Chapter 3, Problem 21P

Two different forecasting techniques (F1 and F2) were used to forecast demand fern cases of bottled water Actual demand and the two sets of forecasts are as follows.

a. Compute MAD for each set of forecast, Given your results, which forecast appears to be more accurate? Explain.

b. Compute the MSE for each set of forecasts. Given your results, which forecast appears to be more accurate?

c. In practice, either MAD or MSE would be employed to compute forecast errors. What factors might lead a manager to choose one rather than the other?

d. Compute MAPE for each data set. Which forecast appears to be more accurate?

Summary Introduction

To compute: Mean Average Deviation (MAD) for each set of forecasts.

Introduction: Mean Absolute Deviation (MAD) is the average distance between the data values and the mean. Mean Squared Error (MSE) is the average of the squares of the deviation and error.

Explanation of Solution

Given information:

Given the following data on demand and forecasts during two periods, decide which method gives more accurate results, by computing the Mean absolute deviation (MAD) for both the methods as shown below.

Calculate the Mean absolute deviation (MAD) as shown below for the two methods:

Compute the Mean absolute deviation (MAD) for the forecasting method F₁ as shown below

$MAD=\frac{{\displaystyle \sum \left|error\right|}}{n}$

Substitute the value of ${\displaystyle \sum \left|error\right|}=32$ and the value of $n=8$ to obtain the Mean absolute deviation (MAD)

$MAD=\frac{32}{8}=\underset{\_}{4}$

Compute the Mean absolute deviation (MAD) for the forecasting method F₂ as shown below

$MAD=\frac{{\displaystyle \sum \left|error\right|}}{n}$

Substitute the value of ${\displaystyle \sum \left|error\right|}=24$ and the value of $n=8$ to obtain the Mean absolute deviation (MAD)

$MAD=\frac{24}{8}=\underset{\_}{3}$

Between the two methods, the second forecasting method F₂ has lower MAD and hence more accurate compared to the first method F₁

Summary Introduction

To compute: Mean Squared Error (MSE) for each set of forecasts.

Introduction: Mean Squared Error (MSE) is the average of the squares of the deviation and error.

Explanation of Solution

Given information:

Given the following data on demand and forecasts during two periods, decide which method gives more accurate results, by computing the Mean squared error (MSE) for both the methods as shown below.

Calculate the Mean squared error (MSE) as shown below for the two methods

Compute the Mean squared error (MSE) for the forecasting method F₁ as shown below

$MSE=\frac{{\displaystyle \sum \left|erro{r}^2\right|}}{n-1}$

Substitute the value of ${\displaystyle \sum \left|erro{r}^2\right|}=176$ and the value of $n=8$ to obtain the Mean squared error (MSE)

$MSE=\frac{176}{8-1}=\underset{\_}{25.14}$

Compute the Mean squared error (MSE) for the forecasting method F₂ as shown below

$MSE=\frac{{\displaystyle \sum \left|erro{r}^2\right|}}{n-1}$

Substitute the value of ${\displaystyle \sum \left|erro{r}^2\right|}=106$ and the value of $n=8$ to obtain the Mean squared error (MSE)

$MSE=\frac{106}{8-1}=\underset{\_}{15.14}$

Between the two methods, the second forecasting method F₂ has lower MSE and hence more accurate compared to the first method F₁.

Summary Introduction

To determine: The factors that lead managers to choose any approach over another.

Introduction: Mean Squared Error (MSE) is the average of the squares of the deviation and error.

Explanation of Solution

MSE magnifies the error by squaring the difference. Therefore, MSE is able to quickly point out wrong forecasting models. However, both MAD and MSE are equally accurate in defining the errors in forecasting. It depends on the individual analyst to choose a particular method for decision making.

Summary Introduction

To compute: Mean Absolute Percentage Error (MAPE) for each set of forecasts.

Explanation of Solution

Compute the Mean Absolute Percentage Error (MAPE) as shown below.

The absolute percentage error is computed by dividing the absolute error value by the actual demand figures.

The Mean Absolute Percentage Error (MAPE) is computed by adding the absolute percentage errors for the eight periods and dividing the sum by eight.

The calculations are shown above in the table derived, using Microsoft Excel.

The second forecasting method F₂ has a lower MAPE of 4.11% compared to the first forecasting method F₁ which gives a MAPE value of 5.34%. Therefore, the second method is more accurate.