Question

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

Month	Sales (000)Units
Feb.	20
Mar.	17
Apr.	13
May.	28
Jun.	17
Jul.	23
Aug.	26

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 .30, assuming a March forecast of 19(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 .60 for August, .10 for July, and .30 for June. (Round your answer to 2 decimal places.)

Weighted average

thousands

Answer 1

Ans

Given

Month	Sales (000) units
Feb	20
March	17
April	13
May	28
June	17
July	23
Aug	26

b.

(1)

The linear trend equation is as below:-

y = a + bt

y = Forecast for peroid t

t = Specified number of time period

a = Value of Ft at t = 0

b = Slope of the line

Now,

b = nƩ(ty) - ƩtƩy / nƩt² - (Ʃt)²

a = Ʃy - bƩt / n

t Month	t²	y Sales (000 units)	ty
2 (Feb)	4	20	40
3 (Mar)	9	17	51
4 (April)	16	13	52
5 (May)	25	28	140
6 (June)	36	17	102
7 (July)	49	23	161
8 (Aug)	64	26	182
Ʃt = 35	Ʃt² = 203	Ʃy = 144	Ʃty = 728
(Ʃt)² = 1225

n = number of month = 7

t = 9 (Sept)

Now

b = 7 * 728 - 35 * 144 / 7 * 203 - 1225

= 5096 - 5040 / 1421 - 1225

= 56 / 196

= 0.29

a = 144 - 0.29 * 35 / 7

= 144 - 10.15 / 7 = 133.85 / 7

= 19.12

Now

y = a + bt

= 19.12 + 0.29 * 9 = 19.12 + 2.61

= 21.73

Hence, as per linear trend equation

Sales Forecast for month of Sept = 21.73 (000 units)

(2)

A five-month moving average is calculated by averaging Feb to June (a) , then March to July (b) & April to Aug (c).

These data points are

a = 20 + 17 + 13 + 28 + 17 / 5

= 95 / 5

= 19

b = 17 + 13 + 28 + 17 + 23 / 5

= 98 / 5

= 19.6

c = 13 + 28 + 17 + 23 + 26 / 5

= 107 / 5

= 21.4

So the Sept Sales Forecast = 21.40 thousand units

(4)

The naive approach takes the last period's actuals as the forecast for the next month

As Aug sales was 26 thousand units (as per given table)

Hence,

Naive Forecast for Sept = 26.00 thousand units

(5)

The weighted average calculation Sep has weights of 1 for each month except Aug 0.60

				Weighted
		(000) units	Weighted	Average
Weight	Month	Sales	Sales	Forecast
1.00	Feb	20	20
1.00	March	17	17
1.00	April	13	13
1.00	May	28	28
1.00	June	17	17
1.00	July	23	23
0.60	Aug	26	15.60
	Sept			19.09

Hence,

Weighted Average of Sept = 19.09 Thousand Units