Question

In: Operations Management

A company has the following history of sales for an item. Month Sales Volume Jan. ...

A company has the following history of sales for an item.

Month Sales Volume

Jan. 120

Feb. 90

Mar. 100

Apr. 75

May 110

Jun. 50

Jul. 75

Aug. 130

Sep. 110

Oct. 90

Compute the monthly demand forecast for April through November using a 3-month moving average. Compute the monthly demand forecast for June through November using a 5-month moving average. Compute the monthly demand forecast for April through November using a 3-month weighted moving average. Use weights of 0.5, 0.33, and 0.17, with the heavier weights on the more recent months. Compute the mean absolute deviation (MAD) for June through October for each of the methods used. Which method would you use to forecast demand for November?

Expert Solution

3-month moving average: It is calculated by the average of the sales volumes of the previous 3 months

So, the 3-month moving average of April = (Sales Volume of Jan + Sales Volume of Feb + Sales Volume of March) / 3

The 3-month moving average from April to November is calculated below:

Month	Sales Volume	3-month moving average
Jan	120
Feb	90
Mar	100
Apr	75	103.33
May	110	88.33
Jun	50	95
Jul	75	78.33
Aug	130	78.33
Sep	110	85
Oct	90	105
Nov		110

5-month moving average: It is calculated by the average of the sales volumes of the previous 5 months

So, the 5-month moving average of June = (Sales Volume of Jan + Sales Volume of Feb + Sales Volume of March Sales Volume of April + Sales Volume of May) / 5

The 5-month moving average from June to November is calculated below:

Month	Sales Volume	5-month moving average
Jan	120
Feb	90
Mar	100
Apr	75
May	110
Jun	50	99
Jul	75	85
Aug	130	82
Sep	110	88
Oct	90	95
Nov		91

3-month weighted moving average: It is calculated by below formula

The 3-month weighted moving average of April = ((Sales Volume of Jan x Weight of Jan)+ (Sales Volume of Feb x Weight of Feb) + (Sales Volume of March x Weight of March) / (Total Weight)

The weights are 0.5, 0.33 and 0.17, and the highest weight shall be allocated to the most recent months.

So in the above formula, the Weight of March shall be 0.5, Weight of Feb shall be 0.33 and Weight of Jan shall be 0.17.

Also, Total weight = 0.5 + 0.33 + 0.17 = 1

The 3-month weighted moving average from April to November is calculated below:

Month	Sales Volume	3-month Weighted moving average
Jan	120
Feb	90
Mar	100
Apr	75	100.1
May	110	85.8
Jun	50	96.75
Jul	75	74.05
Aug	130	72.7
Sep	110	98.25
Oct	90	110.65
Nov		103.4

Mean Absolute Deviation:

Mean Absolute Deviation is calculated as the average value of absolute errors(Sales - Forecast) for all months.

So, for 3-month moving average:

Month	Sales Volume	3-month moving average	Error	Absolute Error
Jan	120
Feb	90
Mar	100
Apr	75	103.33	-28.33	28.33
May	110	88.33	21.67	21.67
Jun	50	95	-45.00	45.00
Jul	75	78.33	-3.33	3.33
Aug	130	78.33	51.67	51.67
Sep	110	85	25.00	25.00
Oct	90	105	-15.00	15.00
Nov		110

MAD = (28.33 + 21.67 + 45 + 3.33 + 51.67 + 25 + 15) / 7 = 190 / 7 = 27.17

For 5-month moving average:

Month	Sales Volume	5-month moving average	Error	Absolute Error
Jan	120
Feb	90
Mar	100
Apr	75
May	110
Jun	50	99	-49	49
Jul	75	85	-10	10
Aug	130	82	48	48
Sep	110	88	22	22
Oct	90	95	-5	5
Nov		91

MAD = ( 49 + 10 + 48 + 22 + 5 ) / 5 = 134 / 5 = 26.8

For 3-month weighted moving average:

Month	Sales Volume	3-month Weighted moving average	Error	Absolute Error
Jan	120
Feb	90
Mar	100
Apr	75	100.1	-25.1	25.1
May	110	85.8	24.2	24.2
Jun	50	96.75	-46.75	46.75
Jul	75	74.05	0.95	0.95
Aug	130	72.7	57.3	57.3
Sep	110	98.25	11.75	11.75
Oct	90	110.65	-20.65	20.65
Nov		103.4

MAD = ( 25.1 + 24.2 + 46.75 + 0.95 + 57.3 + 11.75 + 20.65) / 7 = 186.7 / 7 = 26.67

For forecasting the demand for November, I would use the 3-month weighted average method. This method considers the sales volume for 3 months and also gives more weightage to recent months. The 3-month moving average just considers the average of 3 months and doesn't give any weightage to months. The 5-month moving average considers a broader range ie 5 months, which may not be very accurate to forecast and also doesn't give any weightage to months.

Due to the above reasons, I would use the 3-month weighted average.

keosha answered 2 weeks ago

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