incoming calls. If an
agent is not free when a call arrives, it is placed on hold. If all the trunks are
in use (called saturation), the call receives a busy signal.
•
An accurate forecast of the demand for agents is needed.
Question: How should the demand for agents be forecasted?
Which model is most superior for predicting the demand?
26 - Chap 10
Average Daily Call Volume (3 Years of Data)
CCW's Average Daily Call Volume
Year
1
1
1
1
2
2
2
2
3
3
3
3
Quarter
1
2
3
4
1
2
3
4
1
2
3
4
Call Volume
6,809
6,465
6,569
8,266
7,257
7,064
7,784
8,724
6,992
6,822
7,949
9,650
27 - Chap 10
25 Percent Rule (Current Forecasting Method)
Since sales are relatively stable through the year except for a
substantial increase during the Christmas season, assume that
each quarter’s call volume will be the same as the preceding
quarter, except for adding 25 percent for Quarter 4.
Forecast for Quarter 2 = Call volume for Quarter 1
Forecast for Quarter 3 = Call volume for Quarter 2
Forecast for Quarter 4 = 1.25(Call volume for Quarter 3)
Forecast for next Quarter 1 = (Call volume for Quarter 4) / 1.25
28 - Chap 10
Applying the 25-Percent Rule
Current Forecasting Method for CCW's Average Daily Call Volume
Year Quarter
1
1
1
2
1
3
1
4
2
1
2
2
2
3
2
4
3
1
3
2
3
3
3
4
4
1
4
2
4
3
4
4
Data
6,809
6,465
6,569
8,266
7,257
7,064
7,784
8,724
6,992
6,822
7,949
9,650
Absolute
Squared
Forecasting Forecasting
Forecast
Error
Error
Mean Absolute Deviation
MAD =
6,809
344
118,336
6,465
104
10,816 Mean Square Error
8,211
55
2,998
MSE =
6,613
644
414,994
7,257
193
37,249
7,064
720
518,400
9,730
1,006
1,012,036
6,979
13
164
6,992
170
28,900
6,822
1,127
1,270,129
9,936
286
81,939
7,720
424
317,815
29 - Chap 10
Considering Seasonal Effects
• When there are seasonal patterns in
the data, they can be addressed by
forecasting methods that use seasonal
factors.
• The seasonal factor for any period of a
year (a quarter, a month, etc.)
measures how that period compares to
the overall average for an entire year.
Seasonal factor = (Average for the period) / (Overall average)
• It is easier to analyze data and detect new trends if the data are
first adjusted to remove the seasonal patterns.
Seasonally adjusted data = (Actual call volume) / (Seasonal factor)
30 - Chap 10
Calculation of Seasonal Factors for CCW
Year
1
2
3
S.F.
Quarter
1
2
3
4
Q1
6,809
7,257
6,992
7,019
93.23%
Q2
6,465
7,064
6,822
6,784
90.10%
Q3
6,569
7,784
7,949
7,434
98.73%
Q4
8,266
8,724
9,650
8,880
117.94%
7,529
Three-Year
Average
Seasonal
Factor
7,019
6,784
7,434
8,880
Total = 30,117
Average = 30,117 / 4
= 7,529
7,019 / 7,529 = 0.93
6,784 / 7,529 = 0.90
7,434 / 7,529 = 0.99
8,880 / 7,529 = 1.18
31 - Chap 10
Excel Template for Calculating Seasonal Factors
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
B
C
D
E
F
G
Estimating Seasonal Factors for CCW
Year
1
1
1
1
2
2
2
2
3
3
3
3
Quarter
1
2
3
4
1
2
3
4
1
2
3
4
True
Value
6,809
6,465
6,569
8,266
7,257
7,064
7,784
8,724
6,992
6,822
7,949
9,650
Type of Seasonality
Quarterly
Quarter
1
2
3
4
Estimate for
Seasonal Factor
0.9323
0.9010
0.9873
1.1794
32 - Chap 10
Seasonally Adjusted Time Series for CCW
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
B
C
D
E
F
Seasonally Adjusted Time Series for CCW
Year
1
1
1
1
2
2
2
2
3
3
3
3
Quarter
1
2
3
4
1
2
3
4
1
2
3
4
Seasonal
Factor
0.93
0.90
0.99
1.18
0.93
0.90
0.99
1.18
0.93
0.90
0.99
1.18
Actual
Call Volume
6,809
6,465
6,569
8,266
7,257
7,064
7,784
8,724
6,992
6,822
7,949
9,650
Seasonally Adjusted
Call Volume
7,322
7,183
6,635
7,005
7,803
7,849
7,863
7,393
7,518
7,580
8,029
8,178
33 - Chap 10
Outline for Forecasting Call Volume
1. Select a time-series forecasting method.
2. Apply this method to the seasonally adjusted time series to
obtain a forecast of the seasonally adjusted call volume for the
next time period.
