Operations Management
School of Engineering
The University of the Thai
Chamber of Commerce
Operations Management
UTCC
Page 1
Forecasting
School of Engineering
The University of the Thai Chamber of Commerce
Operations Management
UTCC
Page 2
Agenda
•
•
•
•
•
What is forecast?
Elements of good forecasts
The necessary steps in preparing a forecast
Basic forecasting techniques
How to monitor a forecast
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Operations Management
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จำาน วน ผ ล ผ ล ต สิ น ค้ าเก ษ ต ร ก ล ม ภ าค้ เห น อ ต อ น ล างที่ ได้ ปี 2547
Operations Management
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Motto in OM class
• It’s an old story, but an instructive note: T w o shoe
salesmen arrive on a primitive island where no one
w ears shoes. O ne cables his head office saying “N o
business. S hoes not w orn”, the other sends a
different m essage “S end m ore shoes. N o
com petition.”
John F. Kenedy
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1. Introduction
•
•
•
•
Have you ever forecast??
How much food and drink will I need for the party?
Will I get the job?
Which team will be a world champion in 2006?
To make these forecasts,
• One is current factors or conditions.
• The other is past experience in a similar situation.
Operations Management
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1. Introduction
• Forecasting are the basis for budgeting and
planning for capacity, sales, production and
inventory, personnel, purchasing, and more.
• Forecast play an important role in the planning
process.
• Forecasts affect decisions and activities throughout
an organization, in accounting, finance, human
resources, marketing, MIS, as well as operations,
and other parts of an organization.
Operations Management
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2.1 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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2. FORECAST:
• There are two methods for forecasting.
– Plan the system (involves long term plan
about the types of products and service to
offer).
– Plan to use the system (involves short and
intermediate term plan such as planning
inventory , workforce levels, planning
purchasing, budgeting and scheduling).
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Operations Management
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ก ารออก แบ บ ศู น ย์ ก ระจาย์ สิน ค้ าข องจงห วัด พิ ษ ณุ โลก
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2.1 Features Common to all Forecasts
• Assumes causal system
past ==> future
• Forecasts rarely perfect because of
randomness
• Forecasts more accurate for
groups vs. individuals
• Forecast accuracy decreases
as time horizon increases
Operations Management
I see that you will
get an A this semester.
UTCC
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Forecasting time horizons
- Short-range forecast (not more than one year;
Planning purchasing, Job scheduling, Workforce levels
and so on)
- Medium-range forecast ( 3 months to 3 years;
Production planning and budgeting, Cash budgeting)
- long-range forecast (more than 3 years; planning for
new products, Capital expenditures, Facility location
and R&D
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The influence of product life cycle (PLC)
1 Introduction
2 Growth
3 Maturity
4 Decline
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3. Elements of a Good Forecast
Timely
Reliable
Accurate
Written
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4. Steps in the Forecasting Process
“T h e fo recast”
Step 7 Validate and Implement the results
Step 6 Monitor the forecast
Step 5 Gather and analyze data
Step 4 Select a forecasting technique
Step 3 Establish a time horizon
Step 2 Select the items to be forecasted
Step 1 Determine purpose of forecast
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5. Types of Forecasts
• Judgmental - uses subjective inputs
• Time series - uses historical data assuming the future
will be like the past
• Associative models or Casual Model – use equation
that consists of one or more explanatory variables to
predict the future. For example, demand for paint might
be related to variables such as the price per gallon and
the amount spent on advertising, as well as specific
characteristics of the paint.
Operations Management
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6. Judgmental Forecasts
• Executive opinions
• Sales force opinions
• Consumer surveys
• Outside opinion
•
Delphi method
– Opinions of managers and staffs
– Achieves a consensus forecast
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7. Time Series Forecasts
• is a time-ordered sequence of observations taken at
regular intervals.
• The data may be measurements of demand, earnings,
profits, shipments, accidents, output and productivity.
• Trend - long-term movement in data
• Seasonality - short-term regular variations in data
• Cycle – w avelike variations of m ore than one year’s
duration
• Irregular variations - caused by unusual circumstances
• Random variations - caused by chance (Bird Flu)
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7.1 Forecast Variations
Irregular
variation
Trend
Cycles
90
89
88
Seasonal variations
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7.2 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
th e p reviou s p eriod ’s actu al valu e.
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7.2 Naïve Forecasts
•
•
•
•
•
•
•
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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7.2 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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7.2 Naïve Methods
• Uses a single previous value of a time series as the basis
of a forecast
Period
Actual Change from previous value Forecast
t-1
50
t
53
t+1
Operations Management
+3
53+3 = 56
UTCC
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7.3 Techniques for Averaging
• Generate forecasts that reflect recent values of a
time series.
• Work best when a series tends to vary around an
average
– Moving average
– Weighted moving average
– Exponential smoothing
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7.3.1 Moving average
• Uses a number of the most recent actual data values in
generating a forecast.
n
A
i1
Ft MA

