Operations Management
Forecasting
Part A: Discussing basic concepts of forecasting
including demand forecasting and stating different methods of forecasting
What is Forecasting?
Forecasting is
a scientifically calculated guess. It is basic to all planning activity –
1)
Whether
it is national, regional, organisational, or functional planning; and
2)
Whether
it is a long-range plan or a short- range plan.
The scientific basis of forecasting lies in studying
past, present and future trends, present and future actions and their effects.
What happened in the past is relevant to what is happening now and what could
happen in the future. Thus, forecasting takes into account all the three
dimensions of time – past, present and future. In spite of all the
calculations, forecasting remains a calculated guess. Errors are bound to be
there, but it remains the foundation for management planning.
Many tend to
think that forecasting is important only for marketing planning and not for
production, because the figures for production planning are received from
marketing planning anyway. This is an erroneous view. Production planning need
not necessarily follow marketing planning. There are many situations where production
plans and marketing planning have to be done together and many other situations
where production planning may be done separately from marketing planning.
Therefore, forecasting is a very important activity for production planning, be
it strategic or tactical.
Methods of Forecasting
The most
effective, popular and important methods of forecasting are:
1.
Least
Squares Method
2.
Simple
Moving Average Method
3.
Weighted
Moving Average Method
4.
Exponential
Smoothing Method
5.
Trend-Adjusted
Exponential Smoothing Method
We shall now explore these methods including the
relevant formulas by solving some illustrations as follows.
Part B
Operations Management
Forecasting
Selected Problems and Solutions
Illustration: 1
Following
table gives the demand (in million tonne) for iron ore during the years 2000 to
2010. Find the forecast of the demand for the years 2011 and 2012 using the
Method of Least Squares for forecasting.
|
Year |
Demand |
|
2000 |
10 |
|
2001 |
12 |
|
2002 |
13 |
|
2003 |
16 |
|
2004 |
14 |
|
2005 |
16 |
|
2006 |
20 |
|
2007 |
25 |
|
2008 |
22 |
|
2009 |
30 |
|
2010 |
35 |
Solution: 1
Illustration: 2
Following
table gives the annual exports (in US$ million) of automobile parts of a
company in India. The figures for the past 8 years are as follows:
|
Year |
Exports |
|
2002 |
124 |
|
2003 |
130 |
|
2004 |
142 |
|
2005 |
154 |
|
2006 |
165 |
|
2007 |
179 |
|
2008 |
185 |
|
2009 |
153 |
Compute the
forecast for the year 2010 using 5-year Simple Moving Average Method.
Solution: 2
Illustration: 3
Following
table gives the annual exports (in US$ million) of automobile parts of a
company in India. The figures for the past 8 years are as follows:
|
Year |
Exports |
|
2002 |
124 |
|
2003 |
130 |
|
2004 |
142 |
|
2005 |
154 |
|
2006 |
165 |
|
2007 |
179 |
|
2008 |
185 |
|
2009 |
153 |
Compute the
forecast for the year 2010 using 3-year Weighted Moving Average Method. Weights
are given as follows:
|
History |
Weight |
|
3
years ago |
0.2 |
|
2
years ago |
0.3 |
|
Last
year |
0.5 |
Solution: 3
Illustration: 4
Data on
exports (in US$ million) of an Indian Company are as follows:
|
Year |
Exports |
|
2006 |
165 |
|
2007 |
179 |
|
2008 |
185 |
|
2009 |
153 |
If the
forecast made for the year 2006 was US$ 173 million, using Exponential
Smoothing Method with Alpha value of 0.2, make a forecast for the year 2010.
Solution: 4
Illustration: 5
Following
table gives the annual exports (in US$ million) of automobile parts of a
company in India. The figures for the past 8 years are as follows:
|
Year |
Exports |
|
2002 |
124 |
|
2003 |
130 |
|
2004 |
142 |
|
2005 |
154 |
|
2006 |
165 |
|
2007 |
179 |
|
2008 |
185 |
|
2009 |
153 |
Make the forecast
for the year 2010 using Exponential Smoothing Method and taking α = 0.3.
