Forcasting

Forecasting1Group Members..Muhammad Sarfaraz UW-10-ME-BE-82Hassan Zahid UW-10-ME-BE-84Muhammad Adnan UW-10-ME-BE-862What is forecasting..Forecasting is the art of science of predicting future events. It may involve taking historical data and projecting them into the future with some sort of mathematical model.It is the estimating the future demand for products and services.3Forecasting Time HorizonsShort-range forecastUp to 1 year (usually less than 3 months)Job scheduling, worker assignments, plan for purchasingMedium-range forecast3 months to 3 yearsSales & production planning, budgetingLong-range forecast3 years, or moreNew product planning, facility location

4Types of ForecastsEconomic forecastsAddress the future business conditions (e.g., inflation rate, money supply, etc.)Technological forecastsPredict the rate of technological progressPredict acceptance of new productsDemand forecastsPredict sales of existing products

5The Strategic Importance of ForecastingForecast of demand therefore drive decisions in many areas. Lets look at he impact of product forecast on three activities i-eHuman Resources Hiring, training, laying off workersCapacity Capacity shortages can result in undependable delivery, loss of customers, loss of market shareSupply Chain Management Good supplier relations and price advantages

6Seven Steps in ForecastingDetermine the purpose of the forecastSelect the items to be forecastedDetermine the time horizon of the forecastSelect the forecasting model(s)Gather the dataMake the forecastValidate and implement results

7Forecasting ApproachesQualitative Methods

Used when situation is vague & little data existNew productsNew technologyInvolves intuition, experiencee.g., forecasting sales on InternetQuantitative Methods

Used when situation is stable & historical data existExisting productsCurrent technologyInvolves mathematical techniquese.g., forecasting sales of color televisions

8Overview of Qualitative MethodsJury of executive opinionPool opinions of high-level executives, sometimes augment by statistical modelsDelphi method or judge mental methodPanel of experts, queried iterativelySales force compositeEstimates from individual salespersons are reviewed for reasonableness, then aggregated Consumer (Market research) SurveyAsk the customer

9Overview of Quantitative MethodsTime Series Models:Assumes information needed to generate a forecast is contained in a time series of dataAssumes the future will follow same patterns as the pastCausal Models or Associative ModelsExplores cause-and-effect relationshipsUses leading indicators to predict the futureHousing starts and appliance sales

10Decomposition of Time seriesNaive approachMoving averageExponential smoothing Trend projectionLinear regression analysis

Time-Series ModelsAssociative Model111.Naive ApproachAssumes demand in next period is equal to the actual demand in most recent periode.g., If May sales were 48, then June sales will be 48Sometimes cost effective & efficient

122.Moving Average MethodMoving average uses a number of most recent historical actual data values to generate a forecast.MA is a series of arithmetic means Used if little or no trendUsed often for smoothingProvides overall impression of data over timeEquation:MAnnDemand in Previous Periods13January10February12March13April16May19June23July26Actual3-MonthMonthShed SalesMoving Average(12 + 13 + 16)/3 = 13 2/3(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1/3101213(10 + 12 + 13)/3 = 11 2/3Moving Average Example14||||||||||||JFMAMJJASONDShed Sales30 28 26 24 22 20 18 16 14 12 10 Actual SalesMoving Average ForecastGraph of Moving Average15Used when trend is present Older data usually less importantWeights based on experience and intuitionWeightedmoving average= (weight for period n) x (demand in period n) weightsWeighted Moving Average1616January10February12March13April16May19June23July26Actual3-Month WeightedMonthShed SalesMoving Average[(3 x 16) + (2 x 13) + (12)]/6 = 141/3[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 201/2101213[(3 x 13) + (2 x 12) + (10)]/6 = 121/6Weighted Moving Average1730 25 20 15 10 5 Sales demand||||||||||||JFMAMJJASONDActual salesMoving averageWeighted moving averageFigure 4.2Moving Average And Weighted Moving Average183.Exponential Smoothing MethodIt requires only three items of data this periods forecast, the actual demand for this period and which is referred to as a smoothing constant and having value between 0 and 1 New forecast = Last periods forecast + {Last periods actual demand Last periods forecast}

