FORCASTING

1. PART TWO FORCASTING • Chapter Three • Forecasting

2. Chapter 3 Forecasting

3. FORECAST: • A statement about the future • Used to help managers • Plan the system • Plan the use of the system

4. Uses of Forecasts

5. I see that you willget an A this semester. • Assumes causal systempast ==> future • Forecasts rarely perfect because of randomness • Forecasts more accurate forgroups vs. individuals • Forecast accuracy decreases as time horizon increases

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

7. “The forecast” Step 6 Monitor the forecast Step 5 Prepare the forecast Step 4 Gather 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

8. 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

9. Judgmental Forecasts • Executive opinions • Sales force composite • Consumer surveys • Outside opinion • Opinions of managers and staff • Delphi method

10. Time Series Forecasts • Trend - long-term movement in data • Seasonality - short-term regular variations in data • Irregular variations - caused by unusual circumstances • Random variations - caused by chance

11. Irregularvariation Trend Cycles 90 89 88 Seasonal variations Forecast Variations Figure 3-1

12. Naïve Forecasts • Simple to use • Virtually no cost • Data analysis is nonexistent • Easily understandable • Cannot provide high accuracy • Can be a standard for accuracy

13. Uses for Naïve Forecasts • 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))

14. Uh, give me a minute.... We sold 250 wheels last week.... Now, next week we should sell.... Naive Forecasts

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

16. Figure 3-4 Actual MA5 MA3 n Ai  MAn = i = 1 n Simple Moving Average

17. 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. Ft = Ft-1 + (At-1 - Ft-1)

18. Example of Exponential Smoothing

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

20. Parabolic Exponential Growth Common Nonlinear Trends Figure 3-5

21. Y Yt = a + bt 0 1 2 3 4 5 t Linear Trend Equation • b is similar to the slope. However, since it is calculated with the variability of the data in mind, its formulation is not as straight-forward as our usual notion of slope.

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

23. Linear Trend Equation Example

24. 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

25. 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

26. Computedrelationship Linear Model Seems Reasonable

27. 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 • Tracking signal • Ratio of cumulative error and MAD

28.   Actual forecast MAD = n 2 ( Actual  forecast)  MSE = n - 1 MAD & MSE

29.  (Actual - forecast) Tracking signal = MAD  (Actual - forecast) Tracking signal =  Actual - forecast n Tracking Signal

30. Exponential Smoothing T3-2

31. Linear Trend Equation T3-3

32. Trend Adjusted Exponential Smoothing T3-4

33. Simple Linear Regression T3-5