Transcript Forecasting

Forecasting
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Learning Objectives
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•
•
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List the elements of a good forecast.
Outline the steps in the forecasting
process.
Describe at least three qualitative
forecasting techniques and the
advantages and disadvantages of each.
Compare and contrast qualitative and
quantitative approaches to forecasting.
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Learning Objectives
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Briefly describe averaging techniques,
trend and seasonal techniques, and
regression analysis, and solve typical
problems.
Describe two measures of forecast
accuracy.
Describe two ways of evaluating and
controlling forecasts.
Identify the major factors to consider
when choosing a forecasting technique.
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FORECAST:
• The art and science of predicting future (It
may involve using statistics and mathematical
model, or may be a subjective prediction).
• Forecasting is used to make informed
decisions.
• Short-range (up to 1 Yr): planning purchasing,
job scheduling, workforce levels, job
assignment.
• Medium-rang (3 Mth – 3 Yr): sales planning,
production planning and budgeting.
• Long-range (more than 3 Yr): planning for
new products, facility location or expansion,
and R&D.
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Forecasts
• Forecasts affect decisions and activities
throughout an organization
– Accounting, finance
– Human resources
– Marketing
– MIS
– Operations
– Product / service design
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Uses of Forecasts
Accounting
Cost/profit estimates
Finance
Cash flow and funding
Human Resources
Hiring/recruiting/training
Marketing
Pricing, promotion, strategy
MIS
IT/IS systems, services
Operations
Schedules, MRP, workloads
Product/service design
New products and services
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Features of Forecasts
• Assumes causal system
past ==> future
I see that you will
get an A this semester.
• Forecasts rarely perfect because of
randomness
• Forecasts more accurate for
groups cf. (compared to) individuals
• Forecast accuracy decreases
as time horizon increases
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Elements of a Good Forecast
Timely
Reliable
Accurate
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6 Steps in the Forecasting Process
“The forecast”
Step 6 Monitor the forecast (modify, revise)
Step 5 Make the forecast
Step 4 Obtain, clean and analyze data
(eliminate outliers, incorrect data)
Step 3 Select a forecasting technique
(Moving AVG, Weighted AVG, etc)
Step 2 Establish a time horizon (How long?)
Step 1 Determine purpose of forecast
(How/when it will be used?, Resources)
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Forecast Accuracy
• Error - difference between actual value and
predicted value
• Mean Absolute Deviation (MAD)
–
Average absolute error
• Mean Squared Error (MSE)
–
Average of squared error
• Mean Absolute Percent Error (MAPE)
–
Average absolute percent error
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MAD, MSE, and MAPE
MAD
=
 Actual
 forecast
n
MSE
=
 ( Actual
 forecast)
2
n -1
MAPE =
( Actual
 forecas
t
n
/ Actual*100)
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MAD, MSE and MAPE
• MAD
– Easy to compute
– Weights errors linearly
• MSE
– Squares error
– More weight to large errors
• MAPE
– Puts errors in perspective (the errors are
presented as percentage)
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Example 1
Period
1
2
3
4
5
6
7
8
Actual
217
213
216
210
213
219
216
212
Forecast
215
216
215
214
211
214
217
216
(A-F)
|A-F|
(A-F)^2
(|A-F|/Actual)*100
MAD=
MSE=
MAPE=
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Ans: Example 1
Period
1
2
3
4
5
6
7
8
MAD=
MSE=
MAPE=
Actual
217
213
216
210
213
219
216
212
Forecast
215
216
215
214
211
214
217
216
(A-F)
2
-3
1
-4
2
5
-1
-4
-2
|A-F|
2
3
1
4
2
5
1
4
22
(A-F)^2
4
9
1
16
4
25
1
16
76
(|A-F|/Actual)*100
0.92
1.41
0.46
1.90
0.94
2.28
0.46
1.89
10.26
2.75
10.86
1.28
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Types of Forecasts
• Judgmental - uses subjective
inputs
Qualitative
method
• Time series - uses historical
data assuming the future will be
like the past
Quantitative
method
• Associative models - uses
explanatory variables to predict
the future
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Qualitative method
(Judgmental forecast)
• Executive opinions (long-range planning,
new product development)
• Sales force opinions (direct contact with
customers; however, sales staff are
overly influenced by recent experience)
• Consumer surveys (specific information;
but money and time-consuming)
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Quantitative method
• Naïve approach
• Moving average
Time series
models
• Exponential smoothing
• Trend projection
• Linear regression
Associative
model
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Time Series Forecasts
• Trend - long-term movement in data
• Seasonality - short-term regular
variations in data
• Cycle – wavelike variations of more than
one year’s duration
• Random variations - caused by chance
and unusual circumstances
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Forecast Variations
Random
variatio
n
Trend
Time
Cycles
Time
Year 1
Year 2
Year 3
Seasonal variations
Month
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Naive Forecasts
Uh, give me a minute....
We sold 250 wheels last
week.... Now, next week
we should sell....
The forecast for any period equals
the previous period’s actual value.
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Naïve Forecasts
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Simple to use
Virtually no cost
Quick and easy to prepare
Data analysis is nonexistent
Easily understandable
Cannot provide high accuracy
Can be a standard for accuracy
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Uses for Naïve Forecasts
• Stable time series data
– F(t) = A(t-1)
• Seasonal variations
– F(t) = A(t-n)
• Data with trends
– F(t) = A(t-1) + (A(t-1) – A(t-2))
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Techniques for Averaging
• Moving average
• Weighted moving average
• Exponential smoothing
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Moving Averages
• Moving average – A technique that averages a
number of recent actual values, updated as
new values become available.
