Question

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

Month	Sales (000)Units
Feb.	17
Mar.	20
Apr.	14
May.	22
Jun.	21
Jul.	25
Aug.	29

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 15(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 .55 for August, .20 for July, and .25 for June. (Round your answer to 2 decimal places.)
  

Weighted average _ thousands

Answer 1

(1) A linear trend equation.

Month	t	y	ty	t^2
Feb	2	17	34	4
Mar	3	20	60	9
Apr	4	14	56	16
May	5	22	110	25
Jun	6	21	126	36
Jul	7	25	175	49
Aug	8	29	232	64
Sum	35	148	793	203

Y_t = a + bt

where

t = specified number of time periods from t=0

Y_t = forecast for period t

a=value of Y_t at t=0

b=slope of the line

b =

a =

n=number of periods

y=value of time series

7(793)- (35 148 5551-5180 371 7(203)-1225 1421 - 1225 196 1 .89 b- 148 (1.89)35148-(1.89)35 148 - 66.15 81.85 = 1.69 y(9) 1 1.694 1.89(9) 11.69 +17.01 28.7

So, y(9) = 28.7 thousands

2) A five-month moving average.

So, Moving Average = 22.2 thousands

(3) Exponential smoothing with a smoothing constant equal to .10, assuming a March forecast of 15(000).

where, F_t-1 = Forecasted of previous month

and A_t-1 = Actual of previous month

Month	t	Actual	Forecasted (Ft)
Feb	2	17
Mar	3	20	15
Apr	4	14	15+0.1*(20-15)= 15.5
May	5	22	15.5+0.1*(14-15.5)= 15.35
Jun	6	21	15.35+0.1*(22-15.35)= 16.015
Jul	7	25	16.015+0.1*(21-16.015)= 16.5135
Aug	8	29	16.5135+0.1*(25-16.5135)= 17.362
Sep	9		17.362*0.1*(29-17.362)= 20.21

Forecast = 20.21 thousands

(4) The naive approach.

In Naive approach, the last period's actuals are used as this period's forecasts.

Month	(000)Units (Actual)	Forecast (Actual in Past)
			Feb.	17
Mar.	20	17
Apr.	14	20
May.	22	14
Jun.	21	22
Jul.	25	21
Aug.	29	25
Sep		29

Naive approach :29 thousands

(5) A weighted average using .55 for August, .20 for July, and .25 for June.

Month	Sales
	(000)Units	wt
Feb.	17
Mar.	20
Apr.	14
May.	22
Jun.	21	0.25
Jul.	25	0.2
Aug.	29	0.55

F(t) = $\sum$ (weight*actual)

= (0.55*29)+(0.20*25)+(0.25*21)

= 5.25+5+15.95

= 26.2

Weighted average is 26.2 thousands