3. Multiply this forecast by the corresponding seasonal factor to
obtain a forecast of the actual call volume (without seasonal
adjustment).
34 - Chap 10
The Last-Value (Naïve) Forecasting Method
• The last-value forecasting method ignores all data points in a
time series except the last one.
Forecast = Last value
• The last-value forecasting method is sometimes called the
naïve method, because statisticians consider it naïve to use
just a sample size of one when other data are available.
• However, when conditions are changing rapidly, it may be that
the last value is the only relevant data point.
35 - Chap 10
The Last-Value Method Applied to CCW’s Problem
Last-Value Forecasting Method with Seasonality for CCW
True
Year Quarter Value
1
1
6,809
1
2
6,465
1
3
6,569
1
4
8,266
2
1
7,257
2
2
7,064
2
3
7,784
2
4
8,724
3
1
6,992
3
2
6,822
3
3
7,949
3
4
9,650
4
1
4
2
4
3
4
4
5
1
5
2
5
3
5
4
6
1
Seasonally Seasonally
Absolute
Squared
Adjusted Adjusted Actual Forecasting Forecasting
Value
Forecast Forecast
Error
Error
Type of Seasonality
7,322
Quarterly
7,183
7,322
6,589
124
15,464
6,635
7,183
7,112
543
294,306 Quarter Seasonal Factor
7,005
6,635
7,830
436
190,343
1
0.93
7,803
7,005
6,515
742
550,967
2
0.90
7,849
7,803
7,023
41
1,689
3
0.99
7,863
7,849
7,770
14
185
4
1.18
7,393
7,863
9,278
554
306,804
7,518
7,393
6,876
116
13,527
7,580
7,518
6,766
56
3,086
8,029
7,580
7,504
445
197,847
8,178
8,029
9,475
175
30,777
8,178
7,606
Mean Absolute Deviation
MAD =
295
Mean Square Error
MSE =
145,909
36 - Chap 10
The Averaging Forecasting Method
• The averaging forecasting method uses all the data points in
the time series and simply averages these points.
Forecast = Average of all data to date
• The averaging forecasting method is a good one to use when
conditions are very stable.
• However, the averaging method is very slow to respond to
changing conditions. It places the same weight on all the data,
even though the older values may be less representative of
current conditions than the last value observed.
37 - Chap 10
The Averaging Method Applied to CCW’s Problem
Averaging Forecasting Method with Seasonality for CCW
True
Year Quarter Value
1
1
6,809
1
2
6,465
1
3
6,569
1
4
8,266
2
1
7,257
2
2
7,064
2
3
7,784
2
4
8,724
3
1
6,992
3
2
6,822
3
3
7,949
3
4
9,650
4
1
4
2
4
3
4
4
5
1
5
2
5
3
5
4
6
1
Seasonally Seasonally
Absolute
Squared
Adjusted Adjusted Actual Forecasting Forecasting
Value
Forecast Forecast
Error
Error
Type of Seasonality
7,322
Quarterly
7,183
7,322
6,589
124
15,464
6,635
7,252
7,180
611
373,193 Quarter Seasonal Factor
7,005
7,047
8,315
49
2,415
1
0.93
7,803
7,036
6,544
713
508,687
2
0.90
7,849
7,190
6,471
593
351,969
3
0.99
7,863
7,300
7,227
557
310,729
4
1.18
7,393
7,380
8,708
16
243
7,518
7,382
6,865
127
16,145
7,580
7,397
6,657
165
27,175
8,029
7,415
7,341
608
369,664
8,178
7,471
8,816
834
695,957
7,530
7,003
Mean Absolute Deviation
MAD =
400
Mean Square Error
MSE =
242,876
38 - Chap 10
The Moving-Average Forecasting Method
• The moving-average forecasting method averages the data for
only the most recent time periods.
n = Number of recent periods to consider as relevant for
forecasting
Forecast = Average of last n values
• The moving-average forecasting method is a good one to use
when conditions don’t change much over the number of time
periods included in the average.
