Transcript Document

1
Chapter 13
Forecasting

Demand Management

Qualitative Forecasting Methods

Simple & Weighted Moving Average
Forecasts

Exponential Smoothing
2
Demand Management
A
C(2)
B(4)
D(2)
E(1)
D(3)
F(2)
3
Independent Demand: What a firm can
do to manage it.

.
4
What Is Forecasting?
Sales will be
$200 Million!
5
Types of Forecasts
by Time Horizon

Short-range forecast

Medium-range forecast

Long-range forecast
6
Types of Forecasts
by Item Forecast

Economic forecasts

Technological forecasts

Demand forecasts
7
Types of Forecasts

Qualitative (Judgmental)

Quantitative
8
Components of Demand






Average demand for a period of time
Trend
Seasonal element
Cyclical elements
Random variation
Autocorrelation
9
Finding Components of Demand
Seasonal variation
Sales
x
x x
x
x
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
4
Linear
Trend
x
x
x
10
Cyclical Component



Repeating up & down movements
Due to interactions of factors influencing
economy
Usually 2-10 years duration
Cycle
Response
B
Mo., Qtr., Yr.
11
Random Component


Erratic, unsystematic, ‘residual’ fluctuations
Due to random variation or unforeseen
events
© 1984-1994 T/Maker Co.

Short duration &
nonrepeating
12
Qualitative Methods
Executive Judgment
Historical analogy
Grass Roots
Qualitative
Market Research
Methods
Delphi Method
Panel Consensus
13
Delphi Method
l. Choose the experts to participate.
2. Through a questionnaire (or E-mail), obtain
forecasts from all participants.
3. Summarize the results and redistribute them to
the participants along with appropriate new
questions.
4. Summarize again, refining forecasts and
conditions, and again develop new questions.
5. Repeat Step 4 if necessary. Distribute the final
results to all participants.
14
Quantitative Forecasting Methods
Quantitative
Forecasting
Causal
Models
Time Series
Models
Moving
Average
Exponential
Smoothing
Trend
Projection
Linear
Regression
15
Time Series Analysis


Time series forecasting models try to predict
the future based on past data.
You can pick models based on:
16
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
17
Simple Moving Average Problem (1)
W eek
Dem and
1
650
2
678
3
720
4
785
5
859
6
920
7
850
8
758
9
892
10
920
11
789
12
844
A t-1 + A t-2 + A t-3 +...+A t- n
Ft =
n
 Question: What are the
3-week 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
18
Calculating the moving averages gives us:
W eek
D e m a n d 3 -W e e k
6 -W e e k
1
650
2
678
3
720
4
785
F7=(650+678+720
682.67
+785+859+920)/6
5
859
727.67
6
920
788.00
7
850
854.67
768.67
8
758
876.33
802.00
9
892
842.67
815.33
10
920
833.33
844.00
11
789
856.67
866.50
12
844
867.00
854.83
F4=(650+678+720)/3
=682.67
=768.67
©The McGraw-Hill Companies, Inc., 2000
19
1000
Demand
900
Demand
800
3-Week
700
6-Week
600
500
1
2
3
4
5
6
7
Week
8
9 10 11 12
20
Simple Moving Average Problem (2)
Data

W eek
Dem and
1
820
2
775
3
680
4
655
5
620
6
600
7
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
21
Simple Moving Average Problem (2)
Solution
W eek
Dem and
1
820
2
775
3
680
4
655
5
620
6
600
7
575
3 -W e e k
5 -W e e k
22
Weighted Moving Average Formula
While the moving average formula implies an equal
weight being placed on each value that is being
averaged, the weighted moving average permits an
unequal weighting on prior time periods.
The formula for the moving average is:
Ft = w 1 A t -1 + w 2 A t - 2 + w 3 A t -3 + ...+ w n A t - n
wt = weight given to time period “t”
occurrence. (Weights must add to one.)
n
w
i=1
i
=1
23
Weighted Moving Average Problem
(1) Data
Question: Given the weekly demand and weights, what is
the forecast for the 4th period or Week 4?
W eek
Dem and
1
650
2
678
3
720
4
Weights:
t-1 .5
t-2 .3
t-3 .2
24
Weighted Moving Average Problem (1)
Solution
W eek
Dem and
1
650
2
678
3
720
F o re c a s t
4
F4 = 0.5(720)+0.3(678)+0.2(650)=693.4
693.4
25
Weighted Moving Average Problem (2)
Data
Question: Given the weekly demand information and
weights, what is the weighted moving average
forecast of the 5th period or week?
W eek
Dem and
1
820
2
775
3
680
4
655
Weights:
t-1 .7
t-2 .2
t-3 .1
26
Weighted Moving Average Problem (2)
Solution
W eek
D em and
1
820
2
775
3
680
4
655
5
F orec as t
27
Exponential Smoothing Model
Ft = Ft-1 + a(At-1 - Ft-1)
a
= smoothing constant
28
Exponential Smoothing Problem (1)
Data
W eek
Dem and
1
820
2
775
3
680
4
655
5
750
6
802
7
798
8
689
9
775
10


