CHAPTER

1. CHAPTER 3 Forecasting Homework Problems: # 2,3,4,8(a),22,23,25,27 on pp. 121-128.

2. Forecast • Forecast – a statement about the future value of a variable of interest • We make forecasts about such things as weather, demand, and resource availability • Forecasts are an important element in making informed decisions

3. Uses of Forecasts

4. Two Important Aspects of Forecasts • Expected level of demand • The level of demand may be a function of some structural variation such as trend or seasonal variation • Accuracy • Related to the potential size of forecast error

5. I see that you willget an A this semester. Features Common to All Forecasts • Techniques assume some underlying causal system that existed in the past will persist into the future • Forecasts are not perfect • Forecasts for groups of items are more accurate than those for individual items • Forecast accuracy decreases as the forecasting horizon increases

6. Elements of a Good Forecast The forecast • should be timely • should be accurate • should be reliable • should be expressed in meaningful units • should be in writing • technique should be simple to understand and use • should be cost effective

7. Steps in the Forecasting Process • Determine the purpose of the forecast • Establish a time horizon • Select a forecasting technique • Obtain, clean, and analyze appropriate data • Make the forecast • Monitor the forecast

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. Forecast Accuracy and Control • Forecasters want to minimize forecast errors • It is nearly impossible to correctly forecast real-world variable values on a regular basis • So, it is important to provide an indication of the extent to which the forecast might deviate from the value of the variable that actually occurs • Forecast accuracy should be an important forecasting technique selection criterion

10. Forecast Accuracy and Control (contd.) • Forecast errors should be monitored • Error = Actual – Forecast • If errors fall beyond acceptable bounds, corrective action may be necessary

11. Forecast Accuracy Metrics MAD weights all errors evenly MSE weights errors according to their squared values MAPE weights errors according to relative error

12. Forecast Error Calculation

13. Forecasting Approaches • Qualitative Forecasting • Qualitative techniques permit the inclusion of soft information such as: • Human factors • Personal opinions • Hunches • These factors are difficult, or impossible, to quantify • Quantitative Forecasting • Quantitative techniques involve either the projection of historical data or the development of associative methods that attempt to use causal variables to make a forecast • These techniques rely on hard data

14. Judgmental Forecasts • Forecasts that use subjective inputs such as opinions from consumer surveys, sales staff, managers, executives, and experts • Executive opinions • Sales force opinions • Consumer surveys • Delphi method

15. Time Series Forecasts • Forecasts that project patterns identified in recent time-series observations • Time-series - a time-ordered sequence of observations taken at regular time intervals • Assume that future values of the time-series can be estimated from past values of the time-series

16. 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

17. Forecast Variations Figure 3.1 Irregularvariation Trend Cycles 90 89 88 Seasonal variations

18. Naive Forecasts • Naïve Forecast • Uses a single previous value of a time series as the basis for a forecast • The forecast for a time period is equal to the previous time period’s value • Can be used when • The time series is stable • There is a trend • There is seasonality

19. Time-Series Forecasting-- Averaging • These Techniques work best when a series tends to vary about an average • Averaging techniques smooth variations in the data • They can handle step changes or gradual changes in the level of a series • Techniques • Moving average • Weighted moving average • Exponential smoothing

20. Moving Averages • Technique that averages a number of the most recent actual values in generating a forecast

21. Moving Averages • As new data become available, the forecast is updated by adding the newest value and dropping the oldest and then recomputing the average • The number of data points included in the average determines the model’s sensitivity • Fewer data points used-- more responsive • More data points used-- less responsive

22. Weighted Moving Averages • The most recent values in a time series are given more weight in computing a forecast • The choice of weights, w, is somewhat arbitrary and involves some trial and error

23. Moving Averages Example Given the following data: Period # of complaints 1 60 2 65 3 55 4 58 5 64 A). Prepare the forecasts for period 6 using a 3-period, 5-period moving average. B). Prepare a weighted moving average forecast for period 6 using weights of 0.3, 0.2, and 0.1.

24. Simple Moving Average Actual MA5 MA3 Q. What n to use? Large or small?

25. 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)

26. Exponential Smoothing • 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)

27. Example - Exponential Smoothing

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

29. Other Forecasting Methods - Focus • Focus Forecasting • Some companies use forecasts based on a “best current performance” basis • Apply several forecasting methods to the last several periods of historical data • The method with the highest accuracy is used to make the forecast for the following period • This process is repeated each month

30. Other Forecasting Methods - Diffusion • Diffusion Models • Historical data on which to base a forecast are not available for new products • Predictions are based on rates of product adoption and usage spread from other established products • Take into account facts such as • Market potential • Attention from mass media • Word-of-mouth

31. Technique for Trend • Linear trend equation • Non-linear trends • Parabolic trend equation • Exponential trend equation • Growth curve trend equation

32. Linear Trend Equation • A simple data plot can reveal the existence and nature of a trend • Linear trend equation

33. Estimating slope and intercept • Slope and intercept can be estimated from historical data

34. Linear Trend Equation Example

35. 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

36. Associative Forecasting • Home values may be related to such factors as home and property size, location, number of bedrooms, and number of bathrooms • Associative techniques are based on the development of an equation that summarizes the effects of predictor variables • Predictor variables - variables that can be used to predict values of the variable of interest

37. Simple Linear Regression • Regression - a technique for fitting a line to a set of data points • Simple linear regression - the simplest form of regression that involves a linear relationship between two variables • The object of simple linear regression is to obtain an equation of a straight line that minimizes the sum of squared vertical deviations from the line (i.e., the least squares criterion)

38. Least Squares Line Predictor

39. Standard Error • Standard error of estimate • A measure of the scatter of points around a regression line • If the standard error is relatively small, the predictions using the linear equation will tend to be more accurate than if the standard error is larger

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

41. Correlation Coefficient • Correlation • A measure of the strength and direction of relationship between two variables • Ranges between -1.00 and +1.00 • r2, square of the correlation coefficient • A measure of the percentage of variability in the values of y that is “explained” by the independent variable • Ranges between 0 and 1.00

42. Regression and Correlation Example • Given the following values of X and Y, (a) obtain a linear regression line for the data, and (2) what percentage of the variation is explained by the regression line? • x y xy x2 y2 • 15.00 74.00 1110.0 225.0 5476.0 • 25.00 80.00 2000.0 625.0 6400.0 • 40.00 84.00 3360.0 1600.0 7056.0 • 32.00 81.00 2592.0 1024.0 6561.0 • 51.00 96.00 4896.0 2601.0 9216.0 • 47.00 95.00 4465.0 2209.0 9025.0 • 30.00 83.00 2490.0 900.0 6889.0 • 18.00 78.00 1404.0 324.0 6084.0 • 14.00 70.00 980.0 196.0 4900.0 • 15.00 72.00 1080.0 225.0 5184.0 • 22.00 85.00 1870.0 484.0 7225.0 • 24.00 88.00 2112.0 576.0 7744.0 • 33.00 90.00 2970.0 1089.0 8100.0

43. Simple Linear Regression Assumptions • Variations around the line are random • Deviations around the average value (the line) should be normally distributed • Predictions are made only within the range of observed values

44. Issues to consider • Always plot the line to verify that a linear relationships is appropriate • The data may be time-dependent. • If they are • use analysis of time series • use time as an independent variable in a multiple regression analysis • A small correlation may indicate that other variables are important

45. 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

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. Using Forecast Information • Reactive approach • View forecasts as probable future demand • React to meet that demand • Proactive approach • Seeks to actively influence demand • Advertising • Pricing • Product/service modifications • Generally requires either and explanatory model or a subjective assessment of the influence on demand