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Refer to Solved Problem 4.1. Using smoothing constants of .6 and .9, develop forecasts for the sales of VW Beetles. What effect did the smoothing constant have on the forecast? Use MAD to determine which of the three smoothing constants (.3, .6, or .9) gives the most accurate forecast.

Problem 4.1

The following gives the number of pints of type B blood used at Woodlawn Hospital in the past 6 weeks:

a) Forecast the demand for the week of October 12 using a 3-week moving average.

b) Use a 3-week weighted moving average, with weights of .1, .3, and .6, using .6 for the most recent week. Forecast demand for the week of October 12.

c) Compute the forecast for the week of October 12 using exponential smoothing with a forecast for August 31 of 360 and a = .2.

 
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As you can see in the following table, demand for heart transplant surgery at Washington General Hospital has increased steadily in the past few years:

The director of medical services predicted 6 years ago that demand in year 1 would be 41 surgeries.

a) Use exponential smoothing, first with a smoothing constant of .6 and then with one of .9, to develop forecasts for years 2 through 6.

b) Use a 3-year moving average to forecast demand in years 4, 5, and 6.

c) Use the trend-projection method to forecast demand in years 1 through 6.

d) With MAD as the criterion, which of the four forecasting methods is best?

 
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Refer to the trend-adjusted exponential smoothing illustration in Example 7. Using  = .2 and  = .4, we forecast sales for 9 months, showing the detailed calculations for months 2 and 3. In Solved Problem 4.2, we continued the process for month 4.

In this problem, show your calculations for months 5 and 6 for t tand t.

Problem 4.2

a) Plot the above data on a graph. Do you observe any trend, cycles, or random variations?

b) Starting in year 4 and going to year 12, forecast demand using a 3-year moving average. Plot your forecast on the same graph as the original data.

c) Starting in year 4 and going to year 12, forecast demand using a 3-year moving average with weights of .1, .3, and .6, using .6 for the most recent year. Plot this forecast on the same graph.

d) As you compare forecasts with the original data, which seems to give the better results?

 
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Refer to Problem 4.21. Complete the trendadjusted exponential-smoothing forecast computations for periods 7, 8, and 9. Confirm that your numbers for tt , and t match those in Table 4.2.

Problem 4.21

Refer to the trend-adjusted exponential smoothing illustration in Example 7. Using  = .2 and  = .4, we forecast sales for 9 months, showing the detailed calculations for months 2 and 3. In Solved Problem 4.2, we continued the process for month 4.

In this problem, show your calculations for months 5 and 6 for t tand t.

Problem 4.2

a) Plot the above data on a graph. Do you observe any trend, cycles, or random variations?

b) Starting in year 4 and going to year 12, forecast demand using a 3-year moving average. Plot your forecast on the same graph as the original data.

c) Starting in year 4 and going to year 12, forecast demand using a 3-year moving average with weights of .1, .3, and .6, using .6 for the most recent year. Plot this forecast on the same graph.

d) As you compare forecasts with the original data, which seems to give the better results?

Example 7

Table 4.2

 
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