1. Stevenson 3 Forecasting

2. 3-2 Learning Objectives  List the elements of a good forecast.  Outline the steps in the forecasting process.  Compare and contrast qualitative and quantitative approaches to forecasting.  Briefly describe averaging techniques, trend and seasonal techniques, and regression analysis, and solve typical problems.  Describe measure(s) of forecast accuracy.  Describe evaluating and controlling forecasts.

3. 3-3 FORECAST:  A statement about the future value of a variable of interest such as demand.  Forecasting is used to make informed decisions  Match supply to demand.  Two important aspects:  Level of demand  Degree of accuracy  Long-range – plan the system (strategic)  Short-range – plan to use the system (on- going operations)

4. 3-4 Forecasts  Forecasts affect decisions and activities throughout an organization AccountingCost/profit estimates FinanceCash flow and funding Human ResourcesHiring/recruiting/training MarketingPricing, promotion, strategy MISIT/IS systems, services OperationsSchedules, workloads Product/service designNew products and services

5. 3-5  Assumes causal system past ==> future  Forecasts are rarely perfect  Forecast accuracy decreases as time horizon increases Features of Forecasts

6. 3-6 Elements of a Good Forecast Timely Accurate Reliable Meaningful Written Easy to use Cost Effective

7. 3-7 Steps in the Forecasting Process Step 1 Determine purpose of forecast Step 2 Establish a time horizon Step 3 Select a forecasting technique Step 4 Obtain, clean and analyze data Step 5 Make the forecast Step 6 Monitor the forecast “The forecast”

8. Forecasting Process 12-8 6. Check forecast accuracy with one or more measures 4. Select a forecast model that seems appropriate for data 5. Develop/compute forecast for period of historical data 8a. Forecast over planning horizon 9. Adjust forecast based on additional qualitative information and insight 10. Monitor results and measure forecast accuracy 8b. Select new forecast model or adjust parameters of existing model 7. Is accuracy of forecast acceptable? 1. Identify the purpose of forecast 3. Plot data and identify patterns 2. Collect historical data No Yes

9. 3-9 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

10. 3-10 Judgmental Forecasts  Executive opinions  Sales force opinions  Consumer surveys  Outside opinion  Delphi method  Opinions of managers and staff  Achieves a consensus forecast

11. 3-11 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

12. 3-12 Forecast Variations Trend Irregular variation Seasonal variations 90 89 88 Cycles

13. 3-13 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.

14. 3-14  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

15. 3-15 Techniques for Averaging  Moving average  Weighted moving average  Exponential smoothing

16. 3-16 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. F t = MA n = n A t-n + … A t-2 + A t-1 F t = WMA n = n w n A t-n + … w n-1 A t-2 + w 1 A t-1

17. Moving Average Example 3-17 If the actual demand in period 6 is 38, then the moving average forecast for period 7 is: Calculate a three-period moving average forecast for demand in period 6

18. 3-18 Simple Moving Average Actual MA3 MA5 F t = MA n = n A t-n + … A t-2 + A t-1

19. Weighted Moving Average Example 3-19 PeriodDemandWeight 142 24010% 34320% 44030% 54140%

20. 3-20 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.  Uses most recent period’s actual and forecast data  Weighted averaging method based on previous forecast plus a percentage of the forecast error  A-F is the error term,  is the % feedback F t = F t-1 +  ( A t-1 - F t-1 )

21. 3-21 Exponential Smoothing Example

22. 3-22 Picking a Smoothing Constant .1 .4 Actual

23. 3-23 Common Nonlinear Trends Parabolic Exponential Growth

24. 3-24 Linear Trend Equation  F t = Forecast for period t  t = Specified number of time periods  a = Value of F t at t = 0  b = Slope of the line F t = a + bt 0 1 2 3 4 5 t FtFt

25. 3-25 Calculating a and b b = n(ty) - ty nt 2 - ( t) 2 a = y - bt n   

26. 3-26 Linear Trend Equation Example

27. 3-27 Linear Trend Calculation y = 143.5 + 6.3t a= 812- 6.3(15) 5 = b= 5 (2499)- 15(812) 5(55)- 225 = 12495-12180 275-225 = 6.3 143.5

28. 3-28 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. Regression Methods  Linear regression  mathematical technique that relates a dependent variable to an independent variable in the form of a linear equation  Primary method for Associative Forecasting  Correlation  a measure of the strength of the relationship between independent and dependent variables 12-29