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
29
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
30
Exponential Smoothing Problem (1)
Plotting
Demand
900
800
Demand
700
0.1
600
0.6
500
1
2
3
4
5
6
Week
7
8
9
10
31
Exponential Smoothing Problem (2)
Data
W eek
Dem and
1
820
2
775
3
680
4
655
5
Question: What are the
exponential smoothing
forecasts for periods 2-5
using a =0.5?
Assume F1=D1
32
Exponential Smoothing Problem (2)
Solution
W eek
Dem and
1
820
2
775
3
680
4
655
5
0.5
33
Linear Trend Projection


Used for forecasting linear trend line
Assumes relationship between response
variable Y & time X is a linear function
35
Correlation

Answers ‘how strong is the linear
relationship between 2 variables?’
Coefficient of correlation used

Used mainly for understanding

37
Simple Linear Regression Model
The simple linear regression
model seeks to fit a line through
various data over time.
Y
a
0 1 2 3 4 5
Yt = a + bx
x (Time)
Is the linear regression model.
Yt is the regressed forecast value or dependent
variable in the model, a is the intercept value of the the
regression line, and b is similar to the slope of the
regression line. However, since it is calculated with
the variability of the data in mind, its formulation is not
as straight forward as our usual notion of slope.
38
Simple Linear Regression Formulas for
Calculating “a” and “b”
a = y - bx
b=
 xy - n(y)(x)
2
 x - n(x )
2
39
Simple Linear Regression Problem
Data
Question: Given the data below, what is the simple linear
regression model that can be used to predict sales?
Week
1
2
3
4
5
Sales
150
157
162
166
177
40
The MAD Statistic to Determine
Forecasting Error
n
A
MAD =
t
t=1
n
- Ft
1 MAD  0.8 standard deviation
1 standard deviation  1.25 MAD
41
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
42
MAD Problem Solution
Month
1
2
3
4
5
Sales
220
250
210
300
325
Forecast Abs Error
n/a
255
5
205
5
320
20
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.
43
Tracking Signal Formula



The TS is a measure that indicates whether the
forecast average is keeping pace with any
genuine upward or downward changes in
demand.
Depending on the number of MAD’s selected,
the TS can be used like a quality control chart
indicating when the model is generating too
much error in its forecasts.
The TS formula is:
RSFE Running sum of forecast errors
TS =
=
MAD
Mean absolute deviation
44
Calculating Tracking Signals for Exponential Smoothing
Forecasts
Quarterly Sales Data - Acme Tool Company
a
0.1
Actual
Forecast Forecast
(At)
(Ft)
Error
1 550.00 550.00
2 400.00 550.00
-150.00
3 350.00 535.00
-185.00
4 600.00 516.50
83.50
5 750.00 524.85
225.15
6 500.00 547.37
-47.37
7 400.00 542.63
-142.63
8 650.00 528.37
121.63
9 850.00 540.53
309.47
10 600.00 571.48
28.52
11 450.00 574.33
-124.33
12 700.00 561.90
138.10
Running
Sum of
Forecast
Errors
-150.00
-335.00
-251.50
-26.35
-73.72
-216.34
-94.71
214.76
243.29
118.96
257.06
Absolute
Deviation
150.00
185.00
83.50
225.15
47.37
142.63
121.63
309.47
28.52
124.33
138.10
Sum of
Abs. Dev.
150.00
335.00
418.50
643.65
691.02
833.64
955.28
1264.75
1293.27
1417.60
1555.71
MAD
150.00
167.50
139.50
160.91
138.20
138.94
136.47
158.09
143.70
141.76
141.43
Tracking
Signal
-1.00
-2.00
-1.80
-0.16
-0.53
-1.56
-0.69
1.36
1.69
0.84
1.82