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Forecastingis the art and
science of predicting futureevents.Business forecasting pertains
to more than predictingdemand.
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Forecasts are also used to predict
profits, revenues, costs, productivitychanges, prices and availability of
energy and raw materials, interest
rates, movements of economicindications and prices of stocks andbonds, as well as other variables.
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Features Common to All Forecasts1. Forecasting techniques generally assume that
the same underlying causal system that existed inthe past that will continue to existed in the future.2. Forecasts are rarely perfect; predicted values
usually differ from actual results.3. Forecasts for group of items tend to be more
accurate than forecasts for individual items.4. Forecast accuracy decreases as the time
period covered by the forecast increases.
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Steps in Forecasting1. Determine the purpose of the forecast and
when it will be needed.2. Establish the time horizon that the forecastmust cover.3. Select a forecasting technique.4. Gather and analyze the appropriate data and
then prepare the forecast.
5. Monitor the forecast.
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Approaches of ForecastingIn some situations, forecasters rely solely on judgmentand opinion to make forecasts. If management musthave a forecast quickly, there may not be enough time
to gather and analyze quantitative data.
Rely on analysis of subjective inputs obtained fromvarious sources, such as consumer surveys, the salesstaff, managers and executives, and panels of experts.
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1. Executive Opinions.A small group of upper-level managers(e.g., in marketing, operations, and finance) may meet andcollectively develop a forecast. Is often used as a part of long-range planning and new product development.2. Sales Force Composite.Members of the sales staff or thecustomer service staff are often good sources of informationbecause of their direct contact with consumers. They are oftenaware of any plans the customers may be considering for thefuture.3. Consumer Surveys. The obvious advantage of consumer surveysis that they can tap information that might not be availableelsewhere.4. Outside Opinion.This may concern advice on political oreconomic conditions in a foreign country or some other aspects of
interest with which an organization lacks familiarity.5. Opinions of Managers and Staff. A manager may solicit opinionsfrom a number of other managers and staff people. Delphimethod, an iterative process in which managers and staffcomplete a series of questionnaires, each developed from the
previous one, to achieve a consensus forecast.
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Is the simplest forecasting technique. Theadvantage of a nave forecast is that it has
virtually no cost, it is quick and easy to preparebecause data analysis is nonexistent, and it is
easy to understand. The main disadvantage is
its inability to provide highly accurate
forecasts.
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For example,
Suppose the last two values were 50 and
53. The next forecast would be 56:Period Actual Change from Previous
ValueForecast
1 50
2 53 +33 53+3=
56
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A moving average forecast uses a number of
the most recent actual data values in
generating a forecast.
Moving Average = Demand in previous nperiodsn
where:nis the number of periods in the moving average
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Demand Supply
1 70
2 80
3 65
4 90
5
85
Compute a three-periodmoving averageforecast given the following demand forcars for the last five periods.
Example:
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Solution:The forecast for period 6should be:
Moving Average Forecast = 65 + 90 + 85 = 80 cars
3
Moving Average Forecast = 90 + 85 + 95 = 90 cars3
Note: That inMoving Average, as new actual valuebecomes available, the forecast is updated by addingthe newest value and dropping the oldestand thenrecomputing the average. Consequently, the forecastmovesby reflecting only the most recent values.
If actual demand in period 6 turns out to be 95, the moving
average forecast for period 7 would be:
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A weighted average is similar to a moving average,except that it assigns more weight to the most recentvalues in a time series.
A Weighted Moving Average may be expressedmathematically as:
Weighted Moving Average
= [(weight for period n)(demand in period n)] Weights
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Demand Supply1 70
2 80
3 65
4 90
5 85
Example:Compute a three-periodweighted moving
average forecast given the following demandfor cars for the last five periods; with an assigned
weight of 1,2, and 3.
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Solution:The forecast for period 6would be:
65(1 ) + 90 (2) + 85(3)
6= 83.33 or 83 cars
=90(1) + 85(2) + 95(3)
6= 90.83 or 91 cars
If actual demand in period 6 turns out to be 95, the weightedmoving average forecast for period 7would be:
Weighted MovingAverage Forecast
Weighted Moving
Average Forecast
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Exponential smoothing is a sophisticated weighted
averaging method that is still relatively easy to use andunderstand. Each new forecast is based on theprevious forecast plus a percentage of the differencebetween that forecast and the actual value of theseries at that point. That is:
Where arepresents the value of weighing factorwhich is referred to as smoothing factor that has avalue between 0 and 1, inclusive. This representspercentage forecast error.
