Chapter 17 Forecasting Demand for Services Learning Objectives Demand characteristics Overview of forecasting models Common demand pattern for services Linear regression to account for trend Seasonality indices for seasonal demand Combination of trend and seasonality 17-1

Demand Characteristics Time (a) Trend (d) Trend with seasonal pattern (c) Seasonal pattern (b) Cycle Demand Random movement

Forecasting Models Subjective Models Delphi Methods Causal Models Regression Models Time Series Models Moving Averages Exponential Smoothing 17-3

Using Linear Regression to account for trend b = a = y - b x where n = number of periods x = = mean of the x values y = = mean of the y values xy - nxy x2 - nx2 x n y y = a + bx where a = intercept b = slope of the line x = time period y = forecast for demand for period x

Least Squares Example x(PERIOD) y(DEMAND) xy x2 1 37 37 1 2 40 80 4 1 37 37 1 2 40 80 4 3 41 123 9 4 37 148 16 5 45 225 25 6 50 300 36 7 43 301 49 8 47 376 64 9 56 504 81 10 52 520 100 11 55 605 121 12 54 648 144 78 557 3867 650

Least Squares Example (cont.) y = = 46.42 b = = =1.72 a = y - bx = 46.42 - (1.72)(6.5) = 35.2 3867 - (12)(6.5)(46.42) 650 - 12(6.5)2 xy - nxy x2 - nx2 78 12 557

Linear trend line y = 35.2 + 1.72x Forecast for period 13 = 57.56 units 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 13 Actual Demand Period

Seasonal Adjustments Repetitive increase/ decrease in demand Use seasonal factor to adjust forecast Si = seasonality index of period i Ai(j) = demand in season i (in year j) Note: The method used here is different from the book Seasonal factor = Si =  Ai   Aij

Seasonal Adjustment (cont.) 2005 12.6 8.6 6.3 17.5 45.0 2006 14.1 10.3 7.5 18.2 50.1 2007 15.3 10.6 8.1 19.6 53.6 Total 42.0 29.5 21.9 55.3 148.7 DEMAND (1000’S PER QUARTER) YEAR 1 2 3 4 Total S1 = = = 0.28  A1   Aij 42.0 148.7 S2 = = = 0.20  A2 29.5 S4 = = = 0.37  A4 55.3 S3 = = = 0.15  A3 21.9

Forecast to account for both Trend and Seasonality Step 1: Calculate the seasonal index for each season. Step 2: Use linear regression to forecast the total demand for the following year to account for trend. (In the previous slide example, use the year as dependent variable, and yearly demand as independent variable) a = 40.97, b = 4.30 (Note: 2005/6/7 are years 1/2/3) F(2008) = 40.97 + 4.30(4) = 58.17 Step 3: Use the forecast total demand (obtained in Step 2) and multiply by the seasonal index to determine the forecast seasonal demand. SF1 = (S1) (F2008) = (0.28)(58.17) = 16.28 SF2 = (S2) (F2008) = (0.20)(58.17) = 11.63 SF3 = (S3) (F2008) = (0.15)(58.17) = 8.73 SF4 = (S4) (F2008) = (0.37)(58.17) = 21.53