Chapter 3, Problem 4P

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

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

a. Naive

b. A four-period moving average

c. Exponential smoothing with α = .30; use 20 for week 2 forecast

Summary Introduction

To forecast: The number of requests for week 6 using naïve approach.

Introduction: Forecasting is the planning process that helps to predict the future aspects of the business or operation using present or past data. It uses certain assumptions based the knowledge and experience of the management.

Explanation of Solution

Given information:

Given that an electrical contractor had the following job requests during the last five weeks

Forecast the number of requests for week 6 using the naïve approach as shown below.

Given that the number of job requests for week 5 was 22, the likely job requests for week 6 would also be 22.

Summary Introduction

To forecast: The number of requests for week 6 using a four-period moving average.

Introduction: Forecasting is the planning process that helps to predict the future aspects of the business or operation using present or past data. It uses certain assumptions based the knowledge and experience of the management.

Explanation of Solution

Given information:

Given that an electrical contractor had the following job requests during the last five weeks

Forecast the number of requests for week6 using a four period moving average as shown below.

$\text{Forecast}\text{for}\text{week}\text{6=}\frac{jobsweek2+jobsweek3+jobsweek4+jobsweek5}{4}$

Substitute the values to obtain the forecast for week 6 as shown below.

$\begin{array}{c}\text{Forecast}\text{for}\text{week}\text{6=}\frac{22+18+21+22}{4}\\ =20.75\end{array}$

The forecast for week6 would be 20.75

Summary Introduction

To forecast: The number of requests for week 6 using a exponential smoothing.

Introduction: Forecasting is the planning process that helps to predict the future aspects of the business or operation using present or past data. It uses certain assumptions based the knowledge and experience of the management.

Explanation of Solution

Given information:

Given that an electrical contractor had the following job requests during the last five weeks

Forecast the number of requests for week6 using exponential smoothing as shown below.

Forecast the number of requests for week 6 using an exponential smoothing methodology, given that the forecast for week 2 was 20 and the actual job requests in week 2 was 22, and the exponential smoothing constant $\alpha =0.3$ as shown below.

• Given the week 2 forecast was 20, the actual number of jobs in week2 was 22 and the smoothing constant α was 0.3, prepare a forecast for week 3 as shown below.

$Week3forecast=ForecastedWeek2jobs+0.3\left(ActualWeek2jobs-ForecastedWeek2jobs\right)$ Substitute the values and obtain the forecast

$\begin{array}{c}Week3forecast=20+0.3\left(22-20\right)\\ =20.6\end{array}$

Therefore, forecasted week3 job requests 20.6.

• Given the week3 forecast was 20.6, the actual number of jobs was 18 and the smoothing constant α was 0.3, prepare a forecast for week4 as shown below.

$Week4forecast=ForecastedWeek3jobs+0.3\left(ActualWeek3jobs-ForecastedWeek3jobs\right)$ Substitute the values and obtain the forecast

$\begin{array}{c}Week4forecast=20.6+0.3\left(18-20.6\right)\\ =19.82\end{array}$

Therefore, forecasted week4 job requests 19.82.

• Given the week4 forecast was 19.82, the actual number of jobs was 21 and the smoothing constant α was 0.3, prepare a forecast for week5 as shown below.

$Week5forecast=ForecastedWeek4jobs+0.3\left(ActualWeek4jobs-ForecastedWeek4jobs\right)$ Substitute the values and obtain the forecast

$\begin{array}{c}Week5forecast=19.82+0.3\left(21-19.82\right)\\ =20.17\end{array}$

Therefore, forecasted week5 job requests 20.17.

• Given the week5 forecast was 20.17, the actual number of jobs was 22 and the smoothing constant α was 0.3, prepare a forecast for week 6 as shown below.

$Week6forecast=ForecastedWeek5jobs+0.3\left(ActualWeek5jobs-ForecastedWeek5jobs\right)$ Substitute the values and obtain the forecast

$\begin{array}{c}Week6forecast=20.17+0.3\left(22-20.17\right)\\ =20.72\end{array}$

Therefore, the forecast for week 6 would be 20.72.