Question

After plotting demand for four periods, an emergency room manager has concluded that a trend-adjusted exponential smoothing model is appropriate to predict future demand. The initial estimate of trend is based on the net change of 30 for the three periods from 1 to 4, for an average of +10 units.
Period Actual Period Actual
1 212
6 263
2 221
7 277
3 227
8 281
4 242
9 292
5 260
10

Use α=0.5 and β=0.1, and TAF of 250 for period 5. Obtain forecasts for periods 6 through 10.

Answer 1

Solution and Explanation:

Trend-Adjusted Forecast(TAF) = 250

The initial estimate of trend is based on the net change of 30 for the three periods from 1 to 4, for an average of +10 units

Given data

Period  Actual

1  212

2  221

3  227

4  242

5  260

6  263

7  277

8  281

9  292

α=.5 and β=.1

Initial Trend = $(242-212) / 3=$ = 30/3= 10

$\mathrm{Ft}+1=\alpha \mathrm{Dt}+(1-\underline{\alpha}) \mathrm{Ft}$

$\mathrm{Tt}+1=\beta(\mathrm{Ft}+1-\mathrm{F} t)+(1-\beta) \mathrm{Tt}$

For period 5 Dt= 260 (Period 5 actual demand)

Tt= 10

Ft= 250(TAF)

$\mathrm{Ft}+1=0.5 *(260)+(1-0.5) * 250=255$

$\mathrm{Tt}+1=\beta(\mathrm{Ft}+1-\mathrm{F} t)+(1-\beta) \mathrm{Tt}$

$=0.1(255-250)+(1-0.1) 10=0.5+9=9.5$

So TAF for period 6

$=0.1(255-250)+(1-0.1) 10=0.5+9=9.5$