1. Introduction to Forecasting IDS 605 Spring 1999

2. Forecasting 4 A forecast is an estimate of future demand

3. Forecasting 4 A forecast is an estimate of future demand 4 Forecasts contain error

4. Forecasting 4 A forecast is an estimate of future demand 4 Forecasts contain error 4 Forecasts can be created by subjective means through estimates from informal sources

5. Forecasting 4 A forecast is an estimate of future demand 4 Forecasts contain error 4 Forecasts can be created by subjective means by estimates from informal sources 4 OR forecasts can be determined mathematically by using historical data

6. Forecasting 4 A forecast is an estimate of future demand 4 Forecasts contain error 4 Forecasts can be created by subjective means by estimates from informal sources 4 OR forecasts can be determined mathematically by using historical data 4 OR forecasts can be based on both subjective and mathematical techniques.

7. Forecast Ranges 4 Long Range (i.e., greater than one year) –production capacity –automation needs

8. Forecast Ranges 4 Long Range (i.e., greater than one year) –production capacity –automation needs 4 Medium Range (i.e., several months) –labor needs –capacity allocation in factory

9. Forecast Ranges 4 Long Range (i.e., greater than one year) –production capacity –automation needs 4 Medium Range (i.e., several months) –labor needs –capacity allocation in factory 4 Short Range (i.e., days or weeks) –scheduling production for next week –raw material needed to be delivered

10. Qualitative Approaches 4 Based on judgments about causal factors that underlie the demand of particular products or services 4 Do not require a demand history for the product/service, therefore are useful for new products products/services

11. Qualitative Approaches 4 Executive committee consensus

12. Qualitative Approaches 4 Executive committee consensus 4 Delphi method

13. Qualitative Approaches 4 Executive committee consensus 4 Delphi method 4 Survey of sales force

14. Qualitative Approaches 4 Executive committee consensus 4 Delphi method 4 Survey of sales force 4 Survey of customers

15. Qualitative Approaches 4 Executive committee consensus 4 Delphi method 4 Survey of sales force 4 Survey of customers 4 Historical analogy

16. Qualitative Approaches 4 Executive committee consensus 4 Delphi method 4 Survey of sales force 4 Survey of customers 4 Historical analogy 4 Market research

17. Quantitative Approaches 4 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) 4 Analysis of the past demand pattern provides a good basis for forecasting future demand

18. Quantitative Approaches 4 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

19. 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. =>

20. Quantitative Methods - L.S. Regression Example PeriodFertilizer SalesNumber of Mowers Sold (Tons) (Six-Week Lag) 11.711 21.49 31.911 42.113 52.314 61.710 71.69 8213 91.49 102.216 111.510 121.710 A) Use the least squares method to obtain a linear regression line for the data.

21. Quantitative Methods - L.S. Regression Example PeriodFertilizer SalesNumber of Mowers Sold (X) (Y) X 2 Y 2 (Tons) (X) (Six-Week Lag) (Y) 11.711 18.7 2.89 121 21.49 12.6 1.96 81 31.911 20.9 3.61 121 42.113 27.3 4.41 169 52.314 32.2 5.29 196 61.710 17.0 2.89 100 71.69 14.4 2.56 81 8213 26.0 4.00 169 91.49 12.6 1.96 81 102.216 35.2 4.84 256 111.510 15.0 2.25 100 121.710 17.0 2.89 100

22. Quantitative Methods - L.S. Regression Example PeriodFertilizer SalesNumber of Mowers Sold (X) (Y) X 2 Y 2 (Tons) (X) (Six-Week Lag) (Y) 11.711 18.7 2.89 121 21.49 12.6 1.96 81 31.911 20.9 3.61 121 42.113 27.3 4.41 169 52.314 32.2 5.29 196 61.710 17.0 2.89 100 71.69 14.4 2.56 81 8213 26.0 4.00 169 91.49 12.6 1.96 81 102.216 35.2 4.84 256 111.510 15.0 2.25 100 121.710 17.0 2.89 100 SUM 21.5 135 248.9 39.55 1575

23. Quantitative Methods - L.S. Regression Example

27. Time Series Analysis 4 A time series is a set of numbers where the order or sequence of the numbers is important, e.g., historical demand 4 Analysis of the time series identifies patterns 4 Once the patterns are identified, they can be used to develop a forecast

28. Time Series Models 4 Simple moving average 4 Weighted moving average 4 Exponential smoothing (exponentially weighted moving average) –Exponential smoothing with random fluctuations –Exponential smoothing with random and trend –Exponential smoothing with random and seasonal component

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

30. Time Series Models Simple Moving Average Sample Data (3-period moving average) t D t F t D t -F t | D t -F t | 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

31. Time Series Models Simple Moving Average Sample Data (3-period moving average) t D t F t D t -F t | D t -F t | 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

32. Time Series Models Simple Moving Average Sample Data (3-period moving average) t D t F t D t -F t | D t -F t | 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

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

34. Where t=time period S t =smoothed average at end of period t D t =actual demand in period t  =smoothing constant (0<  <1) F t =forecast for period t

35. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha = 0.2) t D t S t F t D t -F t Quarter Actual Demand Smoothed Average Forecast Error 0 100

36. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t D t S t F t D t -F t Quarter Actual Demand Smoothed Average Forecast Error 0 100 1 ? 100

37. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t D t S t F t D t -F t Quarter Actual Demand Smoothed Average Forecast Error 0 100 1 100 100

38. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t D t S t F t D t -F t Quarter Actual Demand Smoothed Average Forecast Error 0 100 1 100 100 100-100=0

39. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t D t S t F t D t -F t Quarter Actual Demand Smoothed Average Forecast Error 0 100 1 100.2(100)+.8(100)=100 100 100-100=0

40. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t D t S t F t D t -F t Quarter Actual Demand Smoothed Average Forecast Error 0 100 1 100.2(100)+.8(100)=100 100 100-100=0 2 ? 100

41. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t D t S t F t D t -F t 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

42. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t D t S t F t D t -F t 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

43. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t D t S t F t D t -F t 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

44. Time Series Models Exponential smoothing (exponentially weighted moving average) Sample Data (alpha=0.2) t D t S t F t D t -F t 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.

45. 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

46. Characteristics of Good Forecasts 4 Stability 4 Responsiveness 4 Data Storage Requirements

47. BESM Example Cont’d

48. BESM - Expanded 4 The Basic Exponential Smoothing Model (BESM) is nothing more than a cumulative weighted average of all past demand (and the initial smoothed average). 4 Proof:

49. Demand Data with Trend

50. Time Series Models Exponential smoothing with trend enhancement

52. Demand Data with Trend and Seasonality

53. Basic Model Application base smoothing constant, alpha, =.20

56. Trend-Enhanced Application base smoothing constant, alpha, =.20 and trend smoothing constant, beta, =.30

59. Seasonal Indexes 4 seasonal index = actual demand / average demand 4 divide demand by its seasonal index to deseasonalize and 4 multiply demand by its seasonal index to seasonalize.

61. Full Model for Exponential Smoothing 4 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.

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

76. We would like to forecast for quarters 9-12 (at end of qtr. 8)

81. E.S. Homework, Ex. 3