group 3 forecasting

8/13/2019 GROUP 3 Forecasting

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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

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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

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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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