# Forecasting Demand for Services - University of Texas at Austin

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 Saturday Aug. 1 8 15 22 29 Sept. 5 12 Period 1 2 3 4 5 6 7 Occupancy 79 84 83 81 98 100 Three-period Moving Average 82 83 87

93 Forecast 82 83 87 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 ) + or : ST ST-1 [ AT ST 1 ] ST AT (1 ) ST 1 FT 1 ST [ observed error ] Exponential Smoothing Hotel Example Saturday Hotel Occupancy ( =0.5) Saturday Aug. 1 8 15 22 29 Sept. 5

Period t 1 2 3 4 5 6 Actual Occupancy At 79 84 83 81 98 100 Smoothed Value St 79.00 81.50 82.25 81.63 89.81 94.91 Forecast Forecast Error Ft |At - Ft| 79 82 82 82

90 5 1 1 16 10 MAD = 6.6 Forecast Error (Mean Absolute Deviation) = lAlAt Ftl/n Exponential Smoothing Implied Weights Given Past Demand ST AT (1 ) ST 1 Substitute for ST 1 AT (1 )[AT 1 (1 ) ST 2 ] ST AT (1 )[AT 1 (1 ) ST 2 ] ST AT (1 ) AT 1 (1 ) 2 ST 2 If continued: ST AT (1 ) AT 1 (1 ) 2 AT 2 ..... (1 ) T 1 A1 (1 ) T S0 Exponential Smoothing Weight Distribution 0.3 0.3 Weight (1 ) 0.21 0.2 (1 ) 2 0147 .

(1 ) 3 0103 . (1 ) 4 0.072 0.1 (1 )5 0.050 0 0 1 2 3 4 5 Age of Observation (Period Old) Relationship Between and N (exponential smoothing constant) : 0.05 N (periods in moving average) : 39 0.1 0.2 19 9 0.3

5.7 0.4 4 0.5 3 0.67 2 Saturday Hotel Occupancy =0.1 vs. =0.5) 105 100 95 90 85 80 75 Actual Forecast ( 0.5) Forecast Period 6 5 4 3

2 1 ( 0.1) 0 Occupancy Effect of Alpha ( Exponential Smoothing With Trend Adjustment St ( At ) (1 )( St 1 Tt 1 ) Tt ( St St 1 ) (1 )Tt 1 Ft 1 St Tt Commuter Airline Load Factor ( 0.5, 0.3) Week t 1 2 3 4 5 6 7 8 Actual load factor At 31 40 43 52 49 64 58

68 Smoothed value St Smoothed trend Tt 31.00 35.50 39.93 47.10 49.92 58.69 60.88 66.54 0.00 1.35 2.27 3.74 3.47 5.06 4.20 4.63 Forecast Forecast error Ft | At - Ft| 31 37 42 51 53 64 65 9

6 10 2 11 6 3 MAD = 6.7 Exponential Smoothing with Seasonal Adjustment St ( At / I t Ft 1 ( St )( I t I t L) (1 ) St 1 L 1 ) At (1 ) I t St L Ferry Passengers taken to a Resort Island ( 0.2, 0.3) Actual Smoothed Index Period t At value St It 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 2016.35 495 March 15 1733 2035.76 0.829 Forecast Ft Error | At - Ft|

.. .. .. .. .. .. .. .. .. .. .. .. 0.721 1653 1236 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 , , 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 2008 2012 2016 2020 2024 2028 2032 2036 2040 2044 2048 2052 Never Total 1st Round Positive Arguments 2nd Round Negative Arguments 3rd Round

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