Question

1. The following time series represents the hourly customer volume for a small dining establishment.

Hour	Customer volume
7:00 a.m.	5
8:00 a.m.	5
9:00 a.m.	15
10:00 a.m.	20
11:00 a.m.	30
12:00 noon	50
1:00 p.m.	45
2:00 p.m.	30
3:00 p.m.	40
4:00 p.m.	20
5:00 p.m.	10

1. Use an exponential smoothing model with α = 0.50 to produce forecasts for this time series.  Assume that the forecast for the 7:00 a.m. time slot is 5 customers.  
2. What recommendations would you make regarding the use of exponential smoothing in forecasting this time series?

Answer 1

(a)

Calculations:

0.5 Customer volume Forecast Error Error 1 Alpha 2 Hour 3 7:00 a.m. 4 8:00 a.m. 5 9:00 a.m. 6 10:00 a.m. 7 11:00 a.m. 8 12:00 noon 9 1:00 p.m. 10 2:00 pm 11 3:00 p.m. 12 4:00 pm 13 5:00p.m. 14 =$B$1*B3+(1-$B$1)*C3 =B4-C4 =ABS(D4) =$B$1*B4+(1-$B$1)*C4 =B5-C5 ABS(D5) =$B$1*B5+(1-$B$1)*C5 =B6-C6 =ABS(D) =$B$1*B6+(1-$B$1)*C6 =B7-C7 =ABS(D7) =$B$1*B7+(1-$B$1)*C7 =B8-C8 =ABS(DS) =$B$1*B8+(1-$B$1)*C8 =B9-C9 =ABS(D9) =$B$1*B9+(1-$B$1)*C9 =B10-C10 =ABS(D10) =$B$1*B10+(1-$B$1)*C10 =B11-C11 =ABS(D11) =$B$1*B11+(1-$B$1)*C11 =B12-C12 =ABS(D12) =$B$1*B12+(1-$B$1)*C12 =B13-C13 =ABS(D13) MAD --> =AVERAGE(E4:E13)

Results:

0.5 Customer volume Forecast Error Error Alpha Hour 7:00 a.m. 8:00 a.m. 9:00 a.m. 10:00 a.m. 11:00 a.m. 12:00 noon 1:00p.m. 2:00 p.m. 3:00p.m. 4:00 p.m. 5:00 pm 50 5.00 5.00 10.00 15.00 22.50 36.25 40.63 35.31 37.66 28.83 0.00 10.00 10.00 15.00 27.50 8.75 -10.63 4.69 -17.66 -18.83 MAD --> 0.00 10.00 10.00 15.00 27.50 8.75 10.63 4.69 17.66 18.83 12.30

(b)

Customer volume Forecast 7.00 a.m. 8:00 a.m. 9:00 a.m. 10:00 a.m. 11:00 a.m. 12.00 noon 1:00p.m. 2:00 p.m. 3:00 p.m. 4:00 p.m. 5:00 p.m.

As we can see from the plots, the forecast is underestimating the demand up to 1:00 pm and then from 2:00 pm onwards, it starts overestimating.

This can be improved by selecting the proper values of alpha.

For example, we can select a higher value of alpha=0.9 and observe the results:

Customer volume Forecast 7:00 8:00 a.m. a.m. 9:00 10:00 11:00 12:00 1:00 2:00 3:00 a.m. a.m. a.m. noon p.m. p.m. p.m. 4:00 p.m. 5:00 p.m.

Customer volume Forecast Error Error Alpha Hour 7:00 a.m. 8:00 a.m. 9:00 a.m. 10:00 a.m. 11:00 a.m. 12:00 noon 1:00p.m. 2:00 pm 3:00p.m. 4:00 pm 5:00p.m. 5.00 5.00 14.00 19.40 28.94 47.89 45.29 31.53 39.15 21.92 0.00 10.00 6.00 10.60 21.06 -2.89 -15.29 8.47 -19.15 -11.92 MAD --> 0.00 10.00 6.00 10.60 21.06 2.89 15.29 8.47 19.15 11.92 10.54

Note that with higher values of alpha, the over- underestimating tendency reduces and the MAD also reduces. So, choose a higher value for alpha.