Transcript Forecasting

Forecasting
Chapter Objectives
Be able to:
 Discuss the importance of forecasting and
identify the most appropriate type of forecasting
approach, given different forecasting situations.
Apply a variety of time series forecasting
models, including moving average, exponential
smoothing, and linear regression models.
Develop causal forecasting models using linear
regression and multiple regression.
Calculate measures of forecasting accuracy and
interpret the results.
Why Forecast?
• Assess long-term capacity needs
• Develop budgets, hiring plans, etc.
• Plan production or order materials
• Get agreement within firm and across
supply chain partners (CPFR, discussed later)
Types of Forecasts
• Demand
– Firm-level
– Market-level
• Supply
– Materials
– Labor supply
• Price
– Cost of supplies and services
– Cost of money — interest rates, currency rates
– Market price for firm’s product or service
Forecast Laws
Almost always wrong by some amount
More accurate for shorter time periods
More accurate for groups or families
No substitute for calculated values.
Qualitative Forecasting
• Executive opinions
• Sales force composite
• Consumer surveys
• Outside opinions
• Delphi method
• Life cycle analogy*
*See accompanying notes
Forecasting Approaches
Qualitative Methods
• Used when situation is
vague and little data
exists
– New products
– New technology
• Involves intuition,
experience
*****************************
• E.g., forecasting sales
to a new market
Quantitative Methods
• Used when situation is
‘stable’ and historical
data exists
– Existing products
– Current technology
• Heavy use of
mathematical techniques
*******************************
• E.g., forecasting sales of
a mature product
“Q2” Forecasting
Quantitative, then qualitative factors to
“filter” the answer
Demand Forecasting
• Uses historical data
• Basic time series models
• Linear regression
– For time series or causal modeling
• Measuring forecast accuracy
Time Series Models
Period
1
2
3
4
5
6
7
8
Demand
12
15
11
9
10
8
14
12
What assumptions
must we make to
use this data to
forecast?
Time Series Components of
Demand . . .
Demand
. . . randomness
Time
Time Series with . . .
Demand
. . . randomness and trend
Time
Time series with . . .
Demand
. . . randomness, trend, and seasonality
May
May
May
May
Idea Behind Time Series
Models
Distinguish between random
fluctuations and true changes in
underlying demand patterns.
Moving Average Models
Period
1
2
3
4
5
6
7
8
Demand
12
15
11
9
10
8
14
12

n
Ft 1 
 Dt 1i
i 1
n
3-period moving average
forecast for Period 8:
=
=
(14 + 8 + 10) / 3
10.67
Weighted Moving Averages
n
 Wt 1i Dt 1i
Ft 1  i 1
n
 Wt 1i
i 1
Forecast for Period 8
=
[(0.5  14) + (0.3  8) + (0.2  10)] / (0.5 + 0.3 + 0.2)
=
11.4
What are the advantages?
What do the weights add up to?
Could we use different weights?
Compare with a simple 3-period moving average.
Table of Forecasts and
Demand Values . . .
Period
Actual
Demand
Two-Period
Moving
Average
Forecast
Three-Period Weighted
Moving Average
Forecast Weights = 0.5,
0.3, 0.2
1
12
2
15
3
11
13.5
4
9
13
12.4
5
10
10
10.8
6
8
9.5
9.9
7
14
9
8.8
8
12
11
11.4
13
11.8
9
. . . and Resulting Graph
20
Volume
15
Demand
10
2-Period Avg
3-Period Wt. Avg.
5
0
1
2
3
4
5
6
7
8
9
Period
Note how the forecasts smooth out demand variations
Exponential Smoothing I
• Sophisticated weight averaging model
• Needs only three numbers:
Ft
Dt
a
= Forecast for the current period t
= Actual demand for the current period t
= Weight between 0 and 1
Exponential Smoothing II
Formula
Ft+1
= Ft + a (Dt – Ft)
= a × Dt + (1 – a) × Ft
• Where did the current forecast come from?
• What happens as a gets closer to 0 or 1?
• Where does the very first forecast come from?
Exponential Smoothing
Forecast with a = 0.3
Period
Actual
Demand
Exponential
Smoothing
Forecast
1
12
11.00
2
15
11.30
3
11
12.41
4
9
11.99
5
10
11.09
6
8
10.76
7
14
9.93
8
12
11.15
9
11.41
F2 = 0.3×12 + 0.7×11
= 3.6 + 7.7
= 11.3
F3 = 0.3×15 + 0.7×11.3
= 12.41
Resulting Graph
16
14
Demand
12
10
Demand
8
Forecast
6
4
2
0
1
2
3
4
5
Period
6
7
8
9
Trends
What do you think will happen to a moving
average or exponential smoothing model
when there is a trend in the data?
Same Exponential Smoothing
Model as Before:
Period
Actual
Demand
Exponential
Smoothing
Forecast
1
11
11.00
2
12
11.00
3
13
11.30
4
14
11.81
5
15
12.47
6
16
13.23
7
17
14.06
8
18
14.94
9
15.86
Since the model
is based on
historical demand,
it always lags
the obvious
upward trend
Adjusting Exponential
Smoothing for Trend
• Add trend factor and adjust using exponential
smoothing
• Needs only two more numbers:
Tt = Trend factor for the current period t
 = Weight between 0 and 1
• Then: Tt+1 =  × (Ft+1 – Ft) + (1 – ) × Tt
• And the Ft+1 adjusted for trend is = Ft+1 + Tt+1
Simple Linear Regression
• Time series OR causal model
• Assumes a linear relationship:
y
y = a + b(x)
x
Definitions
Y = a + b(X)
Y = predicted variable (i.e., demand)
X = predictor variable
“X” can be the time period or some other type of
variable (examples?)
