Question

National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a seven-month period were as follows: 

	Sales
Month	(000)Units
Feb.	19
Mar.	22
Apr.	8
May.	24
Jun.	19
Jul.	27
Aug .	22

b. Forecast September sales volume using each of the following: 

(1) A linear trend equation. 

(2) A five-month moving average. 

(3) Exponential smoothing with a smoothing constant equal to .25, assuming a March forecast of 17(000). 

(4) The naive approach. 

(5) A weighted average using .50 for August, .15 for July, and.35 for June. 

Answer 1

1) Calculation of the regression equation

Month Period(X) Demand(Y) XY X^2(Square of X)

february 1 19 19 1

March 2 22 44 4

April 3 8 24 9

May 4 24 96 16

June 5 19 95 25

July 6 27 162 36

August 7 22 154 49

X = 1+2+3+4+5+6+7 = 28

Y = 19+22+8+24+19+27+22 = 141

XY = 19+44+24+96+95+162+154= 594

X^2 = 1+4+9+16+25+36+49 = 140

n = Number of periods = 7

X-bar = X / n = 28/7 = 4

Y-bar = Y/n = 141/7 = 20.14

b = ( XY - nX-bar .Y-bar ) / ( X^2 - n. Square of X-bar)

= [594 - (7)(4)(20.14) ] / [140 - (7)(4)(4)]

= (594 - 563.92) / (140 - 112)

= 30.08 / 28

= 1.07

a = Y-bar - b(X-bar) = 20.14 - 1.07(4) = 20.14 - 4.28 = 15.86

Y = a + bx => Y = 15.86 + 1.07x

So the regression equation is Y = 15.86+ 1.07x

September is the period 8 So x=8

Using the regression equation ,the forecast for september = 15.86+ 1.07(8) = 15.86 + 8.56 = 24.42 thousands

2) A five months moving average method averages the actual value for the previous five months to generate the forecast for the next month. This can be calculated as the sum of the actual value for the previous five months / 5

So forecast for September = (8+24+19+27+22)/5

= 100/5

= 20.00 thousands

3) Using the exponential smoothing method the formula to calculate the forecast is as follows :

Ft = F(t-1) + [A(t-1) - F(t-1)]

Where Ft = forecast for period t

A(t-1)= actual value for period previous to t

F(t - 1)= forecast for period previous to t

= smoothing constant

So using the above formula with =0.25 and March forecast of 17 the forecast for April through September are

• For April = 17 + 0.25(22-17) = 17+1.25 =18.25
• For May = 18.25 + 0.25(8-18.25) = 18.25+(-2.56) = 18.25-2.56 = 15.69
• For June = 15.69 + 0.25(24-15.69)= 15.69 + 2.08 = 17.77
• For July = 17.77 + 0.25(19-17.77) = 17.77 + 0.31 = 18.08
• For August = 18.08 + 0.25(27-18.08) = 18.08 + 2.23 = 20.31
• For September = 20.31+ 0.25(22-20.31) = 20.31+0.42 = 20.73

So using the exponential smoothing method the forecast for September is 20.73 thousands

4) Using the naive approach the forecast for a period is equal to the actual value for the immediately previous period. So forecast for September = Actual sales in August = 22 thousands

5) using a three period weighted moving average method the formula to calculate the forecast is : Sum of the product of the actual value and their respective weights for the previous three periods. So using this formula the forecast for September = (0.35 x 19) + (0.15 x 27) + (0.50 x 22)

= 6.65 + 4.05 + 11

= 21.70 thousands