n
n
i
i = an index that corresponds to periods
n = number of periods in the moving average
Ai = actual value in period i
MA = Moving Average
Ft = Forecast for period t
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Example 1
• Compute a three period
moving average forecast
given demand for
shopping carts for the last
five periods.
Period
Age
Demand
1
5
42
2
4
40
3
3
43
4
2
40
5
1
41
43

40

41
F


41
.
33
6
3
If actual demand in period 6
turns out to be 39. What is F7 ?
Operations Management
40

41

39
F


40
7
3
UTCC
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Operations Management
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7.3.2 Weighted Moving Average
• A weighted average is similar to a moving average,
except that it assigns more weight to the most
recent values in a time series.
• For instance, the most recent value might be
assigned a weight of .40, the next most recent value
a weight of .30, the next after that a weight of .20,
and the next after that a weight of .10.
• That weights sum to 1.00, and that the heaviest
weights are assigned to the most recent values.
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7.3.2 Weighted Moving Average
a)
b)
Compute weighted average forecast using a weight .4 for the most
recent period, .3 for the next most recent, .2 for the next, and .1 for
the next.
If the actual demand for period 6 is 39, forecast demand for period 7
using the same weights as in part a.
Operations Management
Period
Demand
1
42
2
40
3
43
4
40
5
41
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7.3.2 Weighted Moving Average
a
.
F

.
4
(
41
)

.
3
(
40
)

.
2
(
43
)

.
1
(
40
)

41
.
0
6
b
.
F

.
4
(
39
)

.
3
(
41
)

.
2
(
40
)

.
1
(
43
)

40
.
2
7
Note that if four weights are used, only the four most recent
demands are used to prepare the forecast.
Operations Management
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7.3.2 Weighted Moving Average
• The weighted average is more reflective of the most
recent occurrences.
• The choice of weights is somewhat arbitrary and
generally involves the use of trial and error to find a
suitable weighting scheme.
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7.3.3 exponential smoothing
• Exponential smoothing is a sophisticated weighted
averaging method that is still relatively easy to use
and understand. Each new forecast is based on the
previous forecast plus a percentage of the
difference between that forecast and the actual
value of the series at that point.
Operations Management
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7.3.3 Exponential Smoothing
Next
fore

Pre
for


(A
P
F
F
F

(A
F
)
t
t
1
t
1
t
1
α represents a percentage of the forecast error.
Therefore, each new forecast is equal to the previous forecast plus a
percentage of the previous error.
Suppose the previous forecast was 42 units, actual demand was 40
units, and α = .10. the new forecasts
F = 42 + .10(40-42) = 41.8
Then if the actual demand turns out to be 43, the next forecast would
be?? Ans. 41.92
Operations Management
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7.3.3 Exponential Smoothing
• An alternate form of formula reveals the weighting of the
previous forecast and the latest actual demand:
F
F

