Question

The Oceanside Hotel is adjacent to City Coliseum, a 24,000-seat arena that is home to the city’s professional basketball and ice hockey teams and that hosts a variety of concerts, trade shows, and conventions throughout the year. The hotel has experienced the following occupancy rates for the nine years since the coliseum opened:

YEAR	OCCUPANCY RATE
1	75%
2	70
3	72
4	77
5	83
6	81
7	86
8	91
9	87

Compute an exponential smoothing forecast with α = .20, an adjusted exponential smoothing forecast with α = .20 and β = .20. Use excel and show formulas in excel.

Answer 1

Answer a: Exponential forecast, alpha= 0.2

Year	Occupancy rate	Exponential forecast, alpha 0.2
1	75	75.0
2	70	75.0
3	72	74.0
4	77	73.6
5	83	74.3
6	81	76.0
7	86	77.0
8	91	78.8
9	87	81.3

• the formula to be used in Simple Exponential smoothing is

F_t+1= alpha*A_t + (1-alpha) F_t

A_t means Actual demand of t'th period, if you want to find out the Forecast through exponential smoothing= forecast of 3rd period = alpha*actual demand of 2nd period +(1-alpha) *forecast demand of 2nd period

• remember forecast of 1st period is 75, alpha= 0.2
• Forecast of 3rd period= alpha*A₂ + (1-alpha) F₂ = 0.2*70+ 0.8*75 = 74

Answer b: Trend adjusted exponential forecast, alpha= 0.2, beta= 0.2

Month, t	Demand, At	Exponential smoothing, Ft	Trend, Tt	forecast including trend, FITt
1	75		0.00	75.00
2	70	75.00	0.00	75.00
3	72	74.00	-0.20	73.80
4	77	73.44	-0.27	73.17
5	83	73.93	-0.12	73.82
6	81	75.65	0.25	75.90
7	86	76.92	0.45	77.37
8	91	79.10	0.80	79.90
9	87	82.12	1.24	83.36

• Alpha= 0.2, Beta= 0.2
• 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 = 75

• 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 1st period is 0

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

FIT_t= T_t + F_t