Question

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

Week: 1 2 3 4 5
Requests: 27 32 31 27 27

Predict the number of requests for week 6 using each of these methods:

a. Naïve.

Number of requests for week 6

b. Four-week moving average. (Round the final answer to 2 decimal places.)

Number of requests for week 6

c. Exponential smoothing with α = 0.40. (Round the intermediate calculations and the final answers to 2 decimal places.)


F3
F4
F5
F6

Answer 1

The predicted number of job requests for week 6 is 27 using the Naïve method, 29.25 using the Four-week Moving Average, and 27 using Exponential Smoothing with α = 0.40.

a. Naïve Method:

- The prediction for week 6 using the naïve method is the same as the number of requests in week 5.

- Therefore, the number of requests for week 6 using the naïve method is 27.

b. Four-week Moving Average:

- Calculate the four-week moving average: (27 + 32 + 31 + 27) / 4 = 29.25

- The number of requests for week 6 using the four-week moving average is 29.25.

c. Exponential Smoothing with α = 0.40:

- Use the exponential smoothing formula:

`\[ F_t = \alpha * D_t-1 + (1 - \alpha ) * F_t-1 \]`

-
`\( F_3 = 27 \)` (given)

-
`F_4`
`= 0.40 * 27 + 0.60 * 27 = 27`

-
`F_5`
`= 0.40 * 27 + 0.60 * 27 = 27`

-
`F_6`
`= 0.40 * 27 + 0.60 * 27 = 27`

- Round the intermediate calculations and the final answers to 2 decimal places.

- The number of requests for week 6 using exponential smoothing is 27.

Therefore, based on the three methods:

- Naïve Method: 27

- Four-week Moving Average: 29.25

- Exponential Smoothing (α = 0.40): 27