19New forecast =Last periods forecast+ a (Last periods actual demand Last periods forecast)Ft = Ft 1 + a(At 1 - Ft 1)whereFt=new forecastFt 1=previous forecasta=smoothing (or weighting) constant (0 a 1)Exponential Smoothing2020Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant a = .20New forecast= 142 + .2(153 142)= 142 + 2.2= 144.2 144 carsExponential Smoothing Example21225 200 175 150 |||||||||123456789QuarterDemanda = .1Actual demanda = .5Impact of Different 22Chose high values of when underlying average is likely to changeChoose low values of when underlying average is stable23Measuring Forecast ErrorForecasts are never perfectNeed to know how much we should rely on our chosen forecasting methodMeasuring forecast error:

Note that over-forecasts = negative errors and under-forecasts = positive errors

2424Mean Absolute Deviation (MAD)MAD = |Actual - Forecast|nMean Squared Error (MSE)MSE = (Forecast Errors)2nCommon Measures of Error25Mean Absolute Percent Error (MAPE)MAPE =100|Actuali - Forecasti|/Actualinni = 1Common Measures of Error26When a trend is present, exponential smoothing must be modifiedForecast including (FITt) = trendExponentiallyExponentiallysmoothed (Ft) +(Tt)smoothedforecasttrendExponential Smoothing with Trend Adjustment2727Ft = a(At - 1) + (1 - a)(Ft - 1 + Tt - 1)Tt = b(Ft - Ft - 1) + (1 - b)Tt - 1Step 1: Compute FtStep 2: Compute TtStep 3: Calculate the forecast FITt = Ft + TtExponential Smoothing with Trend Adjustment2828ForecastActualSmoothedSmoothedIncludingMonth(t)Demand (At)Forecast, FtTrend, TtTrend, FITt11211213.0021732041952462173182893610Table 4.1Exponential Smoothing with Trend Adjustment2929ForecastActualSmoothedSmoothedIncludingMonth(t)Demand (At)Forecast, FtTrend, TtTrend, FITt11211213.0021732041952462173182893610Table 4.1F2 = aA1 + (1 - a)(F1 + T1)F2 = (.2)(12) + (1 - .2)(11 + 2)= 2.4 + 10.4 = 12.8 unitsStep 1: Forecast for Month 2Exponential Smoothing with Trend Adjustment3030ForecastActualSmoothedSmoothedIncludingMonth(t)Demand (At)Forecast, FtTrend, TtTrend, FITt11211213.0021712.8032041952462173182893610Table 4.1T2 = b(F2 - F1) + (1 - b)T1T2 = (.4)(12.8 - 11) + (1 - .4)(2)= .72 + 1.2 = 1.92 unitsStep 2: Trend for Month 2Exponential Smoothing with Trend Adjustment3131ForecastActualSmoothedSmoothedIncludingMonth(t)Demand (At)Forecast, FtTrend, TtTrend, FITt11211213.0021712.801.9232041952462173182893610Table 4.1FIT2 = F2 + T1FIT2 = 12.8 + 1.92= 14.72 unitsStep 3: Calculate FIT for Month 2Exponential Smoothing with Trend Adjustment3232ForecastActualSmoothedSmoothedIncludingMonth(t)Demand (At)Forecast, FtTrend, TtTrend, FITt11211213.0021712.801.9214.7232041952462173182893610Table 4.115.182.1017.2817.822.3220.1419.912.2322.1422.512.3824.8924.112.0726.1827.142.4529.5929.282.3231.6032.482.6835.16Exponential Smoothing with Trend Adjustment3333Figure 4.3|||||||||123456789Time (month)Product demand35 30 25 20 15 10 5 0 Actual demand (At)Forecast including trend (FITt)with = .2 and = .4Exponential Smoothing with Trend Adjustment3434Fitting a trend line to historical data points to project into the medium to long-rangeLinear trends can be found using the least squares techniquey = a + bx^where y= computed value of the variable to be predicted (dependent variable)a= y-axis interceptb= slope of the regression linex= the independent variable^Trend Projections3535Time periodValues of Dependent VariableFigure 4.4Deviation1(error)Deviation5Deviation7Deviation2Deviation6Deviation4Deviation3Actual observation (y value)Trend line, y = a + bx^Least Squares Method36Equations to calculate the regression variablesb =Sxy - nxySx2 - nx2y = a + bx^a = y - bxLeast Squares Method37b = = = 10.54xy - nxyx2 - nx23,063 - (7)(4)(98.86)140 - (7)(42)a = y - bx = 98.86 - 10.54(4) = 56.70TimeElectrical Power YearPeriod (x)Demandx2xy20011741742002279415820033809240200449016360200551052552520056142368522007712249854x = 28y = 692x2 = 140xy = 3,063x = 4y = 98.86Least Squares Example3838b = = = 10.54Sxy - nxySx2 - nx23,063 - (7)(4)(98.86)140 - (7)(42)a = y - bx = 98.86 - 10.54(4) = 56.70TimeElectrical Power YearPeriod (x)Demandx2xy19991741742000279415820013809240200249016360200351052552520046142368522005712249854Sx = 28Sy = 692Sx2 = 140Sxy = 3,063x = 4y = 98.86The trend line isy = 56.70 + 10.54x^Least Squares Example3939 Time Series Components

