Question

National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a seven-month period were as follows: Month Sales (000)Units Feb. 14 Mar. 20 Apr. 11 May. 22 Jun. 21 Jul. 25 Aug. 16 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 .20, assuming a March forecast of 17(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 .70 for August, .10 for July, and .20 for June. (Round your answer to 2 decimal places.) Weighted average thousands

Answer 1

1. A linear trend equation.

Let’s assume that the linear trend equation for sales forecast is represented by the following equation

y = a + b *t…………………….. (1)

Where a is the y-intercept of the line and b is the slope of the line. Formula to calculate the a and b are following

Slop b = (n * Σty – Σt * Σy) / {n * Σ (t^2) - (Σt) ^2}

Intercept a = (Σy – b * Σt) / n

Where,

n is number of period = 7 (number of months)

Σy is the sum of total sales

Σt is the sum of months

Σty is the sum of total sales * months

Σt^2 is the sum of squares of months

	Months (t)	sales (y)	t*y	t^2
Feb	1	14	14	1
March	2	20	40	4
April	3	11	33	9
May	4	22	88	16
June	5	21	105	25
July	6	25	150	36
August	7	16	112	49
Sum	28	129	542	140
n =	7
Slop b = (n * Σty – Σt * Σy) / {n * Σ(t^2) - (Σt)^2} =	0.93
Intercept a = (Σy – b * Σt) / n =	14.71

Slop b = (n * Σty – Σt * Σy) / {n * Σ (t^2) - (Σt) ^2} = (7 * 542 – 28 * 129) / (7 * 140 – 28^2) = 0.93

And Intercept a = (Σy – b * Σt) / n = (129 – 0.93 * 28)/7 = 14.71

Now putting the value of a & b in equation (1), we get

Y = 14.71 + 0.93 * t

Sales for month 8 (September) using the trend projection (linear regression) method, where t = 8

Y = 14.71 + 0.93 * 8 = 22.15 thousands units

Therefore for September month’s sales forecast is 22.15 thousand

2. A five-month moving average.

Five-period moving average forecast for September = (Sale of April + sale of May + sale of June + sale of July + sale of August)/ 5

= (11+22 + 21 +25 +16)/5

= 95 /5 =19

Five-period Moving average = 19 thousands

3. Exponential smoothing with a smoothing constant equal to .20, assuming a March forecast of 17(000).

Formula for exponential smoothing is

F(t+1) = α Yt + (1 –α) Ft

Where F(t+1) is the forecast for the next period

Y is the actual sales for the present period

Ft is the forecast for present period

And α is the smoothing constant

Applying exponential smoothing with a smoothing constant of α = 0.2 we get:

F1 = 17 (March)

F2 (April) = 0.2Y1 + 0.8F1 = 0.2(20) + 0.8(17) = 17.6

F3 (May) = 0.2(11) + 0.8(17.6) = 16.28

F4 (June) = 0.2(22) + 0.8(16.28) = 17.424

F5 (July) = 0.2(21) + 0.8(17.424) = 18.14

F6 (August) = 0.2(25) + 0.8(18.14) = 19.51

F7 (Sept) = 0.2(16) + 0.8(19.51) = 18.81

Forecast for September = 18.81 thousands

4. The naive approach.

Naive approach; September sales volume = 16 thousands (August sales volume)

The forecast from naive approach is simply the value of the last actual data for next period.

5. A weighted average using .70 for August, .10 for July, and .20 for June.

Weighted moving average forecast for September = 16 *0.70 +25*0.10 + 21*0.20

= 17.90

Weighted average = 17.90 thousands