Last Periods Forecast + a (Last Periods actualdemand - Last Periods Forecast )
New Forecast =
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A car dealer predicted a January demand for550 Honda V-tech cars. Actual January demand was680 Honda V-tech cars and a=0.10. Forecast thedemand for February, using the exponentialsmoothing model.
Example 1:
New forecast (February) = 550 + 0.10 [680-550]= 563
Solution:
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Use exponential smoothing model to develop aseries of forecast for the following data and
compute
[Actual - Forecast] = Error for each period
a. use a smoothing factor of 0.10b. use a smoothing factor of 0.40
Example 2:
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PERIOD ACTUAL DEMAND1
50
2 52
3 48
4 51
5 506 54
7 52
8 50
9 55
10 53
11
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PERIOD
ACTUALDEMAND
FORECAST
ERROR
FORECAST
ERROR
1 50 - - - -
2 52 50.00 2 50.00 2
3
48
50.20
-2.2
50.80
-2.8
4 51 49.98 1.02 49.68 1.32
5 50 50.08 -0.08 50.21 -0.21
6 54 50.07 3.93 50.13 3.87
7
52
50.46
1.54
51.68
0.32
8 50 50.61 -0.61 51.81 -1.81
9 55 50.55 4.45 51.09 3.91
10 53 51.00 2 52.65 0.35
11
51.20
52.79
Solution:A. a 0.10 B. a 0.40
[Actual - Forecast] = Error for each period
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Trend Equation. A linear trend equation has the form:Yt= a + btWhere
t = specified number of time periods from t = 0Yt = forecast for period ta = value of Y
t
at t=0b = slope of the line
b = nty- ty
nt2 - (t)2where: n = number of periods
y = value of the time series
The coefficient of line a and b can be computed usingthe two equations:
a = y - btn
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The total sales of television sets of a Manila-
based firm over the last 10 weeks is shown in the
following table. Plot the data, and visually
check if linear trend line would be appropriate.
Then determine the equation of the line and
predict the sales for weeks 11 and 12.
Example:
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WEEK UNIT SALES
1 800
2 810
3 830
4 820
5 850
6 810
7 825
8 8409 805
10 830
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WEEK (t) UNIT SALES (y) ty t2
1 800 800 1
2 810 1,620 4
3 830 2,490 9
4 820 3,280 16
5 850 4,250 25
6 810 4,860 36
7 825 5,775 498 840 6,720 64
9 805 7,245 81
10 830 8,300 100
t = 55
y = 8,220
ty = 45,340
t
2
=
385
a.Plot. x axis = weeky axis = unit sales
Solution:
b.
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b = 10(45,340) - (55)(8,220)10(385) - (55)2
b = 1,300 = 1.6825
a = 8,220 8810
a = 813.20
c. Yt =813.20 + 1.6t
When t = 11
Y11 = 813.20 + 1.6(11)= 830.8
When t = 12
Y12 = 813.20 + 1.6(12)= 832.4
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The objective of linear regression is to obtain anequation of a straight line that minimizes the sum ofequation vertical deviations of points around the line. Thissquares line has the equation:
Yt = a + bX
where: Yt = Predicted (dependent) variableX = Predictor (independent) variableb = slope of the linea = value of Yt at X=0
(Note that it is conventional to represent values ofthe predicted variable on the y axis and values of thepredictor on the x axis).
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The coefficients a and b of the line arecomputed using these two equations:
b = n(xy) (x)( y)n(x
2
) - (x)2
where: n = number of periods observations
a = y - bxn
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Sales, x (Millions) Profits, y (Millions)
15 8
17 921 13
18 10
19 11
22
14
16 8.5
17 10
25 15
20
13
JR Hamburgers has a chain of 10 stores in Metro Manila.Sales figures and profiles for stores are given in the
following table. Obtain the regression line for the data,and predict profits for a store assuming sales of 30 million.
Example:
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Sales, x(Millions) Profits, y(Millions) xy
x
2
15 8 120 225
17 9 153 289
21 13 273 44118 10 180 324
19 11 209 361
22 14 308 484
16 8.5 136 25617 10 170 289
25 15 375 625
20 13 260 400
x = 190 y = 111.5 xy =2,184 x = 3,694
Solutions:
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b = 10(2,184) (190)(111.5)10(3,694)
(190)
2b = 0.78a= 111.5 - 0.78 (3,694)
10
a= -3.67when x = P30millionYt = a + bXY30= -3.67 + 0.78 (30) = 19.73 million
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