Introduction to Forecasting

1. Introduction to Forecasting COB 291 Spring 2000

2. Forecasting • A forecast is an estimate of future demand • Forecasts contain error • Forecasts can be created by subjective means by estimates from informal sources • OR forecasts can be determined mathematically by using historical data • OR forecasts can be based on both subjective and mathematical techniques.

3. Qualitative Approaches • Executive committee consensus • Delphi method • Survey of sales force • Survey of customers • Historical analogy • Market research

4. Quantitative Approaches • Based on the assumption that the “forces” that generated the past demand will generate the future demand (i.e., history will tend to repeat itself) • Analysis of the past demand pattern provides a good basis for forecasting future demand

5. Quantitative Approaches • Simple Linear Regression • Relationship between one independent variable, x, and a dependent variable, y • Assumed to be linear • Form: Y=a+bX • Y=dependent variable • a=y-intercept • X=independent variable • b=slope of the regression line

6. Quantitative Methods - L.S. Regression Example Perfect Lawns, Inc., intends to use sales of lawn fertilizer to predict lawn mower sales. The store manager feels that there is probably a six-week lag between fertilizer sales and mower sales. The pertinent data are shown below. =>

7. Quantitative Methods - L.S. Regression Example Period Fertilizer Sales Number of Mowers Sold (Tons) (Six-Week Lag) 1 1.7 11 2 1.4 9 3 1.9 11 4 2.1 13 5 2.3 14 6 1.7 10 7 1.6 9 8 2 13 9 1.4 9 10 2.2 16 11 1.5 10 12 1.7 10 A) Use the least squares method to obtain a linear regression line for the data.

8. Quantitative Methods - L.S. Regression Example Period Fertilizer Sales Number of Mowers Sold (X) (Y) X2 Y2 (Tons) (X) (Six-Week Lag) (Y) 1 1.7 11 18.7 2.89 121 2 1.4 9 12.6 1.96 81 3 1.9 11 20.9 3.61 121 4 2.1 13 27.3 4.41 169 5 2.3 14 32.2 5.29 196 6 1.7 10 17.0 2.89 100 7 1.6 9 14.4 2.56 81 8 2 13 26.0 4.00 169 9 1.4 9 12.6 1.96 81 10 2.2 16 35.2 4.84 256 11 1.5 10 15.0 2.25 100 12 1.7 10 17.0 2.89 100

9. Quantitative Methods - L.S. Regression Example Period Fertilizer Sales Number of Mowers Sold (X) (Y) X2 Y2 (Tons) (X) (Six-Week Lag) (Y) 1 1.7 11 18.7 2.89 121 2 1.4 9 12.6 1.96 81 3 1.9 11 20.9 3.61 121 4 2.1 13 27.3 4.41 169 5 2.3 14 32.2 5.29 196 6 1.7 10 17.0 2.89 100 7 1.6 9 14.4 2.56 81 8 2 13 26.0 4.00 169 9 1.4 9 12.6 1.96 81 10 2.2 16 35.2 4.84 256 11 1.5 10 15.0 2.25 100 12 1.7 10 17.0 2.89 100 SUM 21.5 135 248.9 39.55 1575

10. Quantitative Methods - L.S. Regression Example

11. Quantitative Methods - L.S. Regression Example

12. Quantitative Methods - L.S. Regression Example

13. Quantitative Methods - L.S. Regression Example

14. Time Series Analysis • A time series is a set of numbers where the order or sequence of the numbers is important, e.g., historical demand • Analysis of the time series identifies patterns • Once the patterns are identified, they can be used to develop a forecast

15. Time Series Models • Simple moving average • Weighted moving average • Exponential smoothing (exponentially weighted moving average) • Exponential smoothing with random fluctuations • Exponential smoothing with random and trend • Exponential smoothing with random and seasonal component

16. Time Series Models Simple Moving Average Sample Data (3-period moving average) t Dt Ft Dt-Ft | Dt-Ft | Quarter Actual Demand Forecast Error Error 1 100 2 110 3 110 4 ? (100+110+110)/3=106.67

17. Time Series Models Simple Moving Average Sample Data (3-period moving average) t Dt Ft Dt-Ft | Dt-Ft | Quarter Actual Demand Forecast Error Error 1 100 2 110 3 110 4 80 (100+110+110)/3=106.67 80-106.67=-26.67 26.67

