Question

An electrical contractor’s records during the last five weeks indicate the number of jobs requests:

Week Sales

1 30

2 32

3 35

4 37

5 39

Predict the number of requests for week 6 using each of the following:

a. The naive approach.

b. A four-week moving average.

c. A weighted average using weights of 0.60 for week 5, 0.30 for week 4, and 0.10 for week 3.

d. Exponential smoothing with a smoothing constant 0.30. Use 20 for week 2 forecast.

Answer 1

Answer to question a :

Number of requests for week 6 using Naïve approach = Actual sales of week 5 = 39

Answer to question b :

Number of requests for week 6 using 4 week moving average

= ( Sales for week 2 + Sales for week 3 + Sales for week 4 + Sales for week 5 ) / 4

= ( 32 + 35 + 37 + 39 ) / 4

= 35.75

Answer to question c :

Weighted average forecast for week 6

= 0.60 x sales for week 5 + 0.30 x sales for week 4 + 0.10 x sales for week 3

= 0.60 x 39 + 0.30 x 37 + 0.10 x 35

= 23.4 + 11.1 + 3.5

= 38

Answer to question d :

Forecast for week t can be written as :

Ft = alpha x At-1 + ( 1 – alpha) x Ft-1 =   0.30 x At-1 + 0.70 x Ft-1

Where,

Ft, Ft-1 = Forecast for period t and t-1 respectively

At-1 = Sales for period t-1

Alpha = Exponential smoothing forecast = 0.3

Accordingly forecast vale for various periods for all weeks including week 6 as follows :

Week	sales	forecast
1	30
2	32	20.00
3	35	23.60
4	37	27.02
5	39	30.01
6		32.71

NUMBER OF REQUESTS FOR WEEK 6 = 32.71