• However, the moving-average method is slow to respond to
changing conditions. It places the same weight on each of the
last n values even though the older values may be less
representative of current conditions than the last value
observed.
39 - Chap 10
The Moving-Average Method Applied to CCW
Moving Average Forecasting Method with Seasonality for CCW
True
Year Quarter Value
1
1
6,809
1
2
6,465
1
3
6,569
1
4
8,266
2
1
7,257
2
2
7,064
2
3
7,784
2
4
8,724
3
1
6,992
3
2
6,822
3
3
7,949
3
4
9,650
4
1
4
2
4
3
4
4
5
1
5
2
5
3
5
4
6
1
6
2
6
3
6
4
Seasonally Seasonally
Absolute
Squared
Adjusted Adjusted Actual Forecasting Forecasting Number of previous
Value
Forecast Forecast
Error
Error
periods to consider
7,322
n=
4
7,183
6,635
Type of Seasonality
7,005
Quarterly
7,803
7,036
6,544
713
508,687
7,849
7,157
6,441
623
388,036
Quarter Seasonal Factor
7,863
7,323
7,250
534
285,255
1
0.93
7,393
7,630
9,003
279
78,036
2
0.90
7,518
7,727
7,186
194
37,675
3
0.99
7,580
7,656
6,890
68
4,648
4
1.18
8,029
7,589
7,513
436
190,405
8,178
7,630
9,004
646
417,789
7,826
7,279
Mean Absolute Deviation
MAD =
437
Mean Square Error
MSE =
238,816
40 - Chap 10
The Exponential Smoothing Forecasting Method
• The exponential smoothing forecasting method places the
greatest weight on the last value in the time series and then
progressively smaller weights on the older values.
Forecast = a (Last value) + (1 – a) (Last forecast)
a is the smoothing constant between 0 and 1.
• This method places a weight of a on the last value, a(1–a)
on the next-to-last value, a(1–a)2 on the next prior value, etc.
– For example, when a = 0.5, the method places a weight
of 0.5 on the last value, 0.25 on the next-to-last, 0.125 on
the next prior, etc.
– A larger value of a places more emphasis on the more
recent values, a smaller value places more emphasis on
the older values.
41 - Chap 10
The Exponential Smoothing Forecasting Method
• The choice of the value of the smoothing constant a has a
substantial effect on the forecast.
– A small value (say, a = 0.1) is appropriate if conditions are
relatively stable.
– A larger value (say, a = 0.5) is appropriate if significant
changes occur frequently.
42 - Chap 10
The Exponential Smoothing Method Applied to CCW with
a = 0.1
Exponential-Smoothing Forecasting Method with Seasonality for CCW
Year Quarter
1
1
1
2
1
3
1
4
2
1
2
2
2
3
2
4
3
1
3
2
3
3
3
4
4
1
4
2
4
3
4
4
5
1
5
2
5
3
5
4
6
1
6
2
6
3
6
4
7
1
True
Value
6,809
6,465
6,569
8,266
7,257
7,064
7,784
8,724
6,992
6,822
7,949
9,650
Seasonally Seasonally
Absolute
Squred
Adjusted Adjusted Actual Forecasting Forecasting Smoothing Constant
Value
Forecast Forecast
Error
Error
a=
0.1
7,322
7,500
6,975
166
27,556
7,183
7,482
6,734
269
72,326
Initial Estimate
6,635
7,452
7,378
809
654,070 Average =
7,500
7,005
7,371
8,697
431
186,003
7,803
7,334
6,821
436
190,405
Type of Seasonality
7,849
7,381
6,643
421
177,365
Quarterly
7,863
7,428
7,353
431
185,361
7,393
7,471
8,816
92
8,474
Quarter Seasonal Factor
7,518
7,463
6,941
51
2,602
1
0.93
7,580
7,469
6,722
100
9,995
2
0.90
8,029
7,480
7,405
544
295,694
3
0.99
8,178
7,535
8,891
759
575,715
4
1.18
7,599
7,067
Mean Absolute Deviation
MAD =
376
Mean Square Error
MSE =
198,797
43 - Chap 10
