Operations Management Chapter 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

Chapter 3

Forecasting

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Forecasting

FORECAST:

• A statement about the future

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

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Forecasting

Forecast Uses

• Plan the system– Generally involves long-range plans related to:

• Types of products and services to offer• Facility and equipment levels• Facility location

• Plan the use of the system– Generally involves short- and medium-range plans related to:

• Inventory management• Workforce levels• Purchasing• Budgeting

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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 quarter.

Common Features

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Forecasting

Elements of a Good Forecast

Timely

AccurateReliable

Mea

ningfu

l

Written

Easy

to u

seCost

effe

ctiv

e

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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 Make the forecast

Step 6 Monitor the forecast

“The forecast”

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Forecasting

Types of Forecasts

• Judgmental - uses subjective inputs (qualitative)

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

• Associative models - uses explanatory variables to predict the future

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Forecasting

Judgmental Forecasts(Qualitative)

•Consumer surveys

•Delphi method

•Executive opinions

– Opinions of managers and staff

•Sales force.

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Forecasting

Time Series Forecasts(Quantitative)

• Trend - long-term movement in data• Seasonality - short-term regular variations in data• Irregular variations - caused by unusual

circumstances• Random variations - caused by chance

• CYCLE- wave like variations lasting more than one year

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Forecasting

Forecast Variations

Trend

Irregularvariation

Cycles

Seasonal variations

908988

Figure 3-1

cycle

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Forecasting

The Forecast of Forecasts

• Naïve

• Simple Moving Average

• Weighted Moving Average

• Exponential Smoothing

• ES with Trend and Seasonality

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Forecasting

• Simple to use

• Virtually no cost

• Data analysis is nonexistent

• Easily understandable

• Cannot provide high accuracy

Naïve Forecast

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Forecasting

NAÏVE METHOD

• No smoothing of data

Period 1 2 3 4 5 6 7 8 AverageDemand 74 86 88Forecast 98 90change 12 2

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Forecasting

Techniques for Averaging

• Moving average

• Weighted moving average

• Exponential smoothing

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Forecasting

Simple Moving Average• Smoothes out randomness by averaging positive and

negative random elements over several periods • n - number of periods (this example uses 4)

Period 1 2 3 4 5 6 7Demand 74 90 100 60 80 90Forecast 81 82.5 82.5

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Forecasting

Points to Know on Moving Averages

• Pro: Easy to compute and understand• Con: All data points were created equal….

…. Weighted Moving Average

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Forecasting

Weighted Moving Average• Similar to a moving average methods except that it assigns

more weight to the most recent values in a time series.• n -- number of periods

i – weight applied to period t-i+1

1 2 3Alpha

Period 1 2 3 4 5 6 7 8 AverageDemand 46 48 47 23 40Forecast 32.70 35.60

t

1ntii1it1t AF

0.6 0.3 0.1

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Forecasting

Exponential Smoothing• Simpler equation, equivalent to WMA – exponential smoothing parameter (0<

• )( 111 tttt FAFF 0.1

Period 1 2 3 4 5 6 7 8 AverageDemand 74 90 100 60Forecast 72 72.2 73.98

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Forecasting

FF22 == 37 + (0.30)(37-37) 37 + (0.30)(37-37)

= 37= 37

FF33 =37+ (0.30)(40-37)=37+ (0.30)(40-37)

= 37.9= 37.9

Exponential Smoothing (α=0.30)

PERIODPERIOD MONTHMONTHDEMANDDEMAND

11 JanJan 3737

22 FebFeb 4040

33 MarMar 4141

44 AprApr 3737

55 May May 4545

66 JunJun 5050

77 Jul Jul 4343

88 Aug Aug 4747

99 Sep Sep 5656

1010 OctOct 5252

1111 NovNov 5555

1212 Dec Dec 5454

)( 111 tttt FAFF

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Forecasting

FORECAST, FORECAST, FFtt + 1 + 1

PERIODPERIOD MONTHMONTH DEMANDDEMAND (( = 0.3) = 0.3) (( = 0.5) = 0.5)

11 JanJan 3737 –– ––22 FebFeb 4040 37.0037.00 37.0037.0033 MarMar 4141 37.9037.90 38.5038.5044 AprApr 3737 38.8338.83 39.7539.7555 May May 4545 38.2838.28 38.3738.3766 JunJun 5050 40.2940.29 41.6841.6877 Jul Jul 4343 43.2043.20 45.8445.8488 Aug Aug 4747 43.1443.14 44.4244.4299 Sep Sep 5656 44.3044.30 45.7145.711010 OctOct 5252 47.8147.81 50.8550.851111 NovNov 5555 49.0649.06 51.4251.421212 Dec Dec 5454 50.8450.84 53.2153.211313 JanJan –– 51.7951.79 53.6153.61

Exponential Smoothing (cont.)

