This document discusses various forecasting techniques including exponential smoothing, decomposition methods, tracking signals, base series, bias, Delphi method, input-output analysis, and regression analysis. It provides sample calculations for exponential smoothing and questions/practice problems regarding different forecasting concepts and methods.

1. CHAPTER 8: Forecasting
Responses to Questions:
1. Exponential Smoothing is a special case of ‘weighted moving averages’.
The time span ‘n’ over which the demand Dt-n becomes negligible is the
period of this moving average. This time span is generally large. Smaller the
value of ‘α’, the larger the span of the moving average.
2. Exponential Smoothing is a time-series method. It tracks a trend to a certain
extent and with a lag in time. Whether it is satisfactory or not depends upon
the objective of the forecasting exercise. This is an ‘averaging’ method and
that is its limitation as well as strength.
3. a) The purpose behind the computations of ‘demand ratios’ is to eliminate
the ‘seasonality’. If say the September demand this year is compared
with September demand last year, it would help in nullifying the seasonal
effect. Then, the ‘trend’ in demand can be tracked better.
b) Generally the base series should be computed over a period that
includes seasonality completely. Generally, seasonality is yearly as the
economic activities are conducted on a yearly - and in that on a monthly
- basis.
4. Forecasts have to be (i) accurate and preferably, (ii) precise. Accuracy
concerns relevance, and, therefore two aspects of the error are important:
a) bias and b) amplitude. As long as the error, in both its aspects, is within
tolerance limits, the forecast has done its job. So, the error is a sufficient
measure of the performance of a given forecasting model.
However, another question to ask would be the time span over which the
forecasting model performs. A model that is doing well now, would it
suddenly go haywire after some time because some important factor was
not considered earlier? How long would the model retain its relevance?
Control over error should not lead one into complacency.
5. Extrapolation assumes that the same trend will continue and the same
factors will keep operating – which is a huge assumption and, therefore, a
limitation. Input-output tables are restricted to economic analysis and do not
consider governmental, technological and other factors. Delphi technique is
basically an expert ‘opinion’. It is after all an opinion, although an opinion
that is reasoned out.
6. Assessment is with regard to its use, adaptability, benefits and costs if and
when the technology is considered for certain purposes. Technology
assessment, selection and use have important long-range impact on the
production/operations system.

2. 2
7. Forecasts could be at the broad level and at the detailed level. Forecasts,
for instance, could be for annual trends and/or they could be for weekly
demands on the system. Both, or forecasts at all levels are required in order
to obtain/construct a full picture.
8. Multiple Regression can be easily run on Statistical packages readily
available (e.g. SPSS). The current data is simple to analyze.
We could calculate manually by Least Squares method of line fitting. The
line is:
Y = a0 + a1X
where Y is the sales, X is the price, and a0 and a1 are constants.
The ‘fit’ is obtained by solving the following equations :
Σ Y = a0N + a1Σ X and
Σ XY = a0X + a1 Σ X2
where N is the number of data points. The above equations are called the
‘normal equations for the least square line’. The computations are given
below.
Y
Sales
X
Price
X2
XY
1143 9.90 98.01 11316
361 19.60 384.16 7076
532 14.50 210.25 7714
997 10.80 116.64 10767
390 17.40 302.76 6786
475 15.30 234.09 7267
722 12.70 161.29 9169
410 16.50 272.25 6765
605 13.70 187.69 8288
910 11.20 125.44 10192
360 18.70 349.69 6732
1094 10.20 104.04 11159
806 12.00 144.00 9672
355 19.20 368.64 6816
ΣΣΣΣY = 9160 ΣΣΣΣX = 201.7 ΣΣΣΣX2
= 3058.95 ΣΣΣΣXY = 119,719
We note that N=14 and solve the ‘normal equations’ giving the equation of our
line of fit as :
Y = - 2.143 + 45.563 X

