Question

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

Month	Sales (000)Units
Feb.	18
Mar.	16
Apr.	15
May.	18
Jun.	20
Jul.	21
Aug.	23

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 .15, assuming a March forecast of 16(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 .65 for August, .15 for July, and .20 for June. (Round your answer to 2 decimal places.)

Weighted average ______thousands

Answer 1

1. 22.99

PERIOD (X)	DEMAND (Y)	X	Y	X * Y	X^2
1	18	1	18	18	1
2	16	2	16	32	4
3	15	3	15	45	9
4	18	4	18	72	16
5	20	5	20	100	25
6	21	6	21	126	36
7	23	7	23	161	49
SIGMA		28	131	554	140

INTERCEPT = (SIGMA(Y) * SIGMA(X^2) - SIGMA(X) * SIGMA(XY)) / (N * SIGMA(X^2) - SIGMA(X)^2)

INTERCEPT = (131 * 140) - (28 * 554) / ((7 * 140) - 28^2) = 14.43

SLOPE = ((N * SIGMA(XY)) - (SIGMA(X) * SIGMA(Y))) - (N * SIGMA(X^2) - SIGMA(X)^2)

SLOPE = ((7 * 554) - (28 * 131) / ((7 * 140) - 28^2) = 1.07

Y = A + B(x), WHERE A IS THE INTERCEPT, B IS THE SLOPE, x IS THE PERIOD = 14.43 + (1.07 * X)

FOR THE VALUE OF X = 8 FORECAST = 14.43 + (1.07 * 8) = 22.99

2. FORECAST = SIGMA(PREVIOUS N DEMANDS) / N

WHERE N = 5

FORECAST 8 = (15 + 18 + 20 + 21 + 23) / 5 = 19.4

3. FORECAST = FORECAST + (ALPHA * (ACTUAL DEMAND - FORECAST))

FORECAST 3 = 16 + (0.15 * (16 - 16) = 16

FORECAST 4 = 16 + (0.15 * (15 - 16) = 15.85

FORECAST 5 = 15.85 + (0.15 * (18 - 15.85) = 16.17

FORECAST 6 = 16.17 + (0.15 * (20 - 16.17) = 16.74

FORECAST 7 = 16.74 + (0.15 * (21 - 16.74) = 17.38

FORECAST 8 = 17.38 + (0.15 * (23 - 17.38) = 18.22

4. NAIVE FORECAST = DEMAND IN PREVIOUS PERIOD = 23

5. FORECAST = SIGMA(WEIGHT FOR PERIOD * DEMAND PER PERIOD) / SUM OF THE WEIGHTS

WHERE LARGEST WEIGHTS ARE MULTIPLIED BY THE MOST RECENT DEMANDS

FORECAST 8 = ((23 * 0.65) + (21 * 0.15) + (20 * 0.2)) / 1 = 22.1

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