Introduction to Operations Management CHAPTER 1. What is Operations Management?
Operations Management Chapter 3
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Transcript of 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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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
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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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 quarter.
Common Features
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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
seCost
effe
ctiv
e
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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 Make the forecast
Step 6 Monitor the forecast
“The forecast”
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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
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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Judgmental Forecasts(Qualitative)
•Consumer surveys
•Delphi method
•Executive opinions
– Opinions of managers and staff
•Sales force.
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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(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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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
cycle
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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
The Forecast of Forecasts
• Naïve
• Simple Moving Average
• Weighted Moving Average
• Exponential Smoothing
• ES with Trend and Seasonality
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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
Naïve Forecast
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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
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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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 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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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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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 the line slope.
Yt = a + bt
0 1 2 3 4 5 t
Y
a
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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
Yes… Linear Regression!!
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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 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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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
Look on page 85
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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
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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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
3-35
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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.
3-37
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
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)