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Chapter 4: Forecastig 15 Forecast is oe of the most importat busiess fuctios because all other busiess decisios are based o a forecast of the future.

1 Chapter 4: Forecastig 15 Forecast is oe of the most importat busiess fuctios because all other busiess decisios are based o a forecast of the future. Decisios such as which markets to pursue, which products to produce, how much ivetory to carry, ad how may people to hire all require a forecast. Poor forecastig results i icorrect busiess decisios ad leaves the compay uprepared to meet future demads. The cosequeces ca be very costly i terms of lost sales ad ca eve force a compay out of busiess. Learig Objectives: 1. Uderstad the three time horizos 2. Explai whe to use each of the four qualitative models 3. Apply the aive, movig average, expoetial smoothig, ad tred methods 4. Compute three measures of forecast accuracy 5. Use a trackig sigal 15 Have you ever goe to a restaurat ad bee told that they are sold out of their specials, or goe to the uiversity bookstore ad foud that the texts for your course are o backorder? 204 / 481 What is Forecastig? Process of predictig a future evet. I realities, forecasts are rarely perfect 16 Most forecastig techiques assume a uderlyig stability i the system Product family ad aggregated forecasts are more accurate tha idividual product forecasts 16 If the forecaster is accurate, her or she usually makes sure that everyoe is aware of his or her talets. Very seldom does oe read articles i Fortue, Forbes, orthewall Street Joural, however, about moey maagers who are cosistetly off by 25% i their stock market forecasts. 205 / 481

2 Forecastig Time Horizos Short-rage forecast Up to 1 year, geerally less tha 3 moths Purchasig, job schedulig, workforce levels, job assigmets, productio levels Ted to be more accurate tha loger-term forecasts Medium-rage forecast 3 moths to 3 years Sales ad productio plaig, budgetig Deal with more comprehesive issues ad support maagemet decisios regardig plaig ad products, plats ad processes Log-rage forecast 3+ years New product plaig, facility locatio, research ad developmet 206 / 481 Types of Forecasts Ecoomic forecasts Address busiess cycle iflatio rate, moey supply, housig starts, etc. Techological forecasts Predict rate of techological progress Impacts developmet of ew products Demad forecasts Predict sales of existig products ad services 207 / 481

3 Strategic Importace of Forecastig Huma Resources: Capacity: Hirig, traiig, layig off workers Capacity shortages ca result i udepedable delivery, loss of customers, loss of market share Supply Chai Maagemet: Good supplier relatios ad price advatages 208 / 481 Steps i Forecastig 1. Determie the use of the forecast 2. Select the items to be forecasted 3. Determie the time horizo of the forecast 4. Select the forecastig model(s) 5. Gather the data 6. Make the forecast 7. Validate ad implemet results 209 / 481

4 Forecastig Approaches 1. Qualitative Methods Based o huma judgemet, opiios;subjective ad o-mathematical. Ca icorporate latest chages i the eviromet ad iside iformatio Ca bias the forecast ad reduce forecast accuracy. Used whe situatio is vague ad little data exist (e.g., ew products, ew techology) Ivolves ituitio, experiece (e.g., forecastig sales o iteret) 2. Quatitative Methods Used whe situatio is stable ad historical data exist (e.g., existig products, curret techology) Ivolves mathematical techiques (e.g., forecastig sales of color tvs); quatitative i ature Cosistet ad objective; able to cosider much iformatio ad data at oe time. Ofte quatifiable data are ot available. Oly as good as the data o which they are based. 210 / 481 Overview of Qualitative Approaches 1. Jury of executive opiio Pool opiios of high-level experts, sometimes augmeted by statistical models; a group of maagers meet ad come up with a forecast. Good for strategic or e product forecastig. Oe perso s opiio ca domiate the forecast. 2. Delphi method Pael of experts, queried iteratively; seeks to develop a cosesus amog a group of experts. Excellet for forecastig log-term product developmet, techological chages, ad scietific advaces. Time-cosumig to develop. 3. Sales force composite Estimates from idividual salespersos are reviewed for reasoableess, the aggregated 4. Cosumer Market Survey Ask the customer, uses surveys ad iterviews to idetify customer prefereces. Good determiat of cosumer prefereces. It ca be difficult to develop a good questioaire. 211 / 481

5 Overview of Quatitative Approaches 1. Naive approach Uses last period s actual value as a forecast. Simple ad easy to use. Oly good if data chage little from period to period. 2. Simple Movig averages A forecast method is which oly of the most recet observatios are averaged. Oly good for level patter. Importat to select the proper movig average. 3. Weighted Movig Average A forecastig method where of the most recet observatios ad past observatios may have differet weights. Good for level patter; allows placig differet weights o past values. Selectio of weights requires good judgemet. 212 / 481 Overview of Quatitative Approaches 4. Expoetial smoothig A weighted average procedure with with weights decliig expoetially as data become older. Provides excellet for short- to medium-legth forecasts Choice of smoothig parameter, α,is critical. 5. Expoetial smoothig with tred adjustmet A expoetial smoothig method with separate equatios for forecastig the level ad tred. Provides good results for tred data. Should oly be used for data with tred. 6. Tred projectio Techique uses the least-squares method to fit a straight lie to past data over time. Easy to use ad uderstad. Data should display a clear tred over time. 7. Liear regressio Uses the least-squares method to model a liear relatioship betwee two variables. Easy to uderstad; provides god forecast accuracy. Make sure a liear relatioship is preset. 213 / 481

6 Naïve approach Assumes ext period s forecast is equal to the curret period s actual value. e.g., if sales were 500 uits i Jauary, the Naïve method would forecast 500 uits for February. Simple ad easy to use, sometimes cost effective ad efficiet. Ca be good startig poit. Oly good if data chage little from period to period. F t+1 = A t where F t+1 = forecast for ext period, t +1 A t = actual value for curret period, t t = the curret period 214 / 481 Simple Movig Average Simple MA is a series of arithmetic meas, whe oly of the most recet observatios are average. Used if little or o tred presets, good for level patter. Used ofte for smoothig Provides overall impressio of data over time Movig Average = Demad i previous periods F t+1 = A t + A t 1 + A t A t Example, = 3 F 2013 = A A A = the umber of periods or data poits to be average; F t+1 =forecast of demad for ext period, t +1;A t = actual value for curret period, t; 215 / 481

7 Figure It Out: Simple Movig Average A hospital is cosiderig the purchase of a ew ambulace. The decisio will rest partly o the aticipated mileage to be drive i The miles drive durig the past 5 years are as follows: Year Actual Milage Forecast the mileage for 2013 usig a 2-year movig average. 216 / 481 Solutio: Simple Movig Average Year Actual Milage (A) Forecasted Milage (F) F 2010 = = F 2011 = = F 2012 = = F 2013 = = / 481

8 Actual Milage ad Forecast with Simple Movig Average 218 / 481 Weighted Movig Average Used whe some tred might be preset. Older data usually less importat. Weights based o experiece ad ituitio. Weighted Movig Average = (weight for period )(Demad i previous periods) weights F t+1 = (w 1 A t + w 2 A t w A t ) (21) (w 1 + w w ) where: w 1, w 2,..., w are weights for the i-th observatio or period; w 1 is a weight for the most recet value. 219 / 481

9 Figure It Out Forecast the mileage for 2013 usig a 2-year movig average. Year Actual Milage Weights Period 3 Last year 2 Two years ago 5 Sum of weights 220 / 481 Solutio: Weighted Movig Average Year Actual Milage (A) Forecasted Milage (F) F 2010 = = F 2011 = = F 2012 = = F 2013 = = / 481

10 Actual Milage ad Forecast with Weighted Movig Average 222 / 481 Potetial Problems With Movig Average Icreasig smooths the forecast but makes it less sesitive to chages. Do ot forecast treds well. Require extesive historical data. 223 / 481

11 Expoetial Smoothig Form of weighted movig average Weights declie expoetially Most recet data weighted most Requires smoothig costat (α) Rages from 0 to 1 Subjectively chose Ivolves little record keepig of past data 224 / 481 Expoetial Smoothig Expoetial Smoothig F t = F t 1 + α(a t 1 F t 1 ) (22) where F t = ew forecast F t 1 = previous period s forecast A t 1 = previous period s actual value α = smoothig (or weightig) costat (0 α 1) Choice of smoothig costat Choose high values of α whe uderlyig average is likely to chage. Choose low values of α whe uderlyig average is stable. 225 / 481

12 Figure It Out - Expoetial Smoothig A restaurat used expoetial smoothig to forecast mothly usage of tabasco sauce. Its forecast for September was 200 bottles, whereas the actual usage i September was 300 bottles. If the restaurat s maagers use α of 0.70, what is their forecast for October? Previous period forecasted usage (F t 1 ) = 200 bottles Previous period actual usage (A t 1 ) = 300 bottles Smoothig costat α =0.70 F t = F t 1 + α(a t 1 F t 1 ) F t = ( ) = 270 bottles. 1. If the maagers use a α of 1.00, what is their forecast of the sauce usage for the moth of October? 2. If the maagers use a aïve method, what is their forecast of the sauce usage for the moth of October? 226 / 481 Figure It Out: Expoetial Smoothig A hospital is cosiderig the purchase of a ew ambulace. The decisio will rest partly o the aticipated mileage to be drive i The miles drive durig the past 5 years are as follows: Year Milage Suppose the operatio maager had predicted i 2007 that 2008, F 2008, milage would be Usig expoetial smoothig method with a weight of α =0.30, forecast for 2009 through / 481

13 Solutio- Expoetial Smoothig For example, Year Actual Milage forecasted Milage ( )= ( )= ( )= ( )= ( )=3557 F 2009 = F α(a F )=F α(a 2008 F 2008 ) F 2009 = ( ) = / 481 Actual Milage ad Forecast with Expoetial Smoothig 229 / 481

14 What if the data has a tred? Expoetial Smoothig with Tred Adjustmet Whe a tred is preset, expoetial smoothig must be modified Forecast icludig Tred (FIT t ) = Expoetially smoothed forecast (F t ) + Expoetial smoothed tred (T t ). 1. Step 1: Compute F t, smoothig the level of the series F t = α(a t 1 )+(1 α)(f t 1 + T t 1 ) (23) 2. Step 2: ComputeT t, smoothig the tred T t = β(f t F t 1 )+(1 β)t t 1 (24) 3. Step 3: Calculate the forecast FIT t = F t + T t, forecastig icludig tred FIT t = F t + T t (25) where: F t = smoothed forecast for time period t; T t = smoothed tred for time period t; FIT t = forecast icludig tred for time period t; α=smoothig costat for forecasts; β=smoothig costat for tred. 230 / 481 Figure It Out- Expoetial Smoothig With Tred A hospital is cosiderig the purchase of a ew ambulace. The decisio will rest partly o the aticipated mileage to be drive i The miles drive durig the past 5 years are as follows: Year actual Milage Smoothed Forecast Smoothed Tred FIT ??? The tred through 2007, T 2007, has bee 200 additioal milage. The forecast for 2007, F 2007, has bee 3200 milage. The actual milage for 2007, A 2007, was The hospital uses α =0.20 ad β =0.10. Usig expoetial smoothig with tred (FIT), forecast for 2009 through / 481

15 Solutio- Expoetial Smoothig With Tred Forecast for 2008: Year A t F t T t FIT t Step 1 : F 2008 = α(a 2007 )+(1 α)(f T 2007 ) F 2008 = (1 0.2) ( ) = 3380 Step 2 : T 2008 = β(f 2008 F 2007 )+(1 β)t 2007 T 2008 =0.1 ( ) + (1 0.1) 200 = 198 Step 3 : FIT 2008 = F T 2008 = = / 481 Measurig Forecast Accuracy Forecasts are rarely perfect. How does a maager kow how much a forecast ca be off the mark ad still be reasoable? The choice of a forecastig model depeds o its accuracy. Forecast error: The forecast error (deviatio) is defied as the differece betwee the actual ad forecast values for a give period E t = A t F t E t = forecast error; A t =actualvalue;f t = forecast value; However, error for oe time period does ot tell us very much. We eed to measure forecast accuracy over time. Positive errors occur whe A t > F t, ad egative errors occur whe A t < F t. Forecast errors ifluece decisios i two ways: i makig choice amog various forecastig techiques i cotrollig the forecastig process 233 / 481

16 Commo used Measures of Forecast Error 1. Mea absolute deviatio (MAD): is a measure of forecast error that computes errors as the average of the absolute errors. actual forecast MAD = 2. Mea squared error (MSE): is a measure of forecast error that computes error as the average of the squared errors (actual forecast) 2 MSE = 3. Mea Absolute Percet Error (MAPE) ( error actual MAPE = ) 100% where error = actual forecast Decisio Rule: Select the forecast method with the lowest MAD, MAD or MAPE. Note that MSE magifies larger errors, which puts higher pealty o large errors. 234 / 481 Trackig Sigal: Moitorig ad Cotrollig Forecasts Whe there is a differece betwee forecast ad actual values, oe eed to check whether the differece is caused by radom variatio or is due to a bias i the forecast. Forecast bias is a persistet tedecy for a forecast to be over or uder the actual value of the data. Oe way to cotrol for forecast bias is to use a trackig sigal. A trackig sigal is a tool used to moitor the quality of a forecast. (actual foercast) Trackig sigal = MAD To moitor forecast accuracy, the values of the trackig sigal are compared agaist predetermied limits. The limits are usually based o judgemet ad experiece ad ca rage fro ±3 to±8. For example, the limit ±4 compares to 3 stadard deviatios. If errors fall outside the chose limits, the forecast should be reviewed. 235 / 481

17 Mea Absolute Deviatio (MAD) Mea absolute deviatio is the average of absolute value of forecast errors. MAD = actual forecast t=1 = A t F t t=1 = E t t=1 A T F t E t E t Year Actual α =0.3 α =0.6 α =0.3 α =0.6 α =0.3 α = Sum MAD The result idicates that α =0.6 is a better choice because we seek a lower MAD. 236 / 481 Mea Squared Error (MSE) The mea squared error (MSE) is the average of the squared differece betwee the actual ad the forecasted values. MSE = (actual forecast) 2 t=1 = (A t F t ) 2 t=1 = Et 2 t=1 A T F t E t Et 2 Year Actual α =0.3 α =0.6 α =0.3 α =0.6 α =0.3 α = Sum MSE The result idicates that α =0.6 is a better choice because we seek a lower MSE. 237 / 481

18 Mea Absolute Percet Error (MAPE) The mea absolute percet error (MAPE) is the average of the absolute differeces betwee the forecast ad the actual values, ad is expressed as a percet of actual values. MAPE = 100 actual t forecast t /Actual t t=1 = At F t = Et A T F t E t 100 E t /A t Year Actual α =0.3 α =0.6 α =0.3 α =0.6 α =0.3 α = Sum MAPE The result idicates that α =0.6 is a better choice. 238 / 481 Try It Out: Mea Absolute Percet Error (MAPE) A forecastig method has produced the followig over the past five moths. Actual Forecast Error Error Error Error /A What are the MAD, MSE ad MAPE? , 2.0, , 4, , 10, , 2, , 10, / 481

19 Usig Regressio Aalysis for Forecastig Liear regressio aalysis is a straight-lie mathematical/statistical model to describe the fuctioal relatioships betwee idepedet ad depedet variables. y t = α + βx t where y t = value of the depedet variable (e.g., milage) α = y-axis itercept β = slope of the regressio lie x t = idepedet variable 240 / 481 Figure It Out 1. A maagemet aalyst is usig expoetial smoothig to predict merchadize returs at a upscale brach of a departmet store chai. Give a actual umber of returs of 154 items i Jauary, a forecast of 174 items for Jauary, ad a smoothig costat of 0.3, what is the forecast for February? How would the forecast be chaged if the smoothig costat were 0.6? Explai the differece i terms of alpha ad resposiveess. 2. A firm has modeled its experiece with idustrial accidets ad foud that the umber of accidets per year (Y ) is related to the umber of employees (X ) by the regressio equatio Y = X. R 2 is The regressio is based o 20 aual observatios. The firm iteds to employ 480 workers ext year. How may accidets do you project? How much cofidece do you have i that forecast? 241 / 481

20 Solutios 1. Merchadize returs: F Feb = F Ja +0.3 (A Ja F Ja ) = ( ) = 168 F Feb = F Ja +0.3 (A Ja F Ja ) = ( ) = 162 The larger the smoothig costat i a expoetially smoothed forecast, the more resposive the forecast. 2. Idustrial accidet: Y = * 480 = = accidets. Cofidece comes from the coefficiet of determiatio; the model explais 68% of the variatio i umber of accidets, which seems acceptable. 242 / 481 Questios Aaïve forecast for September sales of a product would be equal to the forecast for August.(T/F) 2. Whe the smoothig costat α = 1, the expoetial smoothig model is equivalet to the aïve forecastig model.(t/f) 3. Erollmet i a particular class for the last four semesters has bee 120, 126, 110, ad 130. Suppose a oe-semester movig average was used to forecast erollmet (this is sometimes referred to as a aïve forecast). Thus, the forecast for the secod semester would be 120, for the third semester it would be 126, ad for the last semester it would be 110. What would the MSE be for this situatio? 4. Daily demad for ewspapers for the last 10 days has bee as follows: 12, 13, 16, 15, 12, 18, 14, 12, 13, 15 (listed from oldest to most recet). Forecast sales for the ext day usig a two-day movig average. 5. Sales for boxes of Girl Scout cookies over a 4-moth period were forecasted as follows: 100, 120, 115, ad 123. The actual results over the 4-moth period were as follows: 110, 114, 119, 115. What was the MAD of the 4-moth forecast? 17 ANS: 1)F 2) T 3) , 4) 14 5) / 481

II. Descriptive Statistics D. Linear Correlation and Regression. 1. Linear Correlation

II. Descriptive Statistics D. Liear Correlatio ad Regressio I this sectio Liear Correlatio Cause ad Effect Liear Regressio 1. Liear Correlatio Quatifyig Liear Correlatio The Pearso product-momet correlatio