1. 3-1Forecasting Weighted Moving Average Formula w t = weight given to time period “t” occurrence (weights must add to one) The formula for the moving average is:

2. 3-2Forecasting Weighted Moving Average Problem (1) Data Weights: t-1.5 t-2.3 t-3.2 Question: Given the weekly demand and weights, what is the forecast for the 4 th period or Week 4?

3. 3-3Forecasting Weighted Moving Average Problem (1) Solution F 4 = 0.5(720)+0.3(678)+0.2(650)=693.4

4. 3-4Forecasting Weighted Moving Average Problem (2) Data Weights: t-10.7 t-20.2 t-30.1 Question: Given the weekly demand information and weights, what is the weighted moving average forecast of the 5 th period or week?

5. 3-5Forecasting Weighted Moving Average Problem (2) Solution F 5 = (0.1)(755)+(0.2)(680)+(0.7)(655)= 672

6. 3-6Forecasting Exponential Smoothing Model F t = F t-1 +  (A t-1 - F t-1 )

7. 3-7Forecasting Exponential Smoothing Problem (1) Data Question: Given the weekly demand data, what are the exponential smoothing forecasts for periods 2-10 using  =0.10 and  =0.60? Assume F 1 =D 1 Question: Given the weekly demand data, what are the exponential smoothing forecasts for periods 2-10 using  =0.10 and  =0.60? Assume F 1 =D 1

8. 3-8Forecasting

9. 3-9Forecasting Exponential Smoothing Problem (1) Plotting

10. 3-10Forecasting Exponential Smoothing Problem (2) Data Question: What are the exponential smoothing forecasts for periods 2-5 using Alpha =0.5? Assume F 1 =D 1 Question: What are the exponential smoothing forecasts for periods 2-5 using Alpha =0.5? Assume F 1 =D 1

11. 3-11Forecasting Exponential Smoothing Problem (2) Solution F 1 =820+(0.5)(820-820)=820F 3 =820+(0.5)(775-820)=797.75

12. 3-12Forecasting Example 3 - Exponential Smoothing

13. 3-13Forecasting Common Nonlinear Trends Parabolic Exponential Growth Figure 3.5

14. 3-14Forecasting Common Nonlinear Trends Figure 3.5 Parabolic Trends Concaved Upwards and Concaved Downwards The left and right arms are widening as the value increases or the parabola is opening upwards. It represents the quadratic function

15. 3-15Forecasting 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

16. 3-16Forecasting Calculating a and b b = n(ty) - ty nt 2 - ( t) 2 a = y - bt n   

17. 3-17Forecasting Linear Trend Equation Example

18. 3-18Forecasting 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

19. 3-19Forecasting Associative Forecasting 1. Predictor variables - used to predict values of variable interest 2. Regression - technique for fitting a line to a set of points 3. Least squares line - minimizes sum of squared deviations around the line

20. 3-20Forecasting Linear Model Seems Reasonable A straight line is fitted to a set of sample points. Computed relationship

21. 3-21Forecasting 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

22. 3-22Forecasting Simple Linear Regression Formulas for Calculating “a” and “b”

23. 3-23Forecasting Simple Linear Regression Problem Data Question: Given the data below, what is the simple linear regression model that can be used to predict sales in future weeks?

24. 3-24Forecasting Answer: First, using the linear regression formulas, we can compute “a” and “b” 24

25. 3-25Forecasting Y t = 143.5 + 6.3x 180 Perio d 135 140 145 150 155 160 165 170 175 12345 Sales Forecast The resulting regression model is: 25