Question

A textbook publishing company has compiled data on total annual sales of its business texts for the preceding nine years:

Year	1	2	3	4	5	6	7	8	9
Sales (000):	37.80	43.20	49.00	50.50	54.50	58.90	63.20	68.30	74.40

a. Using an appropriate model, forecast textbook sales for each of the next five years. (Round your intermediate calculations to 3 decimal places and final answers to 2 decimal places.)

Year	10	11	12	13	14
Forecast

b. Compute +/- 2s control limits for the control chart for forecast errors using just data from the original nine periods. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Control limits are 0 ±             

c. Suppose actual sales for the next five years turn out as follows:
       

Year	10	11	12	13	14
Sales (000):	77.30	82.90	88.60	93.90	98.00

Is the forecast performing adequately?

Yes

No

Answer 1

A) The forecast for the next five years.

This is done using the weighted moving average method. In this method, we take last 3 sales values and assign them a weight of 50%, 30%, and 20% respectively. The sum of products of the sales values with their weights gives us the next forecast.

For example, forecast for year 10

= (sales of year 9 x 0.5) + (sales of year 8 x 0.3) + (sales of year 7 x 0.2)

= (74.4 x 0.5) + (68.3 x 0.3) + (63.2 x 0.2) = 70.33.

The table below gives the values of the forecasts for year 10-14.

B.) Compute +/- 2s control limits for the control chart for forecast errors using just data from the original nine periods.

To compute the 2s limits, we need to find the mean and standard deviation of the data for 3 years. This can be done using MS Excel by using the function AVERAGE and STDEV.

The mean of the sales for 9 years is coming out to be 55.5333

The standard deviation of the sales for 9 years is coming out to be 11.8571

Now, calculating 2s limits,

Lower Limit = MEAN – (2 x STANDARD DEVIATION) = 55.5333 – (2 x 11.8571) = 31.82

Upper Limit = MEAN + (2 x STANDARD DEVIATION) = 55.5333 + (2 x 11.8571) = 79.25

C.) No, the forecast is not performing adequately. As we go from the year 10 to year 14, the gap between the forecast and actual becomes wider. This can happen due to some factor which has introduced in year 10 and is becoming stronger in subsequent years. The forecast made is low and actual sales are high. This can mean a quality initiative might be placed by the company (which is not accounted by the forecasting team) which is working well year on year thereby increasing the sales.