3. 3
9. a) In fact, the value of α is to be found by trial and error. An α value is
assumed and the forecasts are made which are compared with the actual
demand. This is done for different assumed values of α. The α value
producing a forecast with the least error is accepted. We shall present here
some sample calculations for illustrative purposes.
For the sample illustration we take α = 0.3 and a trend factor of 40, starting
with forecast for April 1997 made in March 1997. Let FAp (forecast for April,
made in March) be assumed to be equal to DMar (demand for March).
Trend-corrected forecast for April = 1445 + (0.7) 40 = 1538
(0.3)
Forecast for May = 0.3 (1490) + 0.7 (1445) = 1459
Trend factor for May = 0.3 (1459 -1445) + 0.7 (40) = 32
Trend-corrected forecast for May = 1459 + (0.7) 32 = 1534
(0.3)
Forecast for June = 0.3 (1610) + 0.7 (1459) = 1504
Trend factor for June = 0.3 (1504 -1459) + 0.7 (32) = 36
Trend-corrected forecast for June = 1504 + (0.7) 36 = 1588
(0.3)
Forecast for July = 0.3 (1575) + 0.7 (1504) = 1525
Trend factor for July = 0.3 (1525 -1504) + 0.7 (36) = 32
Trend-corrected forecast for July = 1525 + (0.7) 32 = 1600
(0.3)
Forecast for August = 0.3 (1605) + 0.7 (1525) = 1549
Trend factor for August = 0.3 (1549 -1525) + 0.7 (32) = 30
Trend-corrected forecast for August = 1549 + (0.7) 30 = 1619
(0.3)
Forecast for September = 0.3 (1590) + 0.7 (1549) = 1561
Trend factor for September = 0.3 (1561 -1549) + 0.7 (30) = 25
Trend-corrected forecast for September = 1561 + (0.7) 25 = 1619
(0.3)
Forecast for October = 0.3 (1665) + 0.7 (1561) = 1592
Trend factor for October = 0.3 (1592 -1561) + 0.7 (25) = 27
Trend-corrected forecast for October = 1592 + (0.7) 27 = 1655
(0.3)
Forecast for November = 0.3 (1730) + 0.7 (1592) = 1633
Trend factor for November = 0.3 (1633 -1592) + 0.7 (27) = 31
Trend-corrected forecast for November = 1633 + (0.7) 31 = 1705
(0.3)

4. 4
Forecast for December = 0.3 (1695) + 0.7 (1633) = 1652
Trend factor for December = 0.3 (1652 -1633) + 0.7 (31) = 28
Trend-corrected forecast for December = 1652 + (0.7) 28 = 1717
(0.3)
Forecast for January = 0.3 (1775) + 0.7 (1652) = 1689
Trend factor for January = 0.3 (1689 -1652) + 0.7 (28) = 31
Trend-corrected forecast for January = 1689 + (0.7) 31 = 1761
(0.3)
The forecast model with α = 0.3 has not done a very bad job. Further trials
can improve the performance.
9. b) The forecast for February 1998 = 0.3 (1880) + (0.7) (1689) = 1746
Trend factor for February 1998 = 0.3 (1746 -1689) + (0.7) (31) = 39
Trend-corrected forecast for February 1988 = 1746+(0.7/0.3) (39) = 1837
We shall assume the same trend correction to hold good for the next two
months.
Forecast for April = Trend-corrected Forecast for February + 2 (trend
correction)
= 1837 + 2 (0.7) 39 = 2019
(0.3)
c) Let us start with the forecast for April 1997.
FApr = α. DMar + 2 (1-α) FMar – (1-α) FFeb
= (0.3) (1445) + 2 (0.7) (1445) – (1 - 0.3) (1340)
= 1519
FMay = α. DApr + 2 (1-α) FApr – (1-α) FMar
= (0.3) (1490) + 2 (0.7) (1519) – (0.7) (1445)
= 1562
FJune = (0.3) (1610) + 2 (0.7) (1562) – (0.7) (1519)
= 1607
FJuly = (0.3) (1575) + 2 (0.7) (1607) – (0.7) (1562)
= 1629
FAug = (0.3) (1605) + 2 (0.7) (1629) – (0.7) (1607)
= 1637
FSept = (0.3) (1590) + 2 (0.7) (1637) – (0.7) (1629)
= 1629

5. 5
FOct = (0.3) (1665) + 2 (0.7) (1629) – (0.7) (1637)
= 1634
FNov = (0.3) (1730) + 2 (0.7) (1634) – (0.7) (1629)
= 1666
FDec = (0.3) (1695) + 2 (0.7) (1666) – (0.7) (1634)
= 1697
FJan = (0.3) (1775) + 2 (0.7) (1697) – (0.7) (1666)
= 1742
Thus, with the same value of α (= 0.3) this “second order system” seems to
be performing as good as the earlier one.
A different value of α may be tried, similar to the above calculations.
10. BPO, in India, is a fast growing industry. Forecasting is a vital activity in
order to make appropriate arrangements for the human resources, which is
a critical factor for this industry. Moreover, there are various kinds of
services possible. The demand can be forecast based on several causative
factors and market surveys in the developed countries where the clients are
generally based. Infrastructure is another important factor for the BPO
industry. While the human resources availability and infrastructure are
essential factors, the causative factors will be linked with the economies in
the foreign countries. The restructuring of the firms there and/or the
rationalization exercises of the firms there would result in their need for
outsourcing their services to India and other countries. One has to also
investigate as to why a firm would prefer India to other destinations like
Philippines or Ireland. Forecasting of off-shoring of services is as yet a
relatively less known exercise. But, such off-shoring is a huge economy-
booster for India. Therefore, the forecasting exercise needs to be done in all
earnestness.

6. 6
CHAPTER 8: Forecasting
Objective Questions:
1. An exponential smoothing with α = 0.2 is roughly equivalent to a moving
average of :
a. 4 periods
b. 6 periods
√c. 9 periods
d. 19 periods
2. Decomposition methods of Forecasting incorporate :
√ a. trend, cyclical and seasonal factors
b. causative factors
c. Input-output factors
d. expert opinions
3. Tracking signals can :
√ a. measure forecast quality.
b. track the demand.
c. be useful only when the demand fluctuations are large.
d. all of the above.
4. If for a demand process suited to α = 0.1, we try to fit a forecasting
procedure with α = 0.3, the forecast will :
a. show a pronounced leveled behaviour.
b. follow the demand better, consequently reducing forecast errors.
c. a & b
√ d. none of the above.
5. ‘Base Series’ are useful in tracking :
a. trends in demand
b. business cycles
√ c. seasonal effects
d. forecast errors
6. The ‘bias’ in forecasting is brought our through :
a. Root mean square
b. Mean absolute deviation (MAD)
√ c. Running sum of forecast errors (RSFE)
d. none of the above
7. Delphi method is based primarily on :
a. life cycle analysis
√ b. experts’ opinion
c. tracking of errors
d. input-output analysis

7. 7
8. Normative forecast involves :
a. going from distant past to the future.
b. going from present to the future.
c. going from recent past to a foreseeable future.
√ d. going from the future to the present.
9. Input-output analysis considers :
√ a. economic factors
b. technological factors
c. business cycles
d. all of the above
10. Exponential Smoothing is related to :
a. multiple regression
√ b. moving average
c. weighted Delphi
d. input-output analysis
11. Following are the forecasts and actual demands :
Week Forecasted demand Actual demand
1 10 8
2 8 10
3 9 11
4 10 12
5 11 11
The MAD for the above is :
a. + 0.8
b. – 0.8
c. – 1.6
√ d. + 1.6
12. For the above data, the RSFE is :
a. + 0.8
√ b. – 0.8
c. – 1.6
d. + 1.6
13. In the case of a simple regression, the ‘coefficient of determination’ is :
a. √explained variation/total variation
√ b. explained variation/total variation
c. total variation/explained variation
d. √total variation/explained variation

8. 8
14. A simple regression gives a good fit when the coefficient of correlation is:
√ a. high
b. low
c. negative
d. steady
15. J.W. Forrester is well-known for:
a. Life cycle analysis
√ b. Dynamic modeling
c. Delphi method
d. Ergonomics
16. By 2020, NOIDA region will have a vehicles population of 500000 and
hence by 2010 it will need to embark on building a road network of 500
km. This is a case of :
a. time-series forecasting
b. extrapolative forecasting
c. input-output analysis
√ d. normative forecasting
17. The average demand during the Quarters I, II, III and IV has been 200,
200, 150 and 250 units respectively. In this case, the seasonal index for
Quarter III expressed as a fraction is :
√ a. 0.75
b. 1.00
c. 1.25
d. 1.50
18. For the above data, the 3-period centered moving average for Quarter III
is :
√ a. 200.0
b. 183.3
c. 175.0
d. 225.0
19. Exponential Smoothing is being used for forecasting. The demand in
October is 200 units while the forecast made for October has been 160
units. Your forecast for November, taking α = 0.2, would be :
a. 160 units
√ b. 168 units
c. 180 units
d. 192 units