3-1 Forecasting

William J. Stevenson

Operations Management

8th edition

3-2 Forecasting

CHAPTER3

Forecasting

McGraw-Hill/IrwinOperations Management, Eighth Edition, by William J. Stevenson

Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.

3-3 Forecasting

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

3-4 Forecasting

New products and servicesProduct/service design

Schedules, MRP, workloadsOperations

IT/IS systems, servicesMIS

Pricing, promotion, strategyMarketing

Hiring/recruiting/trainingHuman Resources

Cash flow and fundingFinance

Cost/profit estimatesAccounting

Uses of ForecastsUses of Forecasts

3-5 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.

3-6 Forecasting

Elements of a Good ForecastElements of a Good Forecast

Timely

AccurateReliable

Meaningful

WrittenEas

y to use

3-7 Forecasting

Steps in the Forecasting ProcessSteps in the Forecasting Process

Step 1 Determine purpose of forecastStep 2 Establish a time horizon

Step 3 Select a forecasting techniqueStep 4 Gather and analyze data

Step 5 Prepare the forecastStep 6 Monitor the forecast

“The forecast”

3-8 Forecasting

Types of ForecastsTypes 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

3-9 Forecasting

Judgmental ForecastsJudgmental Forecasts

• Executive opinions• Sales force opinions• Consumer surveys• Outside opinion• Delphi method

• Opinions of managers and staff• Achieves a consensus forecast

3-10 Forecasting

Time Series ForecastsTime Series Forecasts

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

data• Cycle – wavelike variations of more than one

year’s duration• Irregular variations - caused by unusual

circumstances• Random variations - caused by chance

3-11 Forecasting

Forecast VariationsForecast Variations

Trend

Irregularvariation

Seasonal variations

908988

Figure 3.1

Cycles

3-12 Forecasting

Naive ForecastsNaive Forecasts

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

The forecast for any period equals the previous period’s actual value.

3-13 Forecasting

• 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

Naïve ForecastsNaïve Forecasts3-14 Forecasting

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

• Future = past• Seasonal variations

• F(t) = A(t-n)• Future = past season

• Data with trends• F(t) = A(t-1) + (A(t-1) – A(t-2))

• Future = past + difference from 2 time periods ago

Uses for Naïve ForecastsUses for Naïve Forecasts

3-15 Forecasting

Techniques for AveragingTechniques for Averaging

• Moving average

• Weighted moving average

• Exponential smoothing

3-16 Forecasting

Moving AveragesMoving Averages

• Moving average – A technique that averages a number of recent actual values, updated as new values become available.

• Weighted moving average – More recent values in a series are given more weight in computing the forecast.

MAn =n

Aii = 1∑n

3-17 Forecasting

Simple Moving AverageSimple Moving Average

MAn =n

Aii = 1∑n

35373941434547

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

Actual

MA3

MA5

3-18 Forecasting

Exponential SmoothingExponential 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 + α(At-1 - Ft-1)

3-19 Forecasting

Exponential SmoothingExponential Smoothing

• Weighted averaging method based on previous forecast plus a percentage of the forecast error

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

Ft = Ft-1 + α(At-1 - Ft-1)

3-20 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 3 Example 3 -- Exponential SmoothingExponential Smoothing

3-21 Forecasting

Picking a Smoothing ConstantPicking a Smoothing Constant

35

40

45

50

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

Period

Dem

and α = .1

α = .4

Actual

3-22 Forecasting

Common Nonlinear TrendsCommon Nonlinear Trends

Parabolic

Exponential

Growth

Figure 3.5

3-23 Forecasting

Linear Trend EquationLinear 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

3-24 Forecasting

Calculating a and bCalculating a and b

b = n (ty) - t y

n t2 - ( t)2

a = y - b tn

∑∑∑

∑∑

∑∑

3-25 Forecasting

Linear Trend Equation ExampleLinear Trend Equation Example

t yWeek t2 Sales ty

1 1 150 1502 4 157 3143 9 162 4864 16 166 6645 25 177 885

Σ t = 15 Σ t2 = 55 Σ y = 812 Σ ty = 2499(Σ t)2 = 225

3-26 Forecasting

Linear Trend CalculationLinear 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

3-27 Forecasting

Associative ForecastingAssociative 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

3-28 Forecasting

Linear Model Seems ReasonableLinear 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 152 106 134 1514 2515 2716 2412 2014 2720 4415 347 17

Computedrelationship

3-29 Forecasting

Forecast AccuracyForecast Accuracy

• Error - difference between actual value and predicted value

• Mean Absolute Deviation (MAD)• Average absolute error

• Mean Squared Error (MSE)• Average of squared error

• Mean Absolute Percent Error (MAPE)

• Average absolute percent error

3-30 Forecasting

MAD, MSE, and MAPEMAD, MSE, and MAPE

MAD =Actual forecast−∑

n

MSE =Actual forecast)

-1

2−∑

n

(

MAPE = Actual forecast−

n

/ Actual*100)∑(

3-31 Forecasting

Example 10Example 10

Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual)*1001 217 215 2 2 4 0.922 213 216 -3 3 9 1.413 216 215 1 1 1 0.464 210 214 -4 4 16 1.905 213 211 2 2 4 0.946 219 214 5 5 25 2.287 216 217 -1 1 1 0.468 212 216 -4 4 16 1.89

-2 22 76 10.26

MAD= 2.75MSE= 10.86

MAPE= 1.28

3-32 Forecasting

Controlling the ForecastControlling 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

3-33 Forecasting

Sources of Forecast errorsSources of Forecast errors

• Model may be inadequate• Irregular variations• Incorrect use of forecasting technique

3-34 Forecasting

Tracking SignalTracking Signal

Tracking signal = (Actual-forecast)MAD

∑

•Tracking signal–Ratio of cumulative error to MAD

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

3-35 Forecasting

Choosing a Forecasting TechniqueChoosing 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

3-36 Forecasting

Exponential SmoothingExponential Smoothing

3-37 Forecasting

Linear Trend EquationLinear Trend Equation3-38 Forecasting

Simple Linear RegressionSimple Linear Regression