30. 3-30 Linear Regression Assumptions  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

31. 3-31 Linear Model Seems Reasonable A straight line is fitted to a set of sample points. Computed relationship

32. Linear Regression 12-32 y = a + bx a = y - b x b = where a =intercept b =slope of the line x == mean of the x data y == mean of the y data  xy - nxy  x 2 - nx 2  x n  y n

33. Linear Regression Example 12-33 xy (WINS)(ATTENDANCE) xyx 2 436.3145.216 640.1240.636 641.2247.236 853.0424.064 644.0264.036 745.6319.249 539.0195.025 747.5332.549 49346.72167.7311

34. Linear Regression Example 12-34 x = = 6.125 y = = 43.36 b = = = 4.06 a = y - bx = 43.36 - (4.06)(6.125) = 18.46 49 8 346.9 8  xy - nxy  x 2 - nx 2 (2,167.7) - (8)(6.125)(43.36) (311) - (8)(6.125) 2

35. Linear Regression Example 12-35 ||||||||||| 012345678910 60,000 – 50,000 – 40,000 – 30,000 – 20,000 – 10,000 – Linear regression line, y = 18.46 + 4.06 x Wins, x Attendance, y y = 18.46 + 4.06(7) = 46.88, or 46,880 Attendance forecast for 7 wins

36. Correlation and Coefficient of Determination  Correlation, r  Measure of strength of relationship between the dependent variable (demand) and the independent variable  Varies between -1.00 and +1.00  Coefficient of determination, r 2  Percentage of variation in dependent variable resulting from changes in the independent variable 12-36

37. n  xy -  x  y [ n  x 2 - (  x ) 2 ] [ n  y 2 - (  y ) 2 ] r = Coefficient of determination r 2 = (0.947) 2 = 0.897 r = (8)(2,167.7) - (49)(346.9) [(8)(311) - (49 )2 ] [(8)(15,224.7) - (346.9) 2 ] r = 0.947 Computing Correlation 12-37

38. 3-38 Forecast Accuracy  Error - difference between actual value and predicted value  Mean Absolute Deviation (MAD)  Average absolute error  Weights errors linearly.  Mean Squared Error (MSE)  Average of squared error  Gives more weight to larger errors, which typically cause more problems  Mean Absolute Percent Error (MAPE)  Average absolute percent error  MAPE should be used when there is a need to put errors in perspective. For example, an error of 10 in a forecast of 15 is huge. Conversely, an error of 10 in a forecast of 10,000 is insignificant. Hence, to put large errors in perspective, MAPE would be used.

39. 3-39 MAD, MSE, and MAPE MAD = Actualforecast   n MSE = Actualforecast ) - 1 2   n ( MAPE = Actualforecast  n / Actual*100) 

40. 3-40 Forecast Accuracy Example

41. MAD, MSE, and MAPE 3-41  MAD – easiest to compute, but weighs errors linearly.  MSE – Gives more weight to larger errors; larger errors cause more problems.  MAPE – Puts errors in perspective: e.g., error of 10 in a forecast of 15 is huge, but error of 10 in a forecast of 10,000 is perhaps negligible.

42. 3-42 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

43. 3-43 Tracking Signal Tracking signal = ( Actual - forecast ) MAD  Tracking signal –Ratio of cumulative error to MAD Bias – Persistent tendency for forecasts to be Greater or less than actual values.

44. Forecast Control  Tracking signal  monitors the forecast to see if it is biased high or low  1 MAD ≈ 0.8 б  Control limits of 2 to 5 MADs are used most frequently Tracking signal = =  (D t - F t ) MAD E MAD

45. Tracking Signal Values 3-45

46. Tracking Signal Plot 3-46

47. 3-47 Sources of Forecast errors  Model may be inadequate  Irregular variations  Incorrect use of forecasting technique

48. 3-48 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

49. 3-49 Operations Strategy  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

50. 3-50 Supply Chain Forecasts  Sharing forecasts with supply can  Improve forecast quality in the supply chain  Lower costs  Shorter lead times

51. NEXT SESSION: MID TERM EXAMINATION I Stevenson Chapters 1,2,3 & 6 Slack Chapters 2 Calculators and Equation Sheet allowed Carefully review Equation Sheet Policy If your Equation Sheet does not comply with policy, I will confiscate it Any suspicion of dishonesty will result in immediate expulsion from exam Format: True/False; MCQs; 1 Essay and 2 Problems 3-51