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 27 for the three periods from 1 to 4, for an average of +9.00 units.

Period	Actual	Period	Actual
1	206	6	263
2	233	7	278
3	228	8	288
4	233	9	293
5	253	10

Use α=.50 and β=.10, and TAF of 245 for period 5. Obtain forecasts for periods 6 through 10. (Round your intermediate calculations and final answers to 2 decimal places.)

t Period	TAFt
6
7
8
9
10

Answer 1

Answers are in BOLD

Year	Period, X	Number	Exponential smoothing, Ft	Trend, Tt	forecast including trend, FITt (TAFt)
2009	1	206
2010	2	233
2011	3	228
2012	4	233
2013	5	253		9.00	245.00
2014	6	263	249.00	9.40	258.40
2015	7	278	260.70	9.63	270.33
2016	8	288	274.17	10.01	284.18
2017	9	293	286.09	10.20	296.29
2018	10		294.65	10.04	304.69

• Alpha= 0.5, Beta= 0.1
• the formula to be used in Exponential smoothing, Ft is

F_t+1= FIT_t + alpha*(A_t+1 – FIT_t)

FIT_t is Forecast including trend, F_t+1 means Exponential forecast demand of t+1'th period, if you want to find out the Forecast of 3rd period = Forecast including trend of 2^nd period + alpha*(Actual demand of 3^rd period – Forecast including trend of 2^nd period)

remember FIT₅ = 245

• the formula to be used in Trend smoothing, Tt is

T_t+1= T_t + beta*(F_t+1 – FIT_t)

F_t+1 means Exponential forecast demand of t+1'th period, if you want to find out the Trend smoothing Forecast = forecast of 3rd period = Trend smoothing Forecast of 2^nd period + beta*(Exponential forecast of 3^rd period – Forecast including trend of 2^nd period)

remember Trend of 5th period is (Actual of 4- Actual of 1)/3= (233-206)/3= 9

• the formula to be used in Forecast including Trend, FIT is

FIT_t= T_t + F_t