(A
F
)
t
t
1
t
1
t
1
F
(
1


)F

A
t
t
1
t
1
• For example:
F
F

0
.10
(
A

F
)
t
t
1
t
1
t
1
F
(
0
.9
)
F

0
.1
A
t
t
1
t
1
F = 42 + .10(40-42) = (0.9)(42) + (.10)(40) =
Operations Management
41.8
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Example 2
• The following table illustrates two series of forecasts
for a data set and the resulting error for each
period. One forecast uses α = .10 and one uses α =
.40. The following figure plots the actual data and
both sets of forecasts.
Operations Management
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Example 2 - Exponential Smoothing
P eriod
A c t ual
1
2
3
4
5
6
7
8
9
10
11
12
Operations Management
42
40
43
40
41
39
46
44
45
38
40
A lpha = 0. 1E rror
A lpha = 0. 4E rror
42
41.8
41.92
41.73
41.66
41.39
41.85
42.07
42.36
41.92
41.73
42
41.2
41.92
41.15
41.09
40.25
42.55
43.13
43.88
41.53
40.92
-2.00
1.20
-1.92
-0.73
-2.66
4.61
2.15
2.93
-4.36
-1.92
-2
1.8
-1.92
-0.15
-2.09
5.75
1.45
1.87
-5.88
-1.53
UTCC
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Picking a Smoothing Constant
Actual
50
Demand
.4
45
 .1
40
35
1
2
3
4
5
6
7
8
9 10 11 12
Period
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7.3.3 Exponential Smoothing
• The closer α is to zero, the slower the forecast will be to
adjust to forecast errors. (the greater the smoothing,
emphasis the previous data)
• The closer the value of α is to 1.00, the greater the
responsiveness and the less the smoothing. (emphasis
the present data )







F

A

(
1

)
A

(
1

)
A

...
(
1

)
A
t
t

1
t

2
2
t

3
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n
t

n
Page 44
7.4 Techniques for trend
• Develop an equation that will suitably describe trend
• The trend component may be linear, or it may not.
• Two important techniques that can be used to
develop forecasts
– Trend equation
– Extension of exponential smoothing
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7.4 Common Nonlinear Trends
Figure 3.5
Parabolic
Exponential
Growth
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7.5 Linear Trend Equation
Ft
Ft = a + bt
•
•
•
•
0
Ft = Forecast for period t
t = Specified number of time periods
a = Value of Ft at t = 0
b = Slope of the line
Operations Management
1 2 3 4 5
t
UTCC
Page 47
7.5 Trend equation
The coefficients of the line, a and b, can be computed from
historical data using these components.
b
ntyty
nt2 (t)2
ybt

a
n
or y-bt
n = number of periods
y = value of the time series
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Linear Trend Equation Example
t
Week
1
2
3
4
5
2
t
1
4
9
16
25
y
Sales
150
157
162
166
177
ty
150
314
486
664
885
2
t = 15

t = 55 y= 812 ty= 2499
2
(
t) = 225
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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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Example 3
Cell phone sales for a
California-based firm over the
last 10 weeks are shown in the
following table. Plot the data,
and visually check to see if a
linear trend line would be
appropriate. Then determine
the equation of the trend line,
and predict sales for weeks 11
and 12.
Operations Management
Week
Unit Sales
1
700
2
724
3
720
4
728
5
740
6
742
7
758
8
750
9
770
10
775
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Page 51
Example 3
a. A plot suggests that a linear trend line would be appropriate:
unit sales
800
780
sales
760
740
720
700
680
660
1
2
3
4
5
6
7
8
9
10
week
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Example 3
Week (t)
Unit Sales
(y)
Ty
1
700
700
2
724
1448
3
720
2160
4
728
2912
5
740
3700
6
742
4452
7
758
5306
8
750
6000
9
770
6930
10
775
7750
55
7407
41358
Operations Management
b.
b
ntyty
nt2 (t)2
ybt

a
n
or y-bt
10
(41
,358
)
(
55
)(
7
,407
) 6
,195
b



7
.51
10
(
385
)
55
(
55
)
825
7
,407

7
.51
(
55
)
a

699.40
10
Thus the trend line is
y
699
.
40

7
.
51
t
t
UTCC
Page 53
Example 3
c. Substituting values of t into this equation, the forecasts
for the next two periods are:
y

699
.
40

7
.
51
(
11
)

782
.
01
11
y

699
.
40

7
.
51
(
12
)

