homework solution weighted averages - exponential smoothing - trend cool-man air conditioners manual...
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Homework SolutionWeighted Averages - Exponential Smoothing - Trend
Cool-Man Air Conditioners
ManualManual
Computer-BasedComputer-Based
TM
MGMT E-5070
Part B
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?
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
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
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
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.
WE SELECT THE“FORECASTING”
MODULE
WE WANT TO DEVELOP A NEWPROGRAM
FOR MOVING AVERAGES &EXPONENTIAL SMOOTHING,
WE SELECT “TIME SERIES ANALYSIS”
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
“ 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
We first forecast via
Exponential smoothing( a = 0.30 )
The 6th Year Forecast( 521.8 units )
MAD Forecast Error( 74.56 units )
We now forecast via
Exponential smoothing( a = 0.60 )
The 6th Year Forecast( 565.37 units )
The MAD Forecast Error( 51.8 units )
We now forecast via
Exponential Smoothing( a = 0.90 )
The 6th Year Forecast( 581.4 units )
MAD Forecast Error( 38.1 units )
To forecast via
3-Year Moving Average
each period is weightedevenly ,( “1” )
The 6th Year Forecast( 555 units )
The MAD Forecast Error( 67 units )
We now forecast via
The Trend Projection Method
The 6th Year Forecast( 622.8 units )
Y = 421.2 + (33.6)(6) = 622.8
The Regression Line
Y = 421.2 + 33.6X
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?
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
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
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 )
Forecasting with Excel QM 3
Homework SolutionWeighted Averages - Exponential Smoothing - Trend
Cool-Man Air Conditioners
ManualManual
Computer-BasedComputer-Based
TM
Part B