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Forecasting

AFAFt t +1+1 = = FFt t +1+1 + + TTt t +1+1

wherewhereTT = an exponentially smoothed trend factor = an exponentially smoothed trend factor

TTt t +1+1 = = ((FFt t +1 +1 - - FFtt) + (1 - ) + (1 - ) ) TTtt

wherewhereTTtt = the last period trend factor= the last period trend factor

= a smoothing constant for trend= a smoothing constant for trend

Adjusted Exponential Smoothing

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Forecasting

Adjusted Exponential Smoothing (β=0.30)

PERIODPERIOD MONTHMONTHDEMANDDEMAND

11 JanJan 3737

22 FebFeb 4040

33 MarMar 4141

44 AprApr 3737

55 May May 4545

66 JunJun 5050

77 Jul Jul 4343

88 Aug Aug 4747

99 Sep Sep 5656

1010 OctOct 5252

1111 NovNov 5555

1212 Dec Dec 5454

TT33 = = ((FF3 3 - - FF22) + (1 - ) + (1 - ) ) TT22

= (0.30)(38.5 - 37.0) + (0.70)(0)= (0.30)(38.5 - 37.0) + (0.70)(0)

= 0.45= 0.45

AFAF33 = = FF33 + + TT3 3 = 38.5 + 0.45= 38.5 + 0.45

= 38.95= 38.95

TT1313 = = ((FF13 13 - - FF1212) + (1 - ) + (1 - ) ) TT1212

= (0.30)(53.61 - 53.21) + (0.70)(1.77)= (0.30)(53.61 - 53.21) + (0.70)(1.77)

= 1.36= 1.36

AFAF1313 = = FF1313 + + TT13 13 = 53.61 + 1.36 = 54.96= 53.61 + 1.36 = 54.96

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Forecasting

Adjusted Exponential Smoothing: ExampleFORECASTFORECAST TRENDTREND ADJUSTEDADJUSTED

PERIODPERIOD MONTHMONTH DEMANDDEMAND FFtt +1 +1 TTtt +1 +1 FORECAST AFFORECAST AFtt +1 +1

11 JanJan 3737 37.0037.00 –– ––22 FebFeb 4040 37.0037.00 0.000.00 37.0037.0033 MarMar 4141 38.5038.50 0.450.45 38.9538.9544 AprApr 3737 39.7539.75 0.690.69 40.4440.4455 May May 4545 38.3738.37 0.070.07 38.4438.4466 JunJun 5050 38.3738.37 0.070.07 38.4438.4477 Jul Jul 4343 45.8445.84 1.971.97 47.8247.8288 Aug Aug 4747 44.4244.42 0.950.95 45.3745.3799 Sep Sep 5656 45.7145.71 1.051.05 46.7646.761010 OctOct 5252 50.8550.85 2.282.28 58.1358.131111 NovNov 5555 51.4251.42 1.761.76 53.1953.191212 Dec Dec 5454 53.2153.21 1.771.77 54.9854.981313 JanJan –– 53.6153.61 1.361.36 54.9654.96

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Forecasting

Linear Trend Equation

• b is the line slope.

Yt = a + bt

0 1 2 3 4 5 t

Y

a

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Forecasting

Calculating a and b

b = n (ty) - t y

n t2 - ( t)2

a = y - b t

n

Yes… Linear Regression!!

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Forecasting

Linear Trend Equation Example

t y

Week t2 Sales ty

1 1 150 150

2 4 157 314

3 9 162 486

4 16 166 664

5 25 177 885

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

(t)2 = 225

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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

Look on page 85

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Forecasting

Disadvantage of simple linear regression

1-apply only to linear relationship with an independent variable.

2-one needs a considerable amount of data to establish the relationship ( at least 20).

