National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a s
ID: 2808552 • Letter: N
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
Explanation / Answer
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 * ty – t * y) / {n * (t^2) - (t) ^2}
Intercept a = (y – b * t) / n
Where,
n is number of period = 7 (number of months)
y is the sum of total sales
t is the sum of months
ty is the sum of total sales * months
t^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 * ty – t * y) / {n * (t^2) - (t)^2} =
0.93
Intercept a = (y – b * t) / n =
14.71
Slop b = (n * ty – t * y) / {n * (t^2) - (t) ^2} = (7 * 542 – 28 * 129) / (7 * 140 – 28^2) = 0.93
And Intercept a = (y – b * t) / 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) = Yt + (1 –) 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 is the smoothing constant
Applying exponential smoothing with a smoothing constant of = 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
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 * ty – t * y) / {n * (t^2) - (t)^2} =
0.93
Intercept a = (y – b * t) / n =
14.71
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