1. Forecast 2 Linear trend Forecast error Seasonal demand

2. 3-2 Common Nonlinear Trends Parabolic Exponential Growth Figure 3.5

3. 3-3 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

4. 3-4 Calculating a and b b = n(ty) - ty nt 2 - ( t) 2 a = y - bt n   

5. 3-5 Linear Trend Equation Example

6. 3-6 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

7. 3-7 Techniques for Seasonality 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.

8. 3-8 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

9. 3-9 Linear Model Seems Reasonable A straight line is fitted to a set of sample points. Computed relationship

10. 3-10 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

11. A Good Forecast  Has a small error  Error = Demand - Forecast

12. Measures of Forecast Error b.MSE = Mean Squared Error etet Ideal values =0 (i.e., no forecasting error) c.RMSE = Root Mean Squared Error a.MAD = Mean Absolute Deviation

13. MAD Example MonthSalesForecast 1220n/a 2250255 3210205 4300320 5325315 What is the MAD value given the forecast values in the table below? 5 5 20 10 |A t – F t | FtFt AtAt = 40 4 =10

14. Measures of Error tAtAt FtFt etet |e t |et2et2 Jan12010020 400 Feb 90106 256 Mar101102 April 91101 May11598 June 83103 1. Mean Absolute Deviation (MAD) 2a. Mean Squared Error (MSE) 2b. Root Mean Squared Error (RMSE) -1616 1 -10 17 -20 10 17 20 1 100 289 400 -10 841,446 84 6 = 14 1,446 6 = 241 = SQRT(241) =15.52 An accurate forecasting system will have small MAD, MSE and RMSE; ideally equal to zero. A large error may indicate that either the forecasting method used or the parameters such as α used in the method are wrong. Note: In the above, n is the number of periods, which is 6 in our example

15. MSE/RMSE Example MonthSalesForecast 1220n/a 2250255 3210205 4300320 5325315 What is the MSE value? 5 5 20 10 |A t – F t | FtFt AtAt = 550 4 =137.5 (A t – F t ) 2 25 400 100 = 550 RMSE = √137.5 =11.73

16. 3-16 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

17. 3-17 Sources of Forecast errors Model may be inadequate Irregular variations Incorrect use of forecasting technique

18. 3-18 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. Good tracking signal has low values

19. 3-19 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

20. Collect historical data Select a model – Moving average methods Select n (number of periods) For weighted moving average: select weights – Exponential smoothing Select  Selections should produce a good forecast To Use a Forecasting Method …