Ft = MAn=
At-n + … At-2 + At-1
n
• Weighted moving average – More recent
values in a series are given more weight in
computing the forecast.
Ft = WMAn=
wnAt-n + … wn-1At-2 + w1At-1
n
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Simple Moving Average
Actual
MA5
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45
43
41
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MA3
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1
2
3
Ft = MAn=
4
5
6
7
8
9
10 11 12
At-n + … At-2 + At-1
n
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Exponential Smoothing
Ft = Ft-1 + (At-1 - Ft-1)
• 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.
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Exponential Smoothing
Ft = Ft-1 + (At-1 - Ft-1)
• Weighted averaging method based on
previous forecast plus a percentage of the
forecast error
• A-F is the error term,  is the % feedback
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Example 3 - Exponential Smoothing
Period
Actual
1
2
3
4
5
6
7
8
9
10
11
12
Alpha = 0.1 Error
42
40
43
40
41
39
46
44
45
38
40
42
41.8
41.92
41.73
41.66
41.39
41.85
42.07
42.36
41.92
41.73
Alpha = 0.4 Error
-2.00
1.20
-1.92
-0.73
-2.66
4.61
2.15
2.93
-4.36
-1.92
42
41.2
41.92
41.15
41.09
40.25
42.55
43.13
43.88
41.53
40.92
-2
1.8
-1.92
-0.15
-2.09
5.75
1.45
1.87
-5.88
-1.53
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Picking a Smoothing Constant
Actual
Demand
50
.4
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 .1
40
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1
2
3
4
5
6
7
8
9 10 11 12
Period
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Example 3 - Exponential Smoothing
Period
Actual
1
2
3
4
5
6
7
8
9
10
11
12
Alpha = 0.05 Error
42
40
43
40
41
39
46
44
45
38
40
42
41.90
41.96
41.86
41.81
41.67
41.89
42.00
42.15
41.94
41.84
Alpha =
-2.00
1.10
-1.96
-0.86
-2.81
4.33
2.11
3.00
-4.15
-1.94
0.7 Error
42
40.60
42.28
40.68
40.91
39.57
44.07
44.02
44.71
40.01
40.00
-2
2.4
-2.28
0.32
-1.91
6.43
-0.07
0.98
-6.71
-0.01
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Common Nonlinear Trends
Figure 3.5
Parabolic
Exponential
Growth
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Linear Trend Equation
Ft
Ft = a + bt
0 1 2 3 4 5
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t
Ft = Forecast for period t
t = Specified number of time periods
a = Value of Ft at t = 0
b = Slope of the line
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Calculating a and b
n  (ty) -  t  y
b =
2
2
n t - (  t)
 y - b t
a =
n
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Linear Trend Equation Example
t
Week
1
2
3
4
5
2
t
1
4
9
16
25
 t = 15
t2 = 55
2
(t) = 225
y
Sales
150
157
162
166
177
ty
150
314
486
664
885
 y = 812  ty = 2499
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Linear Trend Calculation
b =
5 (2499) - 15(812)
5(55) - 225
=
12495-12180
275 -225
= 6.3
812 - 6.3(15)
a =
= 143.5
5
y = 143.5 + 6.3t
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Techniques for Seasonality
• Seasonal variations
– Regularly repeating movements in series
values that can be tied to recurring events.
• Seasonal relative
– Percentage of average or trend
• Centered moving average
– A moving average positioned at the center of
the data that were used to compute it.
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Associative Forecasting
• Predictor variables - used to predict
values of variable interest
• Regression - technique for fitting a line
to a set of points
• Least squares line - minimizes sum of
squared deviations around the line
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Linear Model Seems Reasonable
X
7
2
6
4
14
15
16
12
14
20
15
7
Y
15
10
13
15
25
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24
20
27
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Computed
relationship
50
40
30
20
10
0
0
5
10
15
20
25
A straight line is fitted to a set of sample points.
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Linear Regression Assumptions
• Variations around the line are random
• Deviations around the line normally
distributed
• Predictions are being made only within the
range of observed values
• For best results:
– Always plot the data to verify linearity
– Check for data being time-dependent
– Small correlation may imply that other variables
are important
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Controlling the Forecast
• Control chart
– A visual tool for monitoring forecast errors
– Used to detect non-randomness in errors
• Forecasting errors are in control if
– All errors are within the control limits
– No patterns, such as trends or cycles, are
present
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Sources of Forecast errors
• Model may be inadequate
• Irregular variations
• Incorrect use of forecasting technique
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Tracking Signal
•Tracking signal
–Ratio of cumulative error to MAD
(Actual-forecast)

Tracking signal =
MAD
Bias – Persistent tendency for forecasts to be
Greater or less than actual values.
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Choosing a Forecasting Technique
• No single technique works in every
situation
• Two most important factors
– Cost
– Accuracy
• Other factors include the availability of:
– Historical data
– Computers
– Time needed to gather and analyze the data
– Forecast horizon
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Operations Strategy
• Forecasts are the basis for many
decisions
• Work to improve short-term forecasts
• Accurate short-term forecasts improve
– Profits
– Lower inventory levels
– Reduce inventory shortages
– Improve customer service levels
– Enhance forecasting credibility
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Supply Chain Forecasts
• Sharing forecasts with supply can
– Improve forecast quality in the supply chain
– Lower costs
– Shorter lead times
• Gazing at the Crystal Ball (reading in text)
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Exponential Smoothing
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Linear Trend Equation
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Simple Linear Regression
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