Forecasting

1. Forecasting

2. FORECAST: • A statement about the future value of a variable of interest such as demand. • Forecasts affect decisions and activities throughout an organization • Accounting, finance • Human resources • Marketing • MIS • Operations • Product / service design

3. Uses of Forecasts

4. I see that you willget an A this semester. • Assumes causal systempast ==> future • Forecasts rarely perfect because of randomness • Forecasts more accurate forgroups vs. individuals • Forecast accuracy decreases as time horizon increases

5. Timely Accurate Reliable Easy to use Written Meaningful Elements of a Good Forecast

6. “The forecast” Step 6 Monitor the forecast Step 5 Prepare the forecast Step 4 Gather and analyze data Step 3 Select a forecasting technique Step 2 Establish a time horizon Step 1 Determine purpose of forecast Steps in the Forecasting Process

7. Types of Forecasts • Judgmental - uses subjective inputs • Time series - uses historical data assuming the future will be like the past • Associative models - uses explanatory variables to predict the future

8. Judgmental Forecasts • Executive opinions • Sales force opinions • Consumer surveys • Outside opinion • Delphi method • Opinions of managers and staff • Achieves a consensus forecast

9. Time Series Forecasts • Trend - long-term movement in data • Seasonality - short-term regular variations in data • Cycle – wavelike variations of more than one year’s duration • Irregular variations - caused by unusual circumstances • Random variations - caused by chance

10. Forecast Variations Figure 3.1 Irregularvariation Trend Cycles 90 89 88 Seasonal variations

11. Uh, give me a minute.... We sold 250 wheels last week.... Now, next week we should sell.... Naive Forecasts The forecast for any period equals the previous period’s actual value.

12. Naïve Forecasts • Simple to use • Virtually no cost • Quick and easy to prepare • Data analysis is nonexistent • Easily understandable • Cannot provide high accuracy • Can be a standard for accuracy

13. Techniques for Averaging • Moving average • Weighted moving average • Exponential smoothing

14. n Ai  MAn = i = 1 n Moving Averages • Moving average – A technique that averages a number of recent actual values, updated as new values become available. • Weighted moving average – More recent values in a series are given more weight in computing the forecast.

15. n Ai  MAn = i = 1 n Moving Averages • Moving average –

16. n Ai  MAn = i = 1 n Moving Averages • Moving average –

17. n Ai  MAn = i = 1 n Moving Averages • Moving average –

18. n Ai  MAn = i = 1 n Moving Averages • Moving average –

19. n Ai  MAn = i = 1 n Moving Averages • Moving average –

20. n Ai  MAn = i = 1 n Simple Moving Average Actual MA5 MA3

21. n A*wi  WMAn = i = 1 Weighted Moving Averages • Weighted Moving average –

22. n A*wi  WMAn = i = 1 Weighted Moving Averages • Weighted Moving average –

23. n A*wi  WMAn = i = 1 Weighted Moving Averages • Weighted Moving average –

24. n A*wi  WMAn = i = 1 Weighted Moving Averages • Weighted Moving average –

25. n A*wi  WMAn = i = 1 Weighted Moving Averages • Weighted Moving average –

26. Exponential Smoothing • Premise--The most recent observations might have the highest predictive value. • Therefore, we should give more weight to the more recent time periods when forecasting. Ft = Ft-1 + (At-1 - Ft-1)

27. Exponential Smoothing • Weighted averaging method based on previous forecast plus a percentage of the forecast error • A-F is the error term,  is the % feedback Ft = Ft-1 + (At-1 - Ft-1)

28. Exponential Smoothing • Ft = Next Period • Ft-1= Previous Period •  = Smoothing Constant • At-1 = Actual Result Previous Period Ft = Ft-1 + (At-1 - Ft-1)

29. Exponential Smoothing - Problem • Ft = Result of formula • Ft-1= 42 •  = Smoothing = .10 • At-1 = 44 Ft = Ft-1 + (At-1 - Ft-1)

30. Exponential Smoothing - Problem • Ft = 42 + .10(44-42) • Ft = 42 + .10(2) • Ft = 42 + .20 • Ft = 42.20 Ft = Ft-1 + (At-1 - Ft-1)

31. Exponential Smoothing - Problem • Ft = 43 + .10(42.20-43) • Ft = 43 + .10(-.80) • Ft = 43 + -.080 • Ft = 42.92 Ft = Ft-1 + (At-1 - Ft-1)

32. Example 3 - Exponential Smoothing

33. Actual .4  .1 Picking a Smoothing Constant

34. Parabolic Exponential Growth Common Nonlinear Trends Figure 3.5

35. Ft Ft = a + bt 0 1 2 3 4 5 t Linear Trend Equation • Ft = Forecast for period t • t = Specified number of time periods • a = Value of Ft at t = 0 • b = Slope of the line

36. n (ty) - t y    b = 2 2 n t - ( t)   y - b t   a = n Calculating a and b

37. Linear Trend Equation Example

38. 5 (2499) - 15(812) 12495 - 12180 b = = = 6.3 5(55) - 225 275 - 225 812 - 6.3(15) a = = 143.5 5 y = 143.5 + 6.3t Linear Trend Calculation

39. Associative Forecasting • Predictor variables - used to predict values of variable interest • Regression - technique for fitting a line to a set of points • Least squares line - minimizes sum of squared deviations around the line

40. Computedrelationship Linear Model Seems Reasonable A straight line is fitted to a set of sample points.

41. Forecast Accuracy • Error - difference between actual value and predicted value • Mean Absolute Deviation (MAD) • Average absolute error • Mean Squared Error (MSE) • Average of squared error • Mean Absolute Percent Error (MAPE) • Average absolute percent error

42. 2 ( Actual  forecast)  MSE = n - 1  ( Actual forecast / Actual*100) MAPE = n MAD, MSE, and MAPE   Actual forecast MAD = n

43. Example 10

44. Controlling the Forecast • Control chart • A visual tool for monitoring forecast errors • Used to detect non-randomness in errors • Forecasting errors are in control if • All errors are within the control limits • No patterns, such as trends or cycles, are present

45. Sources of Forecast errors • Model may be inadequate • Irregular variations • Incorrect use of forecasting technique

46. Choosing a Forecasting Technique • No single technique works in every situation • Two most important factors • Cost • Accuracy • Other factors include the availability of: • Historical data • Computers • Time needed to gather and analyze the data • Forecast horizon

47. Exponential Smoothing

48. Linear Trend Equation

49. Simple Linear Regression