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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

FORCASTINGPART TWO

•Chapter Three•Forecasting

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Chapter 3

Forecasting

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

FORECAST:

• A statement about the future

• Used to help managers– Plan the system– Plan the use of the system

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

• Assumes causal systempast ==> future

• Forecasts rarely perfect because of randomness

• Forecasts more accurate forgroups vs. individuals

• Forecast accuracy decreases as time horizon increases

I see that you willget an A this semester.

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Elements of a Good Forecast

Timely

AccurateReliable

Mea

ningfu

l

Written

Easy

to u

se

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Steps in the Forecasting Process

Step 1 Determine purpose of forecast

Step 2 Establish a time horizon

Step 3 Select a forecasting technique

Step 4 Gather and analyze data

Step 5 Prepare the forecast

Step 6 Monitor the forecast

“The forecast”

3-8

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Types of Forecasts

• Judgmental - uses subjective inputs

• Time series - uses historical data assuming the future will be like the past

• Associative models - uses explanatory variables to predict the future

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Judgmental Forecasts

• Executive opinions

• Sales force composite

• Consumer surveys

• Outside opinion

• Opinions of managers and staff

–Delphi method

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Time Series Forecasts

• Trend - long-term movement in data

• Seasonality - short-term regular variations in data

• Irregular variations - caused by unusual circumstances

• Random variations - caused by chance

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Forecast Variations

Trend

Irregularvariation

Cycles

Seasonal variations

908988

Figure 3-1

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

• Simple to use

• Virtually no cost

• Data analysis is nonexistent

• Easily understandable

• Cannot provide high accuracy

• Can be a standard for accuracy

Naïve Forecasts

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

• 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 Naïve Forecasts

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Naive Forecasts

Uh, give me a minute.... We sold 250 wheels lastweek.... Now, next week we should sell....

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Techniques for Averaging

• Moving average

• Weighted moving average

• Exponential smoothing

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Simple Moving AverageFigure 3-4

MAn = n

Aii = 1n

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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Exponential Smoothing

Premise--The most recent observations might have the highest predictive value.

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

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

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Period Actual Alpha = 0.1 Error Alpha = 0.4 Error1 422 40 42 -2.00 42 -23 43 41.8 1.20 41.2 1.84 40 41.92 -1.92 41.92 -1.925 41 41.73 -0.73 41.15 -0.156 39 41.66 -2.66 41.09 -2.097 46 41.39 4.61 40.25 5.758 44 41.85 2.15 42.55 1.459 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 -1.5312 41.73 40.92

Example of Exponential Smoothing

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Common Nonlinear Trends

Parabolic

Exponential

Growth

Figure 3-5

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Linear Trend Equation

• b is similar to the slope. However, since it is calculated with the variability of the data in mind, its formulation is not as straight-forward as our usual notion of slope.

Yt = a + bt

0 1 2 3 4 5 t

Y

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Calculating a and b

b = n (ty) - t y

n t2 - ( t)2

a = y - b t

n

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Linear Trend Equation Example

t yW e e k t 2 S a l e s t y

1 1 1 5 0 1 5 02 4 1 5 7 3 1 43 9 1 6 2 4 8 64 1 6 1 6 6 6 6 45 2 5 1 7 7 8 8 5

t = 1 5 t 2 = 5 5 y = 8 1 2 t y = 2 4 9 9( t ) 2 = 2 2 5

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Linear Trend Calculation

y = 143.5 + 6.3t

a = 812 - 6.3(15)

5 =

b = 5 (2499) - 15(812)

5(55) - 225 =

12495-12180

275 -225 = 6.3

143.5

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Associative Forecasting

• Predictor variables - used to predict values of variable 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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Linear Model Seems Reasonable

0

10

20

30

40

50

0 5 10 15 20 25

X Y7 152 106 134 15

14 2515 2716 2412 2014 2720 4415 347 17

Computedrelationship

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Forecast Accuracy

• Error - difference between actual value and predicted value

• Mean absolute deviation (MAD)– Average absolute error

• Mean squared error (MSE)– Average of squared error

• Tracking signal– Ratio of cumulative error and MAD

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

MAD & MSE

MAD = Actual forecastn

MSE = Actual forecast)

-1

2n

(

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Tracking Signal

Tracking signal = (Actual-forecast)

MAD

Tracking signal = (Actual-forecast)Actual-forecast

n

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Exponential SmoothingT3-2

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Linear Trend EquationT3-3

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Trend Adjusted Exponential SmoothingT3-4

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Simple Linear RegressionT3-5