789
.
52
12
Operations Management
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Page 54
Example 3
d. For purposes of illustration, the original data, the trend line,
and the two projections (forecasts) are shown on the following
graph.
unit sales
800
780
sales
760
740
720
700
680
660
1
2
3
4
5
6
7
8
9
10
week
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Page 55
7.6 Associative Forecasting
• Associative techniques rely on identification of
related variables that can be used to predict
values of the variable of interest.
• 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
Operations Management
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7.7 Linear Model Seems Reasonable
X
7
2
6
4
1
1
1
1
1
2
1
Y
4
5
6
2
4
0
5
7
1
1
1
1
2
2
2
2
2
4
3
1
Computed
relationship
5
0
3
5
5
7
4
0
7
4
4
7
50
40
30
20
10
0
0
5
10
15
20
25
A straight line is fitted to a set of sample points.
Operations Management
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Page 57
8. Forecast Accuracy
• Error = actual value - 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
Operations Management
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Page 58
8.1 MAD, MSE, and MAPE
MAD
=
 Actual
 forecast
n
MSE
=
 ( Actual
 forecast)
2
n -1
MAPE =
 ( Actual
 forecast / Actual*100)
n
Operations Management
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Page 59
Example 4
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 (|A-F|/Actual)*100
4
0.92
9
1.41
1
0.46
16
1.90
4
0.94
25
2.28
1
0.46
16
1.89
76
10.26
2.75
10.86
1.28
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Example 4: Solution
• MAD
• MSE
• MAPE
= 22/8
=
= 76/(8-1) =
=
10.26%/8
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2.75
10.86
=
1.28%
UTCC
Page 61
9. 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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9.1 Control Chart
• MSE = 2
• S = MSE

1
.
41
z MSE
• S = MSE
• UCL : 
z
MSE


2
.
82
• UCL : 
z MSE
• LCL : 
z
MSE


2
.
82
• LCL : 
+2.82
-2.82
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10. Sources of Forecast errors
• Model may be inadequate
• Irregular variations
• Incorrect use of forecasting technique
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Page 64
11. Tracking Signal or Control Chart
•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.
Operations Management
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Page 65
12. 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
Operations Management
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Page 66
13. Forecast factors, by range of forecast
Factor
Short Range
Intermediate
Range
Long Range
1. Frequency
Often
Occasional
Infrequent
2. Level of Aggregation
Item
Product family
Total output, type of
product/service
3. Type of model
Smoothing,
projection,
regression
Smoothing,
projection,
regression
Managerial
judgment
4. Degree of management Low
involvement
Moderate
High
5. Cost per forecast
Moderate
high
Operations Management
Low
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Page 67
Problem 1
1. The appropriate naïve
approach
2. A three period moving
average and five period
3. A weighted average
using weights of .50
(most recent), .30, and
.20
4. Exponential smoothing
with a smoothing
constant of .40
Operations Management
Period
Number of Complaints
1
60
2
65
3
55
4
58
5
64
UTCC
Page 68
Solution:
1. The values are stable. Therefore, the most recent
value of the series becomes the next forecast: 64
2. MA3 = (55+58+64)/3 = 59
MA5 = (60+65+55+58+64)/5 = 60.4
3. F = .20(55)+.30(58)+.50(64) = 60.4
Operations Management
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Page 69
Solution:
Period
Number of
complaints
1
60
2
65
60
3
55
62
60+.40(65-60) = 62
4
58
59.2
62+.40(55-62) = 59.2
5
64
58.72
59.2 + .40(58-59.2) = 58.72
60.83
58.72+.40(64-58.72) = 60.83
6
Operations Management
Forecast
calculations
UTCC
Page 70
Problem 2:
• Plot the data on a graph,
and verify visually that a
linear trend line is
appropriate. Develop a line
trend equation for the
following data. Then use
the equation to predict the
next two value of the
series
Operations Management
Period
Demand
1
44
2
52
3
50
4
54
5
55
6
55
7
60
8
56
9
62
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Page 71
Solution 2:
70
Demand
60
50
40
30
20
10
0
0
2
4
6
8
10
Period
Operations Management
UTCC
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Solution 2:
Period (t)
Demand (y)
Ty
1
44
44
2
52
104
3
50
150
4
54
216
5
55
275
6
55
330
7
60
420
8
56
448
9
62
558
448
2545
Operations Management
UTCC
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Solution 2:
b
ntyty
nt2 (t)2
ybt

a
or y-bt
n
Thus the trend line is
9(2,545
)(45
)(
488
)
b
1.75
9(285
)45
(45
)
488

