Your answer is partially correct. Try again The manager of a small health clinic

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Your answer is partially correct. Try again The manager of a small health clinic would like to use exponential smoothing to forecast demand for emergency services in the facility. However, she is not sure whether to use a high or low value of a. To make her decision, she would like to compare the forecast accuracy of a high and low a on historical data She has decided to use an a = 0.7 for the high value and a = 0.1 for the low value For both alpha values, enter exponential smoothing forecasts for weeks 2-6, and calculate the MAD for each alpha value. (Round answers to 1 decimal place, e.g. 15.2) Initatilize the computations using the naive method Deman (in patients serviced) Week 2 4 430 289 367 470 468 365 6 Exponential Smoothing Forecasts a = 0.10 Week Demand a = 0.70 430 289 * 367 4 470 468 365 X MAD 6 (a) which value of a do you think would be better to use? It would be better to use a =

Explanation / Answer

First, let's see the Exponential Smoothing Formula:

Ft+1 = Dt + (1)Ft

Here,

Dt = Actual Demand for period t

Ft = Forecast for period t

Ft+1 = Forecast forperiod t+1

Hence, we start calculating for week 2,

Since we do not know F1, we assume F2 as 430 in both cases

Now, we use the formula for week 3-6

Now, we calculate the rest of the values:

Week 3:

Low: F3= 0.1D2 + (10.1)F2 = 0.1(289) + 0.9(430) = 415.9

High: F3 = 0.7D2+ (10.7)F2 = 0.7(289) + 0.3(430) = 331.3

Week 4:

Low: F4= 0.1D3 + (10.1)F3 = 0.1(367) + 0.9(415.9) = 411

High: F4 = 0.7D3+ (10.7)F3 = 0.7(367) + 0.3(331.3) = 356.3

Week 5:

Low: F5= 0.1D4 + (10.1)F4 = 0.1(470) + 0.9(411) = 416.9

High: F5 = 0.7D4+ (10.7)F4 = 0.7(470) + 0.3(356.3) = 435.9

Week 6:

Low: F6= 0.1D5 + (10.1)F5 = 0.1(365) + 0.9(416.9) = 411.7

High: F6 = 0.7D5+ (10.7)F5 = 0.7(365) + 0.3(435.9) = 386.3

Now, let's calculate MAD:

MAD = (F2 - D2) + (F3 - D3) + (F4 - D4) + (F5 - D5) + (F6 - D6) / 5

MADlow = 430 - 289 + 415.9 - 367 + 411 - 470 + 416.9 - 468 + 411.7 - 365 / 5 = 126.5 / 5 = 25.3

MADhigh = 430 - 289 + 331.3 - 367 + 356.3 - 470 + 435.9 - 468 + 386.3 - 365 / 5 = |-19.2 / 5| = 3.8

Hence, the value of which is better to use = 0.7

Week Demand =0.1 =0.7 1 430 2 289 430 430 3 367 4 470 5 468 6 365 MAD

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