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The monthly sales for Telco Batteries Inc. were as follows:

Problem # 1

The monthly sales for Telco Batteries Inc. were as follows:

                       Sales

Month            (000 units)

January            20

February          21

March              15

April                14

May                 13

June                 16

July                 17

August            18

September       20

October           20

November       21

December        23

  1. Plot the monthly sales data.

  2. Forecast coming January sales using each of the following:

    1. The naïve approach

    2. A 6-month moving average

    3. A 6-month weighted average using 0.1, 0.1, 0.1, 0.2, 0.2 and 0.3, with the heaviest weights applied to the most recent months.

  3. Calculate the mean absolute deviation (MAD) and the mean squared error (MSE) for each of the method above. Which is better among the three methods?

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Answer #1

a. Monthly sales data -

25 15 10 5 13 12 0 11 7 6 5 A 3 1 Month 10 D 20 Sales (000 units)

b. Below are the forecasts for all 3 methods -

Naive Six month Moving Average Six month Moving Average
Month Sales (000 units) Forecast Error Absolute error Error Square Forecast Error Absolute error Error Square Forecast Error Absolute error Error Square
Jan 20
Feb 21 20 1 1 1
March 15 21 -6 6 36
April 14 15 -1 1 1
May 13 14 -1 1 1
June 16 13 3 3 9
July 17 16 1 1 1 16.5 0.5 0.5 0.25 15.8 1.2 1.2 1.44
August 18 17 1 1 1 16 2 2 4 15.9 2.1 2.1 4.41
September 20 18 2 2 4 15.5 4.5 4.5 20.25 16.2 3.8 3.8 14.44
October 20 20 0 0 0 16.33 3.67 3.67 13.44 17.30 2.70 2.70 7.29
November 21 20 1 1 1 17.33 3.67 3.67 13.44 18.20 2.80 2.80 7.84
December 23 21 2 2 4 18.67 4.33 4.33 18.78 19.40 3.60 3.60 12.96
MAD = 1.73 MAD = 3.11 MAD = 2.70
MSE= 5.36 MSE= 11.69 MSE= 8.06

And below are the formulas that are used -

A C G H J Six month Moving Average Naive 1 Sales (000 units)Forecas Error Absolute error Absolute error 2 Month Error Square

A B K M Six month Moving Average (with weights) 1 2 Month Sales (000 units] Forecast Absolute error Error Square Error 20 3 J

c. Mean absolute deviation and Mean Square error has already been calculated above. Mean absolute deviation and Mean squared error is minimum for Naive forecast. Hence naive forecast gives better forecasts than other two methods.

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