1.75
(45
)
a
45.47
9
F
45
.47

1
.75
t
t
F
45
.47

1
.75
(10
)
62
.97
10
F
45
.47

1
.75
(11
)
64
.72
11
Operations Management
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Problem 3
• The manager of a large manufacturer of industrial pumps must chose
between two alter active forecasting techniques. Both techniques have
been used to prepare forecasts for a six-month period. Using MAD as
a criterion, which technique has the better performance record?
Forecast
Month
Demand
Technique 1
Technique 2
1
492
488
495
2
470
484
482
3
485
480
478
4
493
490
488
5
498
497
492
6
492
493
493
Operations Management
UTCC
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Solution 3
Operations Management
UTCC
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Solution 3:
• Technique 1 is superior in this comparison because
its MAD is smaller, although six observations would
generally be too few on which to base a realistic
comparison.
Operations Management
UTCC
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Problem 4:
• Given the demand data that follow, prepare a naïve forecast
for periods 2 through 10. Then determine each forecast
error, and use those values to obtain 2s control limits. If
demand in the next two periods turns out to be 125 and 130,
can you conclude that the forecasts are in control?
Period
1
Demand
118 117 120 119 126 122 117 123 121 124
Operations Management
2
3
4
5
6
7
8
9
UTCC
10
Page 78
Solution 4:
Period
Demand
Forecast
Error
Error square
1
118
-
-
-
2
117
118
-1
1
3
120
117
3
9
4
119
120
-1
1
5
126
119
7
49
6
122
126
-4
16
7
117
122
-5
25
8
123
117
6
36
9
121
123
-2
4
10
124
121
3
9
6
150
Operations Management
UTCC
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Solution 4:
2
error
 150
s


4
.
33 n = Number of errors
n

1
9

1
The control limits are 2(4.33) = +/-8.66
The forecast for period 11 was 124. demand turned out to be 125, for an
error of 125-124 = 1. this is within the limits of +/-8.66. If the next demand
is 130 and the naïve forecast is 125, the error is +5. again, this is within
the limits, so you cannot conclude the forecast is not working properly.
With more values at least five or six you could plot the errors to see
whether you could detect any patterns suggesting the presence of nonrandomness.
Operations Management
UTCC
Page 80
Problem 5:
5. National mixer Inc. sell can
openers. Monthly sales for
a seven-month period
were as follows:
Operations Management
Month
Sales
(000 units)
Feb
19
Mar
18
Apr
15
May
20
Jun
18
Jul
22
Aug
20
UTCC
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Problem 5
a.
b.
Plot the monthly data
Forecast September sales volume using each of the
following:
a.
b.
c.
d.
e.
c.
A linear trend equation.
A five-month moving average
Exponential smoothing with alpha = 0.20, assuming a March
forecast of 19(000).
The naïve approach
A weighted average using .60 for August, .30 for July, and .10
for June.
Which method seems least appropriate? Why?
Operations Management
UTCC
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Problem 6
6. Freight car loadings over a 12 year period at a busy port are
Week
Ton Shipped
Week
Ton Shipped
Week
Ton Shipped
1
405
8
433
15
466
2
410
9
438
16
474
3
420
10
440
17
476
4
415
11
446
18
482
5
412
12
451
6
420
13
455
7
424
14
464
Operations Management
UTCC
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Problem 6:
a. Determine a linear trend line for freight car
loadings.
b. Use the trend equation to predict loadings for
weeks 20 and 21.
c. The manager intends to install new equipment
when the volume exceeds 800 loadings per week.
assuming the current trend continues, the loading
volume will reach that level in approximately what
week?
Operations Management
UTCC
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Problem 7:
7. Two different forecasting techniques were used to forecast
demand fore cases of bottled water. Actual demand and
the two sets of forecasts are as follows:
Forecast
Period
Demand
Technique 1
Technique 2
1
68
66
66
2
75
68
68
3
70
72
70
4
74
71
72
5
69
72
74
6
72
70
76
7
80
71
78
8
78
74
80
Operations Management
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Problem 7:
a) Compute MAD for set of forecasts. Given your results,
which forecast appears to be more accurate? Explain
b) Compute the MSE for each set of forecasts. Given your
results, which forecast appears to be more accurate?
c) In practice, either MAD or MSE would be employed to
compute forecast errors. What factors might lead a
manager to choose one rather than the other?
d) Compute MAPE for each data set. Which forecast
appears to be more accurate?
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