Solution: 5
Illustration: 6
Demand values
for the four quarters of the years 2010 to 2013 are observed as given in the
table below:
|
Year |
Quarter
1 |
Quarter
2 |
Quarter
3 |
Quarter
4 |
|
2010 |
92 |
117 |
104 |
82 |
|
2011 |
96 |
124 |
109 |
87 |
|
2012 |
101 |
131 |
115 |
92 |
|
2013 |
107 |
140 |
124 |
99 |
Find the
seasonal indices for each of the quarters and forecast the demand for the
Quarter 2 of the year 2014 and for the Quarter 1 of the year 2015.
Solution: 6
The demand for a product in each of the last five months is
shown below.
|
Month |
1 |
2 |
3 |
4 |
5 |
|
Demand |
13 |
17 |
19 |
23 |
24 |
Use a 2-month moving average to generate a forecast
for demand in month 6. Apply exponential smoothing with a smoothing constant of
0.9 to generate a forecast for demand in month 6. Which of these two forecasts do
you prefer and why?
Solution: 7
Illustration:
8
The
table below shows the demand for a new aftershave in a shop for each of the
last 7 months.
|
Month |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
Demand |
23 |
29 |
33 |
40 |
41 |
43 |
49 |
Calculate
a 2-month moving average for month two to seven. What would be your forecast
for the demand in month eight? Apply exponential smoothing with a smoothing
constant of 0.1 to derive a forecast for the demand in month eight. Which of
the two forecasts for month eight do you prefer and why?
Solution: 8
Illustration:
9
The
table below shows the demand for a particular brand of razor in a shop for each
of the last nine months.
|
Month |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
Demand |
10 |
12 |
13 |
17 |
15 |
19 |
20 |
21 |
20 |
Calculate
a 3-month moving average for month three to nine. What would be your forecast
for the demand in month ten? Apply exponential smoothing with a smoothing
constant of 0.3 to derive a forecast for the demand in month ten. Which of the
two forecasts for month ten do you prefer and why?
Solution: 9
Illustration:
10
The
table below shows the demand for a particular brand of fax machine in a
department store in each of the last twelve months.
|
Month |
Demand |
|
1 |
12 |
|
2 |
15 |
|
3 |
19 |
|
4 |
23 |
|
5 |
27 |
|
6 |
30 |
|
7 |
32 |
|
8 |
33 |
|
9 |
37 |
|
10 |
41 |
|
11 |
49 |
|
12 |
58 |
Calculate
the 4-month moving average for months 5 to 12. What would be your forecast for
the demand in month 13? Apply exponential smoothing with a smoothing constant
of 0.2 to derive a forecast for the demand in month 13. Which of the two
forecasts for month 13 do you prefer and why?
Solution: 10
Illustration:
11
The
table below shows the demand for a particular brand of microwave oven in a
department store in each of the last twelve months.
|
Month |
Demand |
|
1 |
27 |
|
2 |
31 |
|
3 |
29 |
|
4 |
30 |
|
5 |
32 |
|
6 |
34 |
|
7 |
36 |
|
8 |
35 |
|
9 |
37 |
|
10 |
39 |
|
11 |
40 |
|
12 |
42 |
Make
6-month moving average forecast for the demand in month 13? Apply exponential
smoothing with a smoothing constant of 0.7 to derive a forecast for the demand
in month 13. Which of the two forecasts for month 13 do you prefer and why?
Solution: 11
Illustration:
12
The
table below shows the temperature (degrees C), at 11 p.m., over the last ten
days:
|
Day |
Temperature |
|
1 |
1.5 |
|
2 |
2.3 |
|
3 |
3.7 |
|
4 |
3.0 |
|
5 |
1.4 |
|
6 |
-1.3 |
|
7 |
-2.4 |
|
8 |
-3.7 |
|
9 |
-0.5 |
|
10 |
1.3 |
Make
3-day moving average forecast for the temperature at 11 p.m. on day 11? Apply
exponential smoothing with a smoothing constant of 0.8 to derive a forecast for
the temperature at 11 p.m. on day 11. Which of the two forecasts for the
temperature at 11 p.m. on day 11 do you prefer and why?
