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 )

Homework SolutionWeighted Averages - Exponential Smoothing - Trend

Cool-Man Air Conditioners

ManualManual

Computer-BasedComputer-Based

TM

Part B