homework solution weighted averages - exponential smoothing - trend cool-man air conditioners manual...
TRANSCRIPT
![Page 1: Homework Solution Weighted Averages - Exponential Smoothing - Trend Cool-Man Air Conditioners Manual ManualComputer-Based TM MGMT E-5070 Part B](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649f585503460f94c7d13a/html5/thumbnails/1.jpg)
Homework SolutionWeighted Averages - Exponential Smoothing - Trend
Cool-Man Air Conditioners
ManualManual
Computer-BasedComputer-Based
TM
MGMT E-5070
Part B
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Cool-Man Air ConditionersCool-Man Air Conditioners
REQUIREMENT:
1. What effect did the smoothing coefficient have on the forecast for Cool-Man air conditioners?
2. Which smoothing coefficient gives the most accurate forecast?
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Cool-Man Air Cool-Man Air ConditionersConditioners
Year Actual
Sales
α = 0.30 Forecast
Absolute
Deviation
1 450 410.0 40.0
2 495 422.0 73.0
3 518 443.9 74.1
4 563 466.1 96.9
5 584 495.2 88.8
6 ? 521.8 -
Total ( Σ ) 372.8
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Cool-Man Air Cool-Man Air ConditionersConditioners
Year Actual
Sales
α = 0.60 Forecast
Absolute
Deviation
1 450 410.0 40.0
2 495 434.0 61.0
3 518 470.6 47.4
4 563 499.0 64.0
5 584 537.4 46.6
6 ? 565.8 -
Total ( Σ ) 259.0
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Cool-Man Air Cool-Man Air ConditionersConditioners
Year Actual
Sales
α = 0.90 Forecast
Absolute
Deviation
1 450 410.0 40.0
2 495 446.0 49.0
3 518 490.1 27.9
4 563 515.2 47.8
5 584 558.2 25.8
6 ? 581.4 -
Total ( Σ ) 190.5
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Cool-Man Air ConditionersCool-Man Air Conditioners
MAD α = 0.30 = 372.8 / 5 = 74.56
MAD α = 0.60 = 259.0 / 5 = 51.80
MAD α = 0.90 = 190.5 / 5 = 38.10
Because it has the lowest MAD , the smoothingcoefficient α = 0.90 gives the most accurate
forecast.
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WE SELECT THE“FORECASTING”
MODULE
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WE WANT TO DEVELOP A NEWPROGRAM
FOR MOVING AVERAGES &EXPONENTIAL SMOOTHING,
WE SELECT “TIME SERIES ANALYSIS”
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THE DATA CREATION SCREEN
- Insert the number of past years
- We can label those months oryears any way we want
- We can also insert a title for theproblem
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“ The Data Table ”Appears
We insert the annual sales
We can also still change the periods titles, i.e. 1st Year,
1st Month, etc.
“Naïve Method” is the default method
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We first forecast via
Exponential smoothing( a = 0.30 )
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The 6th Year Forecast( 521.8 units )
MAD Forecast Error( 74.56 units )
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We now forecast via
Exponential smoothing( a = 0.60 )
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The 6th Year Forecast( 565.37 units )
The MAD Forecast Error( 51.8 units )
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We now forecast via
Exponential Smoothing( a = 0.90 )
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The 6th Year Forecast( 581.4 units )
MAD Forecast Error( 38.1 units )
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To forecast via
3-Year Moving Average
each period is weightedevenly ,( “1” )
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The 6th Year Forecast( 555 units )
The MAD Forecast Error( 67 units )
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We now forecast via
The Trend Projection Method
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The 6th Year Forecast( 622.8 units )
Y = 421.2 + (33.6)(6) = 622.8
The Regression Line
Y = 421.2 + 33.6X
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Cool-Man Air ConditionersCool-Man Air Conditioners
REQUIREMENT:
1. Would you use exponential smoothing with a smoothing coefficient of a = 0.30, a three (3) year moving average, or a trend to predict the sales of Cool-Man air conditioners?
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Cool-Man Air ConditionersCool-Man Air ConditionersTHREE YEAR MOVING AVERAGETHREE YEAR MOVING AVERAGE
YearYear Actual SalesActual Sales ForecastForecast Absolute Absolute DeviationDeviation
1 450 - -
2 495 - -
3 518 - -
4 563 487.7 75.3
5 584 525.3 58.7
6 ? 555.0 -
Total ( Σ ) 134.0
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Cool-Man Air ConditionersCool-Man Air ConditionersTIME SERIES FORECASTTIME SERIES FORECAST
YearYear Actual SalesActual Sales ForecastForecast Absolute Absolute DeviationDeviation
1 450450 454.8454.8 4.84.8
2 495495 488.4488.4 6.66.6
3 518518 522.0522.0 4.04.0
4 563563 555.6555.6 7.47.4
5 584584 589.2589.2 5.25.2
6 ?? 622.8622.8 --
Total ( Total ( ΣΣ ) ) 28.028.0
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Cool-Man Air ConditionersCool-Man Air Conditioners
MethodMethod MADMAD CalculationsCalculationsExponential
Smoothing ( a = .30 ) 74.56 372.8 / 5 = 74.56
Three-Year Moving Average 67.0 134 / 2 = 67.0
Regression( Trend Line ) 5.6 28 / 5 = 5.6
Regression ( trend line ) is the preferred method becauseof its low MAD ( mean absolute deviation )
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Forecasting with Excel QM 3
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Homework SolutionWeighted Averages - Exponential Smoothing - Trend
Cool-Man Air Conditioners
ManualManual
Computer-BasedComputer-Based
TM
Part B