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Stevenson 3

Stevenson 3. Forecasting. 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.

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Stevenson 3

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  1. Stevenson3 Forecasting

  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. 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. Forecasts • Forecasts affect decisions and activities throughout an organization

  5. Features of Forecasts • Assumes causal systempast ==> future • Forecasts are rarely perfect • Forecast accuracy decreases as time horizon increases

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

  7. Steps in the Forecasting Process “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

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

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

  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. Forecast Variations Irregularvariation Trend Cycles 90 89 88 Seasonal variations

  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. 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

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

  16. Moving Averages At-n+ … At-2 + At-1 Ft = MAn= n wnAt-n+ … wn-1At-2 + w1At-1 Ft = WMAn= n • 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. Moving Average Example Calculate a three-period moving average forecast for demand in period 6 If the actual demand in period 6 is 38, then the moving average forecast for period 7 is:

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

  19. Weighted Moving Average Example

  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 Ft = Ft-1 + (At-1 - Ft-1)

  21. Exponential Smoothing Example

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

  23. Common Nonlinear Trends Parabolic Exponential Growth

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

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

  26. Linear Trend Equation Example

  27. Linear Trend Calculation 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

  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

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

  32. Linear Regression 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 x2- nx2 x n y n

  33. Linear Regression Example x y (WINS) (ATTENDANCE) xyx2 4 36.3 145.2 16 6 40.1 240.6 36 6 41.2 247.2 36 8 53.0 424.0 64 6 44.0 264.0 36 7 45.6 319.2 49 5 39.0 195.0 25 7 47.5 332.5 49 49 346.7 2167.7 311

  34. Linear Regression Example x = = 6.125 y = = 43.36 b= = = 4.06 a= y - bx = 43.36 - (4.06)(6.125) = 18.46 49 8 xy - nxy x2 - nx2 346.9 8 (2,167.7) - (8)(6.125)(43.36) (311) - (8)(6.125)2

  35. Linear Regression Example 60,000 – 50,000 – 40,000 – 30,000 – 20,000 – 10,000 – Linear regression line, y = 18.46 + 4.06x Attendance, y Attendance forecast for 7 wins y = 18.46 + 4.06(7) = 46.88, or 46,880 | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 Wins, x

  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, r2 • Percentage of variation in dependent variable resulting from changes in the independent variable

  37. Computing Correlation n xy -  x y [n x2 - ( x)2] [n y2 - ( y)2] r = (8)(2,167.7) - (49)(346.9) [(8)(311) - (49)2] [(8)(15,224.7) - (346.9)2] r = r = 0.947 Coefficient of determination r2 = (0.947)2 = 0.897

  38. Forecast Accuracy • Error - difference between actual value and predicted value • Mean Absolute Deviation (MAD) • Average absolute error • Easiest to compute • 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. MAD, MSE, and MAPE 2 ( Actual  forecast)  MSE = n - 1  ( Actual forecast / Actual*100) MAPE = n   Actual forecast MAD = n

  40. Forecast Accuracy Example

  41. 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

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

  43. Forecast Control (Dt - Ft) MAD  E MAD Tracking signal = = • 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

  44. Tracking Signal Values

  45. Tracking Signal Plot

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

  47. 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

  48. 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

  49. Supply Chain Forecasts • Sharing forecasts with supply can • Improve forecast quality in the supply chain • Lower costs • Shorter lead times

  50. Next session: Quiz # 2 - Forecasting

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