The Trick is Determining a and
b:
n
 xi y i 
n
n
i 1
i 1
(  x i )(  y i )
b  i 1
n
 xi 
i 1
a  y  bx
2
n
n
2
(  xi )
i 1
n
Example:
Regression Used for Time Series
Period
(X)
Demand
(Y)
X2
XY
1
110
1
110
2
190
4
380
3
320
9
960
4
410
16
1640
5
490
25
2450
15
1520
55
5540
15 1520
5540 
5
b
 98
2
15
55 
5
1520
15
a
 98   10
5
5
Column Sums
Resulting Regression Model:
Forecast = 10 + 98×Period
600
500
Y
400
Demand
300
Regression
200
100
0
1
2
3
X
4
5
Example:
Simplified Regression I
• If we redefine the X values so that their
sum adds up to zero, regression becomes
much simpler
– a now equals the average of the y values
– b simplifies to the sum of the xy products
divided by the sum of the x2 values
Example:
Simplified Regression II
Period
(X)
1
Period
(X)'
-2
Demand
(Y)
110
X2
XY
4
220
2
-1
190
1
190
3
0
320
0
0
4
1
410
1
410
5
2
490
4
980
0
1520
10
980
0 1520
980 
5
b
 98
2
0
10 
5
1520
0
a
 98   304
5
5
Dealing with Seasonality
Quarter
Period
Winter 02
Spring
Summer
Fall
Winter 03
Spring
Summer
Fall
1
2
3
4
5
6
7
8
Demand
80
240
300
440
400
720
700
880
What Do You Notice?
Forecasted Demand = –18.57 + 108.57 x Period
Period
Actual
Demand
Regression
Forecast
Forecast Error
Winter 02
1
80
90
-10
Spring
2
240
198.6
41.4
Summer
3
300
307.1
-7.1
Fall
4
440
415.7
24.3
Winter 03
5
400
524.3
-124.3
Spring
6
720
632.9
87.2
Summer
7
700
741.4
-41.4
Fall
8
880
850
30
Regression picks up trend, but
not seasonality effect
1000
800
600
Demand
400
Forecast
200
0
1
2
3
4
5
6
7
8
Calculating Seasonal Index:
Winter Quarter
(Actual / Forecast) for Winter Quarters:
Winter ‘02:
Winter ‘03:
(80 / 90) = 0.89
(400 / 524.3) = 0.76
Average of these two = 0.83
Interpret!
Seasonally adjusted forecast
model
For Winter Quarter
[ –18.57 + 108.57×Period ] × 0.83
Or more generally:
[ –18.57 + 108.57 × Period ] × Seasonal Index
Seasonally adjusted
forecasts
Forecasted Demand = –18.57 + 108.57 x Period
Period
Actual
Demand
Regression
Forecast
Demand/
Forecast
Seasonal
Index
Seasonally
Adjusted
Forecast
Forecast
Error
Winter 02
1
80
90
0.89
0.83
74.33
5.67
Spring
2
240
198.6
1.21
1.17
232.97
7.03
Summer
3
300
307.1
0.98
0.96
294.98
5.02
Fall
4
440
415.7
1.06
1.05
435.19
4.81
Winter 03
5
400
524.3
0.76
0.83
433.02
-33.02
Spring
6
720
632.9
1.14
1.17
742.42
-22.42
Summer
7
700
741.4
0.94
0.96
712.13
-12.13
Fall
8
880
850
1.04
1.05
889.84
-9.84
Would You Expect the Forecast Model
to Perform This Well With Future Data?
1000
800
600
Demand
400
forecast
200
0
1
2
3
4
5
6
7
8
More Regression Models I
Non-linear models
– Example:
y = a + b × ln(x)
More Regression Models II
Multiple regression
– More than one independent variable
y
y = a + b1 × x + b2 × z
x
z
Causal Models
Time series models assume that demand is
a function of time. This is not always true.
1. Pounds of BBQ eaten at party.
2. Dollars spent on drought relief.
3. Lumber sales.
Linear regression can be used in these
situations as well.
Measuring Forecast
Accuracy
How do we know:
If a forecast model is “best”?
If a forecast model is still working?
What types of errors a particular
forecasting model is prone to make?
Need measures of forecast accuracy
Measures of Forecast
Accuracy
Error = Actual demand – Forecast
or
Et = Dt – Ft
Mean Forecast Error (MFE)
For n time periods where we have actual
demand and forecast values:
n
MFE 
  Ei )
i 1
n
Mean Absolute Deviation
(MAD)
For n time periods where we have actual
demand and forecast values:
n
MAD 
 Ei
i 1
n
What does this tell us that MFE doesn’t?
Example
Period Demand Forecast
3
4
5
6
7
8
11
9
10
8
14
12
13.5
13
10
9.5
9
11
Error
-2.5
-4.0
0
-1.5
5.0
1.0
Absolute
Error
2.5
4.0
0.0
1.5
5.0
1.0
What is the MFE? The MAD? Interpret!
MFE and MAD:
A Dartboard Analogy
Low MFE and MAD:
The forecast errors
are small and unbiased
An Analogy (continued)
Low MFE, but high
MAD:
On average, the
darts hit the
bulls eye (so much
for averages!)
An Analogy (concluded)
High MFE and MAD:
The forecasts
are inaccurate and
biased
Collaborative Planning,
Forecasting, and Replenishment
(CPFR)
Supply chain partners, supported
by information technology, working
together
CPFR Elements
• Mutual business objectives &
measures
• Joint sales and operations plans
• Collaboration on sales forecasts &
replenishment plans
• Electronic interchange of
information
Case Study in Forecasting
Top-Slice Drivers