National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a s

Question

National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a seven-month period were as follows: Month Sales (000)Units Feb. 16 Mar. 19 Apr. 10 May. 29 Jun. 17 Jul. 25 Aug. 25 b. Forecast September sales volume using each of the following: (1) A linear trend equation.(Round your intermediate calculations and final answer to 2 decimal places.) Yt thousands (2) A five-month moving average. (Round your answer to 2 decimal places.) Moving average thousands (3) Exponential smoothing with a smoothing constant equal to .10, assuming a March forecast of 18(000). (Round your intermediate forecast values and final answer to 2 decimal places) Forecast thousands (4) The naive approach. Naive approach thousands (5) A weighted average using .50 for August, .20 for July, and .30 for June. (Round your answer to 2 decimal places.) Weighted average thousands

Explanation / Answer

1 ) Let the linear trend equation is :

Y = a + b.t

Where,

Y ( dependent variable ) = Forecasted sales ( in ‘000)

T = serial no of month ( e.g 1 for February, 2 or March, 3 for April, 4 for May, 5 for June, 6 for July , 7 for august and 8 for September )

A,b = Constants

We place all the values of months and corresponding sales value as provided in excel sheet and apply the formula LINEST ( ) to obtain the values of a and b .

Accordingly, values of a and b are :

A= 13.571

B =1 .642

Therefore ,

Y = 13.571 + 1.642 .t

Therefore ,

Forecast for September ( t = 8 ) = 13.571 + 1.642 x 8 = 13.571 + 13.136 =26.707thousands ( 26.71 thousands)

2) Forecast for September using 5 month’s moving average

= Sum of monthly sales April through August ( in thousands )

= ( 10 + 29 + 17 + 25 + 25 ) / 5

= 21.2   thousands

3) Formula for exponential smoothing :

Ft = alpha x At-1 + ( 1 – alpha) x Ft-1 = 0.1 x At-1 + 0.9 x Ft-1

Where,

Ft, Ft-1 = forecasts for period t and t-1 respectively

At-1 = actual sales for period t-1

Alpha = exponential smoothing constant = 0.1

On basis of above formula and forecast for month of March being 18( ‘000) , forecast for September = 19.59 ( thousands )

4) As per Naïve approach:

Ft = At-1

Therefore ,

Forecast for September = Actual sales for August = 25 thousands

5) Forecast for August using weighted average

= 0.5 x 25 + 0.2 x 25 + 0.3 x 17 ( thousands )

=12.5 + 5 + 5.1 ( thousands)

= 22.6 ( thousands )

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