As you can see in the following table, demand for heart transplant surgery at Va

Question

As you can see in the following table, demand for heart transplant surgery at Vancouver General Hospital has increased steadily in the past few years: Year 1 2 3 4 5 6 Heart Transplant 45 50 52 56 58 ? The director of medical services predicted six years ago that demand in year 1 would be 41 surgeries. Use exponential smoothing, first with a smoothing constant of 0.6 and then with one of 0.9, to develop forecasts for years 2 through 6. Use a three-year moving average to forecast demand in years 4, 5, and 6. Use the trend-projection method to forecast demand in years 1 through 6. With MAD as the criterion, which of the four forecasting methods is best?

Explanation / Answer

Answer:

Exponential smoothing, = 0.6:

Year Demand Smoothing = 0.6 Deviation 1 45 41 4.0 2 50 41.0 + 0.6(45–41) = 43.4 6.6 3 52 43.4 + 0.6(50–43.4) = 47.4 4.6 4 56 47.4 + 0.6(52–47.4) = 50.2 5.8 5 58 50.2 + 0.6(56–50.2) = 53.7 4.3 6 ? 53.7 + 0.6(58–53.7) = 56.3 = 25.3 MAD = 5.06

Exponential smoothing, = 0.9: Exponential A

Exponential Absolute Year Demand Smoothing = 0.9 Deviation

1 45 41 4.0 2 50 41.0 + 0.9(45–41) = 44.6 5.4 3 52 44.6 + 0.9(50–44.6 ) = 49.5 2.5 4 56 49.5 + 0.9(52–49.5) = 51.8 4.2 5 58 51.8 + 0.9(56–51.8) = 55.6 2.4 6 ? 55.6 + 0.9(58–55.6) = 57.8 = 18.5 MAD = 3.7

B.3-year moving average: Three-Year Absolute Year Demand Moving Average Deviation 1 45 2 50 3 52 4 56 (45 + 50 + 52)/3 = 49 7 5 58 (50 + 52 + 56)/3 = 52.7 5.3 6 ? (52 + 56 + 58)/3 = 55.3 = 12.3 MAD = 6.2

(c) Trend projection: Absolute Year Demand Trend Projection Deviation 1 45 42.6 + 3.2 1 = 45.8 0.8 2 50 42.6 + 3.2 2 = 49.0 1.0 3 52 42.6 + 3.2 3 = 52.2 0.2 4 56 42.6 + 3.2 4 = 55.4 0.6 5 58 42.6 + 3.2 5 = 58.6 0.6 6 ? 42.6 + 3.2 6 = 61.8 = 3.2 MAD = 0.64 2 2 – – – Y a bX XY nXY b X nX a Y bX X Y XY X 2 1 45 45 1 2 50 100 4 3 52 156 9 4 56 224 16 5 58 290 25 Then: X = 15, Y = 261, XY = 815, X 2 = 55, X = 3, Y = 52.2 Therefore: 6 815 – 5 3 52.2 3.2 55 – 5 3 3 52.20 – 3.20 3 42.6 42.6 3.2 6 61.8 b a Y

(d) Comparing the results of the forecasting methodologies for parts (a), (b), and (c). Forecast Methodology MAD Exponential smoothing, = 0.6 5.06 Exponential smoothing, = 0.9 3.7 3-year moving average 6.2 Trend projection 0.64 Based on a mean absolute deviation criterion, the trend projection is to be preferred over the exponential smoothing with = 0.6, exponential smoothing with = 0.9, or the 3-year moving average forecast methodologies.

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