1. TIM 270 Service Engineering and Management Lecture 6: Forecasting

2. Announcements   Homework 1 and 2 have been graded Collect from me when suitable   Homework 3 due next week   Project proposal due next week   Homework 4 posted online   $15 fee for Littlefield software – please bring check payable to ‘Responsive Learning Technologies’ (or cash and I will write check)

3. Forecasting Demand for Services

4. Forecasting Models   Subjective Models Delphi Methods   Causal Models Regression Models   Time Series Models Moving Averages Exponential Smoothing

5. Delphi Forecasting Question: In what future election will a woman become president of the united states for the first time? Year 1 st Round Positive Arguments 2 nd Round Negative Arguments 3 rd Round 2012 2016 2020 2024 2028 2032 2036 2040 2044 2048 2052 Never Total

6. N Period Moving Average Let : MA T = The N period moving average at the end of period T A T = Actual observation for period T Then: MA T = (A T + A T-1 + A T-2 + …..+ A T-N+1 )/N Characteristics: Need N observations to make a forecast Very inexpensive and easy to understand Gives equal weight to all observations Does not consider observations older than N periods

7. Moving Average Example Saturday Occupancy at a 100-room Hotel Three-period Saturday Period Occupancy Moving Average Forecast Aug. 1 1 79 8 2 84 15 3 8382 22 4 818382 29 5 98 8783 Sept. 5 6 1009387 12 793

8. Exponential Smoothing Let : S T = Smoothed value at end of period T A T = Actual observation for period T F T+1 = Forecast for period T+1 Feedback control nature of exponential smoothing New value (S T ) = Old value (S T-1 ) + [ observed error ] or :

9. Exponential Smoothing Hotel Example Saturday Hotel Occupancy ( =0.5) Actual Smoothed Forecast Period Occupancy Value Forecast Error Saturday t A t S t F t |A t - F t | Aug. 1 1 7979.00 8 2 8481.50 79 5 15 3 8382.25 82 1 22 4 8181.63 82 1 29 5 9889.81 8216 Sept. 5 6 10094.91 9010 Mean Absolute Deviation (MAD) = 6.6 Forecast Error (MAD) = ΣlA t – F t l/n

10. Exponential Smoothing Implied Weights Given Past Demand Substitute for If continued:

11. Exponential Smoothing Weight Distribution Relationship Between and N (exponential smoothing constant) : 0.05 0.1 0.2 0.3 0.4 0.5 0.67 N (periods in moving average) : 39 19 9 5.7 4 3 2

12. Saturday Hotel Occupancy Effect of Alpha ( =0.1 vs. =0.5) Actual Forecast

13. What explains changes over time?

14. Pull out the Influence of Seasonality and Trend

15. Estimate the relationship of price and promotion changes to volume

16. Once estimated separately, all these effects can be combined to predict volume. This is the model.

17. Exponential Smoothing With Trend Adjustment Commuter Airline Load Factor Week Actual load factor Smoothed value Smoothed trend Forecast Forecast error t A t S t T t F t | A t - F t | 1 31 31.00 0.00 2 40 35.50 1.35 31 9 3 43 39.93 2.27 37 6 4 52 47.10 3.74 42 10 5 49 49.92 3.47 51 2 6 64 58.69 5.06 53 11 7 58 60.88 4.20 64 6 8 68 66.54 4.63 65 3 MAD = 6.7

18. Exponential Smoothing with Seasonal Adjustment Ferry Passengers taken to a Resort Island Actual Smoothed IndexForecast Error Period t A t value S t I t F t | A t - F t| 2003 January 1 1651 ….. 0.837 ….. February 2 1305 ….. 0.662 ….. March 3 1617 ….. 0.820 ….. April 4 1721 ….. 0.873 ….. May 5 2015 ….. 1.022 ….. June 6 2297 ….. 1.165 ….. July 7 2606 ….. 1.322 ….. August 8 2687 ….. 1.363 ….. September 9 2292 ….. 1.162 ….. October 10 1981 ….. 1.005 ….. November 11 1696 ….. 0.860 ….. December 12 1794 1794.00 0.910 ….. 2004 January 13 1806 1866.74 0.876 - - February 14 1731 2016.35 0.7211236495 March 15 1733 2035.76 0.8291653 80

19. Statistical Analysis in R   Open-source software for advanced statistical analysis   Homework 4 is designed to introduce you to analysis using R

20. More sophisticated forecasting techniques   Nonlinear Regression   Data mining   Machine Learning   Simulation-based