3-all observations are weighted equally

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Forecasting

Forecast Accuracy

• Forecast error– difference between forecast and actual demand

– MAD• mean absolute deviation

– MAPD• mean absolute percent deviation

– Cumulative error

– Average error or bias

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Forecasting

Mean Absolute Deviation (MAD)

wherewhere tt = period number= period number

AAtt = demand in period = demand in period tt

FFtt = forecast for period = forecast for period tt

nn = total number of periods= total number of periods= absolute value= absolute value

AAtt - - FFtt nnMAD =MAD =

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Forecasting

MAD ExampleMAD Example

11 3737 37.0037.00 –– ––22 4040 37.0037.00 3.003.00 3.003.0033 4141 37.9037.90 3.103.10 3.103.1044 3737 38.8338.83 -1.83-1.83 1.831.8355 4545 38.2838.28 6.726.72 6.726.7266 5050 40.2940.29 9.699.69 9.699.6977 4343 43.2043.20 -0.20-0.20 0.200.2088 4747 43.1443.14 3.863.86 3.863.8699 5656 44.3044.30 11.7011.70 11.7011.70

1010 5252 47.8147.81 4.194.19 4.194.191111 5555 49.0649.06 5.945.94 5.945.941212 5454 50.8450.84 3.153.15 3.153.15

557557 49.3149.31 53.3953.39

PERIODPERIOD DEMAND, DEMAND, AAtt FFtt ( ( =0.3) =0.3) ((AAtt - - FFtt)) | |AAtt - - FFtt||

At - Ft nMAD =

=

= 4.85

53.3911

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Forecasting

Other Accuracy Measures

Mean absolute percent deviation (MAPD)Mean absolute percent deviation (MAPD)

MAPD =MAPD =|A|Att - F - Ftt||

AAtt

Cumulative errorCumulative error

E = E = eett

Average errorAverage error

(E )=(E )=eett

nn

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Forecasting

Comparison of Forecasts

FORECASTFORECAST MADMAD MAPDMAPD EE ((EE))

Exponential smoothing (Exponential smoothing (= 0.30)= 0.30) 4.854.85 9.6%9.6% 49.3149.31 4.484.48

Exponential smoothing (Exponential smoothing (= 0.50)= 0.50) 4.044.04 8.5%8.5% 33.2133.21 3.023.02

Adjusted exponential smoothingAdjusted exponential smoothing 3.813.81 7.5%7.5% 21.1421.14 1.921.92

((= 0.50, = 0.50, = 0.30)= 0.30)

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Forecasting

Forecast Control

• Tracking signal– monitors the forecast to see if it is biased high

or low

Tracking signal = =Tracking signal = =((AAtt - - FFtt))

MADMAD

EE

MADMAD

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Forecasting

Tracking Signal Values

11 3737 37.0037.00 –– –– ––22 4040 37.0037.00 3.003.00 3.003.00 3.003.0033 4141 37.9037.90 3.103.10 6.106.10 3.053.0544 3737 38.8338.83 -1.83-1.83 4.274.27 2.642.6455 4545 38.2838.28 6.726.72 10.9910.99 3.663.6666 5050 40.2940.29 9.699.69 20.6820.68 4.874.8777 4343 43.2043.20 -0.20-0.20 20.4820.48 4.094.0988 4747 43.1443.14 3.863.86 24.3424.34 4.064.0699 5656 44.3044.30 11.7011.70 36.0436.04 5.015.01

1010 5252 47.8147.81 4.194.19 40.2340.23 4.924.921111 5555 49.0649.06 5.945.94 46.1746.17 5.025.021212 5454 50.8450.84 3.153.15 49.3249.32 4.854.85

DEMANDDEMAND FORECAST,FORECAST, ERRORERROR EE = =PERIODPERIOD AAtt FFtt AAtt - - FFtt ((AAtt - - FFtt)) MADMAD

TS3 = = 2.006.103.05

Tracking signal for period 3

––1.001.002.002.001.621.623.003.004.254.255.015.016.006.007.197.198.188.189.209.2010.1710.17

TRACKINGTRACKINGSIGNALSIGNAL

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Forecasting

Sources of forecast errors

• The model may be inadequate.

• Irregular variation may be occur.

• The forecasting technique may be used incorrectly or the results misinterpreted.

• There are always random variation in the data.

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Forecasting

End Notes

• The two most important factors in choosing a forecasting technique:– Cost– Accuracy

• Keep it SIMPLE!

• =FORECAST(70,{23,34,12},{67,76,56}) (if you can…let the computer do it)

Operations Management Chapter 3

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