40Demand for product or service||||1234YearAverage demand over four yearsSeasonal peaksTrend componentActual demandRandom variationFigure 4.1Components of Demand4141Trend ComponentPersistent, overall upward or downward patternDue to population, technology etc.Several years duration

42Seasonal ComponentRegular pattern of up & down fluctuationsDue to weather, customs, etc.Occurs within 1 year

Number ofPeriodLengthSeasonsWeekDay7MonthWeek4-4.5MonthDay28-31YearQuarter4YearMonth12YearWeek5243Cyclical ComponentRepeating up & down movementsDue to interactions of factors influencing economyCan be anywhere between 2-30+ years duration

0510152044Random ComponentErratic, unsystematic, residual fluctuationsDue to random variation or unforeseen eventsUnion strikeTornadoShort duration & non-repeating

MTWTF45Factors to be considered in the selection of forecasting methodThe amount & type of available dataSome methods require more data than othersDegree of accuracy requiredIncreasing accuracy means more dataLength of forecast horizonDifferent models for 3 month vs. 10 yearsPresence of data patternsLagging will occur when a forecasting model meant for a level pattern is applied with a trend

4647Forecasting SoftwareSpreadsheetsMicrosoft Excel, Quattro Pro, Lotus 1-2-3 Limited statistical analysis of forecast dataStatistical packagesSPSS, SAS, NCSS, MinitabForecasting plus statistical and graphicsSpecialty forecasting packagesForecast Master, Forecast Pro, Autobox, SCA4748Summary Three basic principles of forecasting are: forecasts are rarely perfect, are more accurate for groups than individual items, and are more accurate in the shorter term than longer time horizons.The forecasting process involves five steps: decide what to forecast, evaluate and analyze appropriate data, select and test model, generate forecast, and monitor accuracy.Forecasting methods can be classified into two groups: qualitative and quantitative. Qualitative methods are based on the subjective opinion of the forecaster and quantitative methods are based on mathematical modeling.4849Continue...There are four basic patterns of data: level or horizontal, trend, seasonality, and cycles. In addition, data usually contain random variation. Some forecast models used to forecast the level of a time series are: nave, simple mean, simple moving average, weighted moving average, and exponential smoothing. Separate models are used to forecast trends and seasonality.A simple causal model is linear regression in which a straight-line relationship is modeled between the variable we are forecasting and another variable in the environment. The correlation is used to measure the strength of the linear relationship between these two variables.4950 continueThree useful measures of forecast error are mean absolute deviation (MAD), mean square error (MSE) and tracking signal.There are four factors to consider when selecting a model: amount and type of data available, degree of accuracy required, length of forecast horizon, and patterns present in the data.

50ThanxAny question???51