International Operations Management

.............................................................................
.............................................................................
Elsevier US
Job code KIB
Chapter: Ch11-H7983 6-12-2006 9:22 p.m.
Page:373
Trimsize:7.25 in in
Fonts used Sabon & Frutiger
Margins:Top:36 pt
Gutter:66 pt
Font Size pt
Text Width PC
Depth:43 Lines
International Operations Management
373
or
F
t
+1
= F
t
+ Y
t
− F
t

(11.3)
where F
t
+1
is the forecast value of the dependent variable for period
t
+ 1 F
t
is the forecast value of the dependent variable for period t Y
t
is the actual value of the dependent variable for period t; and  is the value of the smoothing constant.
As it can be seen from the above equations, exponential smoothing is an average forecasting approach that requires only three pieces of data the forecast for the most recent time period F
t
, the actual value for that time period Y
t
 and the value of the smoothing constant. The smoothing constant is a weighting factor (its value lies between 0 and 1) that reflects the weight given to the most recent data values (the larger the value given to  the more strongly the model reacts to most recent data).
The value of the smoothing constant also determines the degree of smoothing and how responsive the model is to fluctuations in the data. As it can be seen from Equation (11.3), exponential smoothing is simply the old forecast F
t
 adjusted by  times the error Y
t
−F
t
 in the old forecast.
That means that when the value of  is close to 0, the new forecast will be very similar to the old. On the other hand, when the value of  is close to, the new forecast will include a substantial adjustment for any error that occurred in the preceding forecast.
Application of Equation (11.3) with a smoothing constant value of

= 03 will produce the following forecasts:
F
2
= 130 + 03130 − 130 = 130
F
3
= 130 + 0370 − 130 = 112
F
4
= 112 + 03140 − 112 = 1204
F
5
= 1204 + 03150 − 1204 = 12928
F
6
= 12928 + 0390 − 12928 = 1175
F
7
= 1175 + 03180 − 11750 = 13625
Note that as the forecast value for week 1 did not exist, we took it to be the same as the actual value for that period (i.e., we assumed a perfect forecast).
An exponential smoothing model with a different value of  will obviously produce different forecasts. For example, a smoothing constant value of

= 08 will produce the following forecasts:
F
2
= 130 + 08130 − 130 = 130
F
3
= 130 + 0870 − 130 = 82

.............................................................................
.............................................................................
Elsevier US
Job code KIB
Chapter: Ch11-H7983 6-12-2006 9:22 p.m.
Page:374
Trimsize:7.25 in in
Fonts used Sabon & Frutiger
Margins:Top:36 pt
Gutter:66 pt
Font Size pt
Text Width PC
Depth:43 Lines
374
International Business
F
4
= 82 + 08140 − 82 = 1284
F
5
= 1284 + 08150 − 1284 = 14568
F
6
= 14568 + 0890 − 14568 = 10114
F
7
= 10114 + 08180 − 10114 = 16423
As it can be seen from the above example, the operations manager can tryout a number of different forecasting models on some historical data,
in order to see how each of these models would have worked had it been used in the past. The accuracy of these forecasting models can be measured by a number of simple tests. A popular test for measuring forecast accuracy is the mean absolute percentage error (MAPE) test, which is based on the following equation:
MAPE
=

e
t
/Y
t

n
× where Y
t
is the actual value of the dependent variable for period t e
t
is the forecast error for period t (i.e., e
t
= Y
t
−F
t
); and n is the number of forecast errors. Y
t
= The MAPE values for the forecasts produced by the two exponential smoothing models can be produced as follows:
Model 1 
= 03
t
Y
t

F
t

e
t

e
t
/Y
t

1 130 13000
–
–
2 70 13000
−6000 086 3
140 11200 2800 020 4
150 12040 2960 020 5
90 12928
−3928 044 6
180 11750 6250 035 7
130 13625
–
–
MAPE
=

e
t
/Y
t

n
× 100 =
205 5
× 100 = 41%

.............................................................................
.............................................................................
Elsevier US
Job code KIB
Chapter: Ch11-H7983 6-12-2006 9:22 p.m.
Page:375
Trimsize:7.25 in in
Fonts used Sabon & Frutiger
Margins:Top:36 pt
Gutter:66 pt
Font Size pt
Text Width PC
Depth:43 Lines
International Operations Management
375
Model 2 
= 08 :
t
Y
t

F
t

e
t

e
t
/Y
t

1 130 13000
–
–
2 70 13000
−6000 086 3
140 8200 5800 041 4
150 12840 2160 014 5
90 14568
−5568 062 6
180 10114 7886 044 7
16423
–
–
MAPE
=

e
t
/Y
t

n
× 100 =
247 5
× 100 = 494%
The first exponential smoothing model has therefore produced more accurate forecasts than the second, as it has a lower average forecast error. Based on this and on the assumption that the future will not be dramatically different from the past, the operations manager of the company could use an exponential smoothing forecasting model with a low value of  in order to predict the number of component parts that will be required in the future.
Different forecasting models would obviously produce different forecasts.
For a good discussion of the various forecasting methods, both statistical and judgmental, refer to Hanke et al.
20

Download 340.14 Kb.

Share with your friends: