McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved. Chapter 3 Forecasting

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 –Forecasts are an important element in making informed decisions

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 Accuracy –Related to the potential size of forecast error

3-4 Features Common to All Forecasts 1.Techniques assume some underlying causal system that existed in the past will persist into 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

3-5 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

3-6 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

3-7 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

3-8 Forecast Accuracy and Control (contd.) Forecast errors should be monitored –Difference between the actual value and the value that was predicted for a given period. –Error = Actual – Forecast –If errors fall beyond acceptable bounds, corrective action may be necessary

3-9 Forecast Accuracy Metrics MAD weights all errors evenly( mean absolute deviation) MSE weights errors according to their squared values( mean squared error MAPE weights errors according to relative error ( mean absolute percent error)

3-10 Forecast Error Calculation Period Actual (A) Forecast (F) (A-F) Error |Error|Error 2 [|Error|/Actual]x % % % % % Sum % n = 5n-1 = 4n = 5 MADMSEMAPE = 2.6= 9.75 =100%-2.25%= 97.75% level of confidence.

3-11 Forecasting Approaches Qualitative Forecasting –Qualitative techniques 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

3-12 Judgmental Forecasts Forecasts that use inputs such as opinions from consumer surveys, sales staff, managers, executives, and experts –Executive opinions –Salesforce opinions –Consumer surveys –Delphi method

3-13 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

3-14 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

3-15 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

3-16 Moving Average Technique that averages a number of the most recent actual values in generating a forecast

3-17 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

3-18 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

3-19 Exponential Smoothing A weighted averaging method that is based on the previous forecast plus a percentage of the forecast error

3-20 Techniques for Trend Linear trend equation Non-linear trends –Parabolic trend equation –Exponential trend equation –Growth curve trend equation

3-21 Linear Trend A simple data plot can reveal the existence and nature of a trend Linear trend equation

3-22 Estimating slope and intercept Slope and intercept can be estimated from historical data

3-23 Moving & weighted average Period age Demand lecturer: Ahmed El Rawas

3-24 Moving average Calculate the moving average for period 6 where n= 3 ( the 3 most recent demand) MA for period 6 = / 3= lecturer: Ahmed El Rawas

3-25 Weighted average It assigns more weight to the most recent values in a time series. Calculate the weighted average for period 6 using the weight 0.4, 0.3, 0.2, 0.1 ( the total must be equal 1 or 100% ) WA for period 6 = 0.4(41) + 0.3(40) + 0.2(43) + 0.1(40) = 41 lecturer: Ahmed El Rawas

3-26 Exponential smoothing Each new forecast is based on the previous forecast plus a % of the difference between that forecast and the actual value of the series at that point. Next forecast= previous + alpha( actual- previous) lecturer: Ahmed El Rawas

3-27 Exponential smoothing Period actual demand Find the exp smoothing for period 2,3,4 where alpha = 0.1 lecturer: Ahmed El Rawas

3-28 Exponential smoothing When we don’t have information about previous forecast we use naïve forecast that is equal to actual value of the previous period. Period 2= ( 42-42) = 42 Period 3= (40-42) = 41.8 Period 4= ( ) = lecturer: Ahmed El Rawas

3-29 Linear trend equation Ft = a + b t where Ft= forecast for period t a= value of ft at t=0 B= slope of the line t= specific number of time periods from t=0 lecturer: Ahmed El Rawas

3-30 Linear trend equation b= n∑ty - ∑t ∑y / n∑t² – (∑t )² a= ∑y – b∑t / n Where N= number of period Y= value of the time series lecturer: Ahmed El Rawas

3-31 Linear trend equation Week(t) Unit sale(y) ty t² ∑15 ∑3690 ∑11220 ∑55 lecturer: Ahmed El Rawas

3-32 Linear trend equation Find the forecast for period 6 b= 5 ( 11220) – (15) (3690) / 5 (55) - 15²= / = 750 / 50 = 15 a= 3690 – (15) (15) / 5 = 693 Ft = ( 15 ) (6) = 783 lecturer: Ahmed El Rawas

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)

3-34 Least Squares Line

3-35 Correlation Coefficient Correlation –A measure of the strength and direction of relationship between two variables –Ranges between and r 2, 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