The Exponential Smoothing Method Applied to CCW with
a = 0.5
Exponential-Smoothing Forecasting Method with Seasonality for CCW
Year Quarter
1
1
1
2
1
3
1
4
2
1
2
2
2
3
2
4
3
1
3
2
3
3
3
4
4
1
4
2
4
3
4
4
5
1
5
2
5
3
5
4
6
1
6
2
6
3
6
4
7
1
True
Value
6,809
6,465
6,569
8,266
7,257
7,064
7,784
8,724
6,992
6,822
7,949
9,650
Seasonally Seasonally
Absolute
Squred
Adjusted Adjusted Actual Forecasting Forecasting Smoothing Constant
Value
Forecast Forecast
Error
Error
a=
0.5
7,322
7,500
6,975
166
27,556
7,183
7,411
6,670
205
41,893
Initial Estimate
6,635
7,297
7,224
655
429,120 Average =
7,500
7,005
6,966
8,220
46
2,106
7,803
6,986
6,497
760
578,137
Type of Seasonality
7,849
7,394
6,655
409
167,289
Quarterly
7,863
7,622
7,545
239
56,909
7,393
7,742
9,136
412
169,521
Quarter Seasonal Factor
7,518
7,568
7,038
46
2,111
1
0.93
7,580
7,543
6,789
33
1,110
2
0.90
8,029
7,561
7,486
463
214,484
3
0.99
8,178
7,795
9,199
451
203,796
4
1.18
7,987
7,428
Mean Absolute Deviation
MAD =
324
Mean Square Error
MSE =
157,836
44 - Chap 10
The Exponential Smoothing Method Applied to CCW with
a = 0.9
Exponential-Smoothing Forecasting Method with Seasonality for CCW
Year Quarter
1
1
1
2
1
3
1
4
2
1
2
2
2
3
2
4
3
1
3
2
3
3
3
4
4
1
4
2
4
3
4
4
5
1
5
2
5
3
5
4
6
1
6
2
6
3
6
4
7
1
True
Value
6,809
6,465
6,569
8,266
7,257
7,064
7,784
8,724
6,992
6,822
7,949
9,650
Seasonally Seasonally
Absolute
Squred
Adjusted Adjusted Actual Forecasting Forecasting Smoothing Constant
Value
Forecast Forecast
Error
Error
a=
0.9
7,322
7,500
6,975
166
27,556
7,183
7,339
6,605
140
19,718
Initial Estimate
6,635
7,199
7,127
558
311,304 Average =
7,500
7,005
6,692
7,896
370
136,737
7,803
6,974
6,486
771
595,081
Type of Seasonality
7,849
7,720
6,948
116
13,398
Quarterly
7,863
7,836
7,758
26
693
7,393
7,860
9,275
551
303,337
Quarter Seasonal Factor
7,518
7,440
6,919
73
5,314
1
0.93
7,580
7,510
6,759
63
3,919
2
0.90
8,029
7,573
7,497
452
204,021
3
0.99
8,178
7,984
9,421
229
52,566
4
1.18
8,159
7,587
Mean Absolute Deviation
MAD =
293
Mean Square Error
MSE =
139,470
45 - Chap 10
MAD and MSE for the Various Forecasting Method
Forecasting Method
CCW’s 25 percent rule
Last-value method
Averaging method
Moving-average method
Exponential smoothing a=0.5
Exponential smoothing a=0.9
MAD
424
295
400
437
324
293
MSE
317,815
145,909
242,876
238,816
157,836
139,470
Forecast
7,720
7,606
7,003
7,279
7,428
7,587
Since the exponential smoothing method with a = 0.9 gives
the smallest MAD/MSE, it is the most superior method to make
the forecast for the CCW problem.
46 - Chap 10
Comparison of the Forecasting Methods
• Last value method: Suitable for a time series that is so
unstable that even the next-to-last value is not considered
relevant for forecasting the next value.
• Averaging method: Suitable for a very stable time series where
even its first few values are considered relevant for forecasting
the next value.
• Moving-average method: Suitable for a moderately stable time
series where the last few values are considered relevant for
forecasting the next value.
• Exponential smoothing method: Suitable for a time series in
the range from somewhat unstable to rather stable, where the
value of the smoothing constant needs to be adjusted to fit the
anticipated degree of stability.
47 - Chap 10