Chapter 3, Problem 2P

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

Month	Sales (000 units)
Feb.	19
Mar.	18
Apr.	15
May	20
Jun.	18
Jul.	22
Aug.	20

a. Plot the monthly data on a sheet of graph paper.

b. Forecast September sales volume using each of the following:

(1) The naive approach

(2) A five month moving average

(3) A weighted average using .60 for August, .30 for July, and .10 for June

(4) Exponential smoothing with a smoothing constant equal to .20, assuming a a March forecast of 19(000)

(5) A linear trend equation

c. Which method seems least appropriate Why? (Hint: Refer to your plot from part a.)

d. What does use of the term sales rather than demand presume?

Summary Introduction

To plot: The monthly data on a sheet of graph paper.

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:

The monthly sales data of RF tags for a seven-month period is given as shown below:

Plot the monthly data on a graph with Sales on the Y axis and months on the X-axis as shown below:

Summary Introduction

To determine: The forecast for September sales using the following approaches.

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

1. 1) Forecast the September sales using the naïve approach as shown below:

The forecast for the month of September as per the naïve approach, will be the same as the sales for the month of August, which is 20,000 units of sales.

1. 2) Calculate the forecast for the month of September using a five-month period moving average as shown below:

$Forecast=\frac{AprilSales+MaySales+JuneSales+JulySales+AugustSales}{5}$

Substitute in the above equation the values of $AprilSales=15,000units$, $MaySales=20,000units$, $JuneSales=18,000units$, $JulySales=22,000units$ and $AugustSales=20,000units$ to obtain the forecast as shown below:

$Forecast=\frac{15,000+20,000+18,000+22,000+20,000}{5}=\underset{\_}{19,000}$

1. 3) Calculate the forecast for September using the weighted average method, where the weights are 0.60 for August, 0.30 for July and 0.10 for June as shown below:

$0.60\times 20,000+0.30\times 22,000+0.10\times 18,000=\underset{\_}{20,400}.$

1. 4) To compute the forecast using an exponential smoothing constant α equal to 0.20 and assuming a March forecast of 19,000 units, first calculate the forecasts for the months of March, April, May, June, July and August as shown below:

Given that the March actual was 18,000 units and the forecast was 19,000 units, the error in the forecast was 1,000 units. Therefore, the forecast for the month of April would be as follows:

$\begin{array}{c}19,000+0.2\times \left(Marchactual-Marchforecast\right)=19,000+0.2\times \left(18,000-19,000\right)\\ =18,800.\end{array}$

Given that the April actual was 15,000 units and the forecast was 18,800 units, the error in the April forecast was 3,800 units. Therefore, the forecast for the month of May would be as follows:

$\begin{array}{c}18,800+0.2\times \left(Aprilactual-Aprilforecast\right)=18,800+0.2\times \left(15,000-18,800\right)\\ =18,040.\end{array}$

Given that the May actual was 20,000 units and the forecast was 18,040 units, the error in the May forecast was 1,960 units. Therefore, the forecast for the month of June would be as follows:

$\begin{array}{c}18,040+0.2\times \left(Mayactual-Mayforecast\right)=18,040+0.2\times \left(20,000-18,040\right)\\ =18,432.\end{array}$

Given that the June actual was 18,000 units and the forecast was 18,432 units, the error in the June forecast was 432 units. Therefore, the forecast for the month of July would be as follows:

$\begin{array}{c}18,432+0.2\times \left(Juneactual-Juneforecast\right)=18,432+0.2\times \left(18,000-18,432\right)\\ =18,345.\end{array}$

Given that the July actual was 22,000 units and the forecast was 18,345 units, the error in the July forecast was 3,655 units. Therefore, the forecast for the month of August would be as follows:

$\begin{array}{c}18,345+0.2\times \left(Julyactual-Julyforecast\right)=18,345+0.2\times \left(22,000-18,345\right)\\ =19,070.\end{array}$

Given that the August actual was 20,000 units and the forecast was 19,070 units, the error in the August forecast was 930 units. Therefore, the forecast for the month of September would be as follows:

$\begin{array}{c}19,070+0.2\times \left(Augustactual-Augustforecast\right)=19,070+0.2\times \left(20,000-19,070\right)\\ =19,256.\end{array}$

Therefore, the forecast for the month of September using exponential smoothing would be 19,256 units.

Summarize the above calculations in a table as shown below:

5) Calculate the forecast for September using linear trend equation:

A linear trend equation for the monthly sales using Microsoft Excelis graphically shown below:

Substitute the value of $x=8$ to obtain the value of y the forecast for September sales as shown below:

$\begin{array}{c}y=0.5\times 8+16.857\\ =20.857\end{array}$

The forecast sales in September works out to be 20,857 units.

Summary Introduction

To determine: The method which seems to least appropriate.

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

Among the five approaches calculated above, the linear trend approach seems to be the least appropriate. The equation $y=0.5\times x+16.857$ has a very minimal slope of 0.5 and the sales hover around an average of 19,000 units. The number of observations are low (only 7) to get a meaningful best line fit.

Summary Introduction

To determine: The use of the term sales rather than demand presume.

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

When the term sales is used for demand, it is presumed that there are no stock-outs. In other words, in every month the sales were the same as demand figures.