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- 1. McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved. Chapter 3 Forecasting
- 2. 3-2 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
- 3. 3-3 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 • Degree of Accuracy – Related to the potential size of forecast error
- 4. 3-4 Uses for forecasts 1. Help Managers plan the system: involves Long- range plans such as • Types of Products & Services to offer • What facilities and equipment to have • Where to locate….etc 2. Help Managers plan the use of the system: involves short and intermediate range plans such as • Planning inventory • Workforce levels • Purchasing and production • Budgeting • scheduling
- 5. 3-5 Features Common to All Forecasts 1. Techniques assume that the same underlying causal system that existed in the past will continue to exist in the future 2. Forecasts are not perfect 3. Forecasts for groups of items are more accurate than those for individual items 4. Forecast accuracy decreases as the forecasting horizon increases
- 6. 3-6 Elements of a Good Forecast The forecast • should be timely: time is needed to respond to the information in a forecast • should be accurate: degree of accuracy should be stated • should be reliable; it should work consistently • should be expressed in meaningful units (ex. $ or units) • should be in writing • technique should be simple to understand and use • should be cost effective
- 7. 3-7 Steps in the Forecasting Process 1. Determine the purpose of the forecast 2. Establish a time horizon 3. Select a forecasting technique 4. Obtain, clean, and analyze appropriate data 5. Make the forecast 6. Monitor the forecast
- 8. 3-8 Forecast Accuracy and Control • Forecasters want to minimize forecast errors – 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
- 9. 3-9 Forecast Accuracy and Control (contd.) • Forecast errors should be monitored – Error = Actual – Forecast – If errors fall beyond acceptable bounds, corrective action may be necessary
- 10. 3-10 Forecast Accuracy Metrics n ∑ − = tt ForecastActual MAD ( )2 tt 1 ForecastActual MSE − − = ∑ n n ∑ × − = 100 Actual ForecastActual MAPE t tt MAD weights all errors evenly MSE weights errors according to their squared values MAPE weights errors according to relative error
- 11. 3-11 Forecast Error Calculation Period Actual (A) Forecast (F) (A-F) Error |Error| Error2 [|Error|/Actual]x100 1 107 110 -3 3 9 2.80% 2 125 121 4 4 16 3.20% 3 115 112 3 3 9 2.61% 4 118 120 -2 2 4 1.69% 5 108 109 1 1 1 0.93% Sum 13 39 11.23% n = 5 n-1 = 4 n = 5 MAD MSE MAPE = 2.6 = 9.75 = 2.25%
- 12. 3-12 Forecasting Approaches • Qualitative Forecasting – Qualitative techniques consist mainly of subjective inputs. They permit the inclusion of soft information such as: • Human factors • Personal opinions – 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
- 13. 3-13 Forecasting Techniques 1. Judgmental Forecasts • Forecasts that use subjective inputs such as opinions from consumer surveys, sales staff, managers, executives, and experts – Executive opinions: a small group of upper-level managers may meet and collectively develop a forecast – Sales force opinions: members of sale staff or customer service staff are often good sources of information because of their direct contact with customers – Consumer surveys: Soliciting inputs from customers through surveys – Delphi method: an iterative (repetitive) process in which managers and staff complete a series of questionnaires, each developed from the previous one to achieve a consensus forecast
- 14. 3-14 2. Time-Series Forecasts • Time Series Forecasts attempt to project past experience into the future – Time-series - a time-ordered sequence of observations taken at regular time intervals (hourly, daily, weekly, annually) • Assume that future values of the time-series can be estimated from past values of the time-series 3. Associative models use equations that consist of one or more explanatory variables that can be used to predict demand. For ex. Demand for paint might be related to variables such as price, amount spent on advertising, specific characteristics of the paint such as its drying time or ease of cleanup
- 15. 3-15 Time-Series Behaviors • Trend: a long term upward or downward movement in data. Ex: changing incomes, populations shift • Seasonality: short-term regular variations related to the calendar or time of day. Ex:Resturants • Cycles: wavelike variations lasting more than 1 year. Ex. Economic, political, and agricultural conditions • Irregular variations: Caused by unusual circumstances, not reflective of typical behavior such as severe weather conditions • Random variation: residual variations after all other behaviors are accounted for
- 16. 3-16 Time-Series Forecasting - Naïve Forecast • 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
- 17. 3-17 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
- 18. 3-18 Moving Average • Technique that averages a number of the most recent actual values in generating a forecast averagemovingin theperiodsofNumber 1periodinvalueActual averagemovingperiodMA periodfor timeForecast where MA 1 1 t = −= = = == − = −∑ n tA n tF n A F t t t n i it t
- 19. 3-19 Moving Average • As new data become available, the forecast is updated by adding the newest value and dropping the oldest and then recomputing the 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
- 20. 3-20 Weighted Moving Average • 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 Ft =wnAt−n +wn−1At−(n−1) +...+w1At−1 where wt =weightforperiodt, wt−1 =weightforperiodt−1, etc. At =theactualvalueforperiodt, At−1 =theactualvalueforperiodt−1, etc.