18. Time Series Models Simple Moving Average Sample Data (3-period moving average) t Dt Ft Dt-Ft | Dt-Ft | Quarter Actual Demand Forecast Error Error 1 100 2 110 3 110 4 80 (100+110+110)/3=106.67 80-106.67=-26.67 26.67 5 ? (110+110+80)/3 = 100.00

19. Time Series Models Simple Moving Average Sample Data (3-period moving average) t Dt Ft Dt-Ft | Dt-Ft | Quarter Actual Demand Forecast Error Error 1 100 2 110 3 110 4 80 (100+110+110)/3=106.67 80-106.67=-26.67 26.67 5 100 (110+110+80)/3 = 100.00 0 0

20. Time Series Models Exponential smoothing (exponentially weighted moving average)

21. Time Series Models Exponential smoothing (exponentially weighted moving average) Where t=time period St=smoothed average at end of period t Dt=actual demand in period t a=smoothing constant (0<a<1) Ft=forecast for period t

22. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha = 0.2) t Dt St Ft Dt-Ft Quarter Actual Demand Smoothed Average Forecast Error 0 100

23. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t Dt St Ft Dt-Ft Quarter Actual Demand Smoothed Average Forecast Error 0 100 1 ? 100

24. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t Dt St Ft Dt-Ft Quarter Actual Demand Smoothed Average Forecast Error 0 100 1 100 100

25. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t Dt St Ft Dt-Ft Quarter Actual Demand Smoothed Average Forecast Error 0 100 1 100 100 100-100=0

26. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t Dt St Ft Dt-Ft Quarter Actual Demand Smoothed Average Forecast Error 0 100 1 100 .2(100)+.8(100)=100 100 100-100=0

27. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t Dt St Ft Dt-Ft Quarter Actual Demand Smoothed Average Forecast Error 0 100 1 100 .2(100)+.8(100)=100 100 100-100=0 2 ? 100

28. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t Dt St Ft Dt-Ft Quarter Actual Demand Smoothed Average Forecast Error 0 100 1 100 .2(100)+.8(100)=100 100 100-100=0 2 110 100 110-100=10

29. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t Dt St Ft Dt-Ft Quarter Actual Demand Smoothed Average Forecast Error 0 100 1 100 .2(100)+.8(100)=100 100 100-100=0 2 110 .2(110)+.8(100)=102 100 110-100=10

30. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t Dt St Ft Dt-Ft Quarter Actual Demand Smoothed Average Forecast Error 0 100 1 100 .2(100)+.8(100)=100 100 100-100=0 2 110 .2(110)+.8(100)=102 100 110-100=10 3 ? 102

31. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t Dt St Ft Dt-Ft Quarter Actual Demand Smoothed Average Forecast Error 0 100 1 100 .2(100)+.8(100)=100 100 100-100=0 2 110 .2(110)+.8(100)=102 100 110-100=10 3 110 102 110-102=8 Make forecasts for periods 4-12.

32. Time Series Models Forecast Error 2 error measures: Bias tells direction (i.e., over or under forecast) Mean Absolute Deviation tells magnitude of forecast error

33. Characteristics of Good Forecasts • Stability • Responsiveness • Data Storage Requirements

34. BESM Example Cont’d

35. BESM - Expanded • The Basic Exponential Smoothing Model (BESM) is nothing more than a cumulative weighted average of all past demand (and the initial smoothed average). • Proof:

36. Demand Data with Trend

37. Time Series Models Exponential smoothing with trend enhancement

39. Demand Data with Trend and Seasonality

40. Basic Model Applicationbase smoothing constant, alpha, =.20

43. Trend-Enhanced Applicationbase smoothing constant, alpha, = .20 and trend smoothing constant, beta, = .30

46. Seasonal Indexes • seasonal index = actual demand / average demand • divide demand by its seasonal index to deseasonalize and • multiply demand by its seasonal index to seasonalize.

48. Full Model for Exponential Smoothing • NOTE: This model will allow you to forecast with trend only, with trend and seasonality, with seasonality only, or with no trend and no seasonality.

49. Full Model for Exponential Smoothing (cont’d)