Chapter 3 Forecasting

1. Chapter 3 Forecasting Car buyer- Models & Option Does the dealer know! Basic Managerial function- Planning

2. A statement about the future value of a variable of interest such as demand. Forecasting is used to make informed decisions. Long-range (Plan system) Short-range (Plan use of system) I see that you willget an A this semester. Forecast Traffic Weather

3. Example! Uses of Forecasts

4. Assumes causal system. past ==> future Forecasts rarely perfect because of randomness Forecasts more accurate for groups vs. individuals Forecast accuracy decreases as time horizon increases Features of Forecasts

5. Elements of a Good Forecast

7. “The forecast” Step 6 Monitor the forecast Step 5 Make the forecast Step 4 Obtain, clean 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 Traffic Weather

9. 1. Judgmental ForecastsUses subjective inputs • Executive opinions • Sales force opinions • Consumer surveys • Outside opinion • Delphi method • Opinions of managers and staff (Experts) • Anonymous, encourage honesty, • Questionnaire sequence • Achieves a consensus forecast • Other usage of this method

10. 2. Time Series ForecastsUses historical data • Trend - long-term movement in data • Seasonality - short-term regular variations in data • Specific dates, days, times • Cycle – wavelike variations of more than one year’s duration • Economic, political, GDP … • Irregular variations - caused by unusual circumstances • Atypical- remove from analysis • Random variations - caused by chance • Include?

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

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

13. 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 Naïve Forecasts

14. Stable time series data F(t) = A(t-1) Seasonal variations F(t) = A(t-n) Data with trends F(t) = A(t-1) + (A(t-1) – A(t-2)) Uses for Naïve Forecasts

15. Moving average Weighted moving average Exponential smoothing Techniques for Averaging

16. At-n+ … At-2 + At-1 Ft = MAn= n wnAt-n+ … wn-1At-2 + w1At-1 Ft = WMAn= n 2. Time Series Forecasts 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.

17. At-n+ … At-2 + At-1 Ft = MAn= n Simple Moving Average Actual MA5 MA3

18. At-n+ … At-2 + At-1 At-3+ At-2 + At-1 At-5+ At-4+ At-3 + At-2 + At-1 Ft = MAn= Ft = MA3= Ft = MA5= n 3 5

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

20. Example 3 - Exponential Smoothing

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

22. Parabolic Exponential Growth Time series forecastingCommon Nonlinear Trends Figure 3.5

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

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

25. Linear Trend Equation Example

26. 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

27. Seasonal variations Regularly repeating movements in series values that can be tied to recurring events. Seasonal relative Percentage of average or trend Centered moving average A moving average positioned at the center of the data that were used to compute it. Techniques for Seasonality

28. Types of Forecasts3. 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

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

30. Variations around the line are random Deviations around the line normally distributed Predictions are being made only within the range of observed values For best results: Always plot the data to verify linearity Check for data being time-dependent Small correlation may imply that other variables are important Linear Regression Assumptions

31. 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 Forecast Accuracy

32. MAD, MSE, and MAPE  | Actual – forecast | MAD = n  (Actual – forecast ) 2 MSE = n - 1 ( | Actual – forecast | / Actual )*100 MAPE = n

33. MAD Easy to compute Weights errors linearly MSE Squares error More weight to large errors MAPE Puts errors in perspective MAD, MSE and MAPE

34. Example 10

35. 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 Controlling the Forecast

36.  (Actual - forecast) Tracking signal = MAD Tracking Signal • Tracking signal • Ratio of cumulative error to MAD Bias – Persistent tendency for forecasts to be Greater or less than actual values.

37. 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 Choosing a Forecasting Technique

38. Forecasts are the basis for many decisions Work to improve short-term forecasts Accurate short-term forecasts improve Profits Lower inventory levels Reduce inventory shortages Improve customer service levels Enhance forecasting credibility Operations Strategy

39. Sharing forecasts with supply can Improve forecast quality in the supply chain Lower costs Shorter lead times Gazing at the Crystal Ball (reading in text) Supply Chain Forecasts

41. HW-C3 Due 20th Feb Problems P109-117 1, 7, 15, 24, 27

42. List the elements of a good forecast. Outline the steps in the forecasting process. Describe at least three qualitative forecasting techniques and the advantages and disadvantages of each. Compare and contrast qualitative and quantitative approaches to forecasting. Learning Objectives

43. Briefly describe averaging techniques, trend and seasonal techniques, and regression analysis, and solve typical problems. Describe two measures of forecast accuracy. Describe two ways of evaluating and controlling forecasts. Identify the major factors to consider when choosing a forecasting technique. Learning Objectives

44. Exponential Smoothing

45. Linear Trend Equation

46. Simple Linear Regression