- 21. 3-21 Exponential Smoothing • A weighted averaging method that is based on the previous forecast plus a percentage of the forecast error periodpreviousthefromsalesordemandActual constantSmoothing= periodpreviousfor theForecast periodforForecast where )( 1 1 111 = = = −+= − − −−− t t t tttt A F tF FAFF α α
- 22. 3-22 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
- 23. 3-23 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
- 24. 3-24 Techniques for Trend • Linear trend equation • Non-linear trends – Parabolic trend equation – Exponential trend equation – Growth curve trend equation
- 25. 3-25 Linear Trend • A simple data plot can reveal the existence and nature of a trend • Linear trend equation Ft =a+bt where Ft =Forecast for periodt a=Value ofFt at t =0 b=Slope of the line t =Specifiednumber of time periods fromt =0
- 26. 3-26 Estimating slope and intercept • Slope and intercept can be estimated from historical data b = n ty − t y∑∑∑ n t2 − t∑( )∑ 2 a = y −b t∑∑ n or y −bt where n = Number of periods y = Value of the time series
- 27. 3-27 Trend-Adjusted Exponential Smoothing • The trend adjusted forecast consists of two components – Smoothed error – Trend factor TAFt+1 =St +Tt where St =Previousforecastplussmoothederror Tt =Currenttrendestimate
- 28. 3-28 Trend-Adjusted Exponential Smoothing • Alpha and beta are smoothing constants • Trend-adjusted exponential smoothing has the ability to respond to changes in trend TAFt+1 =St +Tt St =TAFt +α At −TAFt( ) Tt =Tt−1+β TAFt −TAFt−1−Tt−1( )
- 29. 3-29 Techniques for Seasonality • Seasonality is expressed in terms of the amount that actual values deviate from the average value of a series • Models of seasonality – Additive • Seasonality is expressed as a quantity that gets added or subtracted from the time-series average in order to incorporate seasonality – Multiplicative • Seasonality is expressed as a percentage of the average (or trend) amount which is then used to multiply the value of a series in order to incorporate seasonality
- 30. 3-30 Seasonal Relatives • Seasonal relatives – The seasonal percentage used in the multiplicative seasonally adjusted forecasting model • Using seasonal relatives – To deseasonalize data • Done in order to get a clearer picture of the nonseasonal components of the data series • Divide each data point by its seasonal relative – To incorporate seasonality in a forecast • Obtain trend estimates for desired periods using a trend equation • Add seasonality by multiplying these trend estimates by the corresponding seasonal relative
- 31. 3-31 Techniques for Cycles • Cycles are similar to seasonal variations but are of longer duration • Explanatory approach – Search for another variable that relates to, and leads, the variable of interest • Housing starts precede demand for products and services directly related to construction of new homes • If a high correlation can be established with a leading variable, it can develop an equation that describes the relationship, enabling forecasts to be made
- 32. 3-32 Associative Forecasting Techniques – 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
- 33. 3-33 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)
- 34. 3-34 Least Squares Line yc = a+ bx where yc = Predicted (dependent) variable x = Predicted (independent) variable b =Slope of the line a = Value of yc when x = 0 (i.e., the height of the line at the y intercept) and b = n xy − x y∑∑∑ n x2 − x∑( )∑ 2 a = y −b x∑∑ n or y −bx where n = Number of paired observations
- 35. 3-35 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 Se = y − yc( ) 2 ∑ n−2 where Se =standard error of estimate y =the value of each data point n =number of data points
- 36. 3-36 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 r2 = n xy∑( )− x∑( ) y∑( ) n x2 ∑( )− x∑( ) 2 n y2 ∑( )− y∑( ) 2
- 37. 3-37 Simple Linear Regression Assumptions 1. Variations around the line are random 2. Devaiations around the average value (the line) should be normally distributed 3. Predictions are made only within the range of observed values
- 38. 3-38 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
- 39. 3-39 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

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