CHAPTER 2 FORECASTING

LEARNING OBJECTIVES Define forecasting, forecasts approaches Understand the three time horizons Describe, Explain and Apply the naïve, moving average, exponential smoothing, and trend method Compute the measures of forecast accuracy Apply a tracking signal

Forecasting? Forecast a statement about the future value of a variable of interest. Forecasting the art and science of predicting future events.

Forecasts Forecasts affect decisions and activities throughout an organization  Accounting, finance  Human resources  Marketing  Operations  Product / service design

Uses of Forecasts AccountingCost/profit estimates FinanceCash flow and funding Human ResourcesHiring/recruiting/training MarketingPricing, promotion, strategy OperationsSchedules, MRP, workloads Product/service design New products and services

I see that you will get an A this semester.

Elements of a Good Forecast Timely Accurate Reliable Meaningful Written Easy to use

Forecasting Time Horizons Short-range forecast Medium-range forecast Long-range forecast

Distinguishing Differences Medium/long range- more comprehensive issues and support management decisions regarding planning and products, plants and processes Short-term- employs different methodologies than longer-term Short-term- more accurate than longer-term forecasts

Influence of Product Life Cycle Best period to increase market share R&D engineering is critical Practical to change price or quality image Strengthen niche Poor time to change image, price, or quality Competitive costs become critical Defend market position Cost control critical IntroductionGrowthMaturityDecline Company Strategy/Issues Internet search engines Sales Xbox 360 Drive-through restaurants CD-ROMs 3 1/2” Floppy disks LCD & plasma TVs Analog TVs iPods

Types of Forecasts Economic forecasts Technological forecasts Demand forecasts

Seven Steps in Forecasting Determine the use of the forecast Select the items to be forecasted Determine the time horizon of the forecast Select the forecasting model(s) Gather the data Make the forecast Validate and implement results

Forecasting Approaches Qualitative Quantitative

Qualitative Approