Forecasting Chpater 2 for Mech 4th b Tech Gokul

8/3/2019 Forecasting Chpater 2 for Mech 4th b Tech Gokul

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FORECASTING

CHAPTER

Forecasting


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FORECAST: A statement about the future value of a variable of

interest such as demand.

Forecasts affect decisions and activities throughout

an organization Accounting, finance

Human resources

Marketing

MIS

Operations

Product / service design


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3

Forecasting

Techniques and Routes

Forecasting is the establishment of future

expectations by the analysis of past data,or the formation of opinions.

Forecasting is an essential element ofcapital budgeting.

Capital budgeting requires the commitmentof significant funds today in the hope of longterm benefits. The role of forecasting is the

estimation of these benefits.

.


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Accounting Cost/profit estimates

Finance Cash flow and funding

Human Resources Hiring/recruiting/training

Marketing Pricing, promotion, strategy

MIS IT/IS systems, services

Operations Schedules, MRP, workloads

Product/service design New products and services

Uses of Forecasts


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Assumes causal systempast ==> future

Forecasts rarely perfect because ofrandomness

Forecasts more accurate forgroups vs. individuals

Forecast accuracy decreasesas time horizon increases

I see that you willget an A this semester.


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Elements of a Good Forecast

Timely

AccurateReliable

Written


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Steps in the Forecasting Process

Step 1 Determine purpose of forecast

Step 2 Establish a time horizon

Step 3 Select a forecasting techniqueStep 4 Gather and analyze data

Step 5 Prepare the forecast

Step 6 Monitor the forecast

The forecast


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Types of Forecasts

Judgmental - uses subjective inputs

Time series - uses historical dataassuming the future will be like the past

Associative models - uses explanatoryvariables to predict the future


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9

Forecasting Techniques and

RoutesTechniques Routes

Top-down routeBottom-up routeQuantitative Qualitative

Simple regressionsMultiple regressionsTime trendsMoving averages

Delphi methodNominal grouptechniqueJury of executiveopinionScenario projection


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Judgmental Forecasts

Executive opinions Sales force opinions

Consumer surveys

Outside opinion

Delphi method

Opinions of managers and staff Achieves a consensus forecast


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Time Series Forecasts

Trend- long-term movement in data Seasonality - short-term regular variations in

data

Cyclewavelike variations of more than oneyears duration

Irregular variations - caused by unusual

circumstancesRandom variations - caused by chance


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Forecast Variations

Trend

Irregularvariation

Seasonal variations

90

89

88

Figure 3.1

Cycles


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Naive Forecasts

Uh, give me a minute....We sold 250 wheels last

week.... Now, next week

we should sell....

The forecast for any period equalsthe previous periods actual value.


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Simple to use Virtually no cost

Quick and easy to prepare

Data analysis is nonexistent

Easily understandable

Cannot provide high accuracy

Can be a standard for accuracy

Nave Forecasts


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Stable time series data F(t) = A(t-1)

Seasonal variations

F(t) = A(t-n) Data with trends

F(t) = A(t-1) + (A(t-1)A(t-2))

Uses for Nave Forecasts


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Techniques for Averaging

Moving average

Weighted moving average

Exponential smoothing


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Moving Averages

Moving averageA technique that averages anumber of recent actual values, updated as new

values become available.

Weighted moving averageMore recent values in a

series are given more weight in computing theforecast.

MAn =nAii = 1

n


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Simple Moving Average

MAn = n

Aii = 1

n

35

37

39

41

43

45

47

1 2 3 4 5 6 7 8 9 10 11 12

Actual

MA3

MA5


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Exponential Smoothing

Premise--The most recent observations mighthave the highest predictive value.

Therefore, we should give more weight to themore recent time periods when forecasting.

Ft = Ft-1 + (At-1 - Ft-1)


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Weighted averaging method based on previous

forecast plus a percentage of the forecast error

A-F is the error term, is the % feedback

Ft = Ft-1 + (At-1 - Ft-1)


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Period Actual Alpha = 0.1 Error Alpha = 0.4 Error

1 42

2 40 42 -2.00 42 -2

3 43 41.8 1.20 41.2 1.8

4 40 41.92 -1.92 41.92 -1.92

5 41 41.73 -0.73 41.15 -0.15

6 39 41.66 -2.66 41.09 -2.09

7 46 41.39 4.61 40.25 5.75

8 44 41.85 2.15 42.55 1.45

9 45 42.07 2.93 43.13 1.87

10 38 42.36 -4.36 43.88 -5.8811 40 41.92 -1.92 41.53 -1.53

12 41.73 40.92

Example 3 - Exponential Smoothing


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Picking a Smoothing Constant

35

40

45

50

1 2 3 4 5 6 7 8 9 10 11 12

Period

Dem

and .1

.4

Actual


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Common Nonlinear Trends

Parabolic

Exponential

Growth

Figure 3.5


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Linear Trend Equation

Ft = Forecast for period t

t = Specified number of time periods

a = Value of Ft at t = 0

b = Slope of the line

Ft = a + bt

0 1 2 3 4 5 t

Ft


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Calculating a and b

b =n (ty) - t y

n t2 - ( t)2

a =y - b t

n


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Linear Trend Equation Example

t yWeek t

2Sales ty

1 1 150 150

2 4 157 314

3 9 162 4864 16 166 664

5 25 177 885

t = 15 t2 = 55 y = 812 ty = 2499( t)

2= 225


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Linear Trend Calculation

y = 143.5 + 6.3t

a =812 - 6.3(15)

5=

b = 5 (2499) - 15(812)5(55) - 225

= 12495 -12180275 - 225

= 6.3

143.5


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Associative Forecasting

Predictor variables - used to predict values ofvariable interest

Regression - technique for fitting a line to a set

of points

Least squares line - minimizes sum of squared

deviations around the line


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Linear Model Seems Reasonable

A straight line is fitted to a set of sample points.

0

10

20

30

40

50

0 5 10 15 20 25

X Y7 15

2 10

6 13

4 15

14 2515 27

16 24

12 20

14 27

20 4415 34

7 17

Computedrelationship


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Forecast Accuracy

Error - difference between actual value and predictedvalue

Mean Absolute Deviation (MAD)

Average absolute error Mean Squared Error (MSE)

Average of squared error

Mean Absolute Percent Error (MAPE)

Average absolute percent error


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MAD, MSE, and MAPE

MAD =Actual forecast

n

MSE = Actual forecast)

-1

2

n

(

MAPE =Actual forecas

t

n

/ Actual*100)(


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Example 10

Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual)*100

1 217 215 2 2 4 0.92

2 213 216 -3 3 9 1.41

3 216 215 1 1 1 0.46

4 210 214 -4 4 16 1.90

5 213 211 2 2 4 0.946 219 214 5 5 25 2.28

7 216 217 -1 1 1 0.46

8 212 216 -4 4 16 1.89

-2 22 76 10.26

MAD= 2.75

MSE= 10.86

MAPE= 1.28


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Controlling the Forecast

Control chart A visual tool for monitoring forecast errors

Used to detect non-randomness in errors

Forecasting errors are in control if All errors are within the control limits

No patterns, such as trends or cycles, are

present


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Sources of Forecast errors

Model may be inadequate Irregular variations

Incorrect use of forecasting technique


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Tracking Signal

Tracking signal = (Actual-forecast)MAD

Tracking signalRatio of cumulative error to MAD

Bias Persistent tendency for forecasts to beGreater or less than actual values.


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Choosing a Forecasting Technique

No single technique works in every situation Two most important factors

Cost

Accuracy Other factors include the availability of:

Historical data

Computers Time needed to gather and analyze the data

Forecast horizon


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Linear Trend Equation


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Simple Linear Regression

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Forecasting Chpater 2 for Mech 4th b Tech Gokul