Forecasting Demand for Services

Learning Objectives Recommend the appropriate forecasting model for a given situation. Conduct a Delphi forecasting exercise. Describe the features of exponential smoothing. Conduct time series forecasting using exponential smoothing with trend and seasonal adjustments.

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

N Period Moving Average Let : MAT = The N period moving average at the end of period T AT = Actual observation for period T Then: MAT = (AT + AT-1 + AT-2 + …..+ AT-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

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 83 82 22 4 81 83 82 29 5 98 87 83 Sept. 5 6 100 93 87 12 7 93

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

Exponential Smoothing Hotel Example Saturday Hotel Occupancy ( =0.5) Actual Smoothed Forecast Period Occupancy Value Forecast Error Saturday t At St Ft |At - Ft| Aug. 1 1 79 79.00 8 2 84 81.50 79 5 15 3 83 82.25 82 1 22 4 81 81.63 82 1 29 5 98 89.81 82 16 Sept. 5 6 100 94.91 90 10 MAD = 6.6 Forecast Error (Mean Absolute Deviation) = ΣlAt – Ftl/n

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

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

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

Exponential Smoothing With Trend Adjustment Commuter Airline Load Factor Week Actual load factor Smoothed value Smoothed trend Forecast Forecast error t At St Tt Ft | At - Ft| 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

Exponential Smoothing with Seasonal Adjustment Ferry Passengers taken to a Resort Island Actual Smoothed Index Forecast Error Period t At value St It Ft | At - Ft| 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 0.721 1236 495 March 15 1733 2035.76 0.829 1653 80

Topics for Discussion What characteristics of service organizations make forecast accuracy important? For each of the three forecasting methods, what are the developmental costs and associated cost of forecast error? Suggest independent variables for a regression model to predict the sales volume for a proposed video rental store location. Why is the N-period moving-average still in common use if the simple exponential smoothing model is superior? What changes in α, β, γ would you recommend to improve the performance of the trendline seasonal adjustment forecast shown in Figure 11.4?

Interactive Exercise: Delphi Forecasting Question: In what future election will a woman become president of the united states? Year 1st Round Positive Arguments 2nd Round Negative Arguments 3rd Round 2008 2012 2016 2020 2024 2028 2032 2036 2040 2044 2048 2052 Never Total