Solution: 12
Illustration:
13
The
table below shows the sales of a toy robot over the last 11 months.
|
Month |
Sales |
|
1 |
3651 |
|
2 |
4015 |
|
3 |
3874 |
|
4 |
3501 |
|
5 |
3307 |
|
6 |
3105 |
|
7 |
2986 |
|
8 |
3100 |
|
9 |
3209 |
|
10 |
3450 |
|
11 |
3507 |
Estimate
a 4-month moving average forecast for the sales in month 12? Apply exponential
smoothing with a smoothing constant of 0.9 to derive a forecast for the sales
in month 12. Which of the two forecasts for month 12 do you prefer and why?
Solution: 13
Illustration:
14
The
table below shows the movement of the price of a commodity over 12 months.
|
Month |
Price |
|
1 |
25 |
|
2 |
30 |
|
3 |
32 |
|
4 |
33 |
|
5 |
32 |
|
6 |
31 |
|
7 |
30 |
|
8 |
29 |
|
9 |
28 |
|
10 |
28 |
|
11 |
29 |
|
12 |
31 |
Make a 6 month moving average forecast
for month 13? Apply exponential smoothing with smoothing constants of 0.7 and
0.8 to derive forecasts for month 13. Which of the two forecasts based on
exponential smoothing for month 13 do you prefer and why?
Solution: 14
Illustration:
15
Given
the following information, make a forecast for May using exponential smoothing
with trend.
|
Month |
January |
February |
March |
April |
|
Demand |
700 |
760 |
780 |
790 |
For exponential smoothing with trend,
assume that the previous forecast (for January) including trend was 800 units
and the previous trend component was 50 units. Also α=0.30 and b=
0.10.
Solution: 15
Illustration:
16
The
following are quarterly data for the past two years. From these data, prepare a
forecast for the upcoming year using suitable methods.
|
Period |
Actual |
|
1 |
300 |
|
2 |
540 |
|
3 |
885 |
|
4 |
580 |
|
5 |
416 |
|
6 |
760 |
|
7 |
1191 |
|
8 |
760 |
Solution: 16
Illustration:
17
The
following table contains the demand from the last 10 months.
|
Month |
Demand |
|
1 |
31 |
|
2 |
34 |
|
3 |
33 |
|
4 |
35 |
|
5 |
37 |
|
6 |
36 |
|
7 |
38 |
|
8 |
40 |
|
9 |
40 |
|
10 |
41 |
Required
a)
Calculate the simple
exponential smoothing forecast for these data using α = 0.30, an initial
forecast of 31.
b) Calculate the
exponential smoothing with trend forecast for these data using α = 0.30 and β =
0.30, an initial trend forecast of 1 and an initial exponential smoothing
forecast of 30.
c)
Calculate the Mean
Absolute Deviation (MAD) for each forecast to identify the best one.
Solution: 17
Illustration:
18
PM Computer Services assembles customised personal computers from generic
parts. They need a good forecast of demand for their computers so that they
will know how many parts to purchase and stock. They have compiled demand data
for the last 12 months as given below.
|
Period |
Month |
Demand |
|
1 |
January |
37 |
|
2 |
February |
40 |
|
3 |
March |
41 |
|
4 |
April |
37 |
|
5 |
May |
45 |
|
6 |
June |
50 |
|
7 |
July |
43 |
|
8 |
August |
47 |
|
9 |
September |
56 |
|
10 |
October |
52 |
|
11 |
November |
55 |
|
12 |
December |
54 |
There is an upward trend in the demand. Use Trend-Adjusted Exponential Smoothing
Method with smoothing parameter, α = 0.5 and trend parameter, β = 0.3 to
compute the demand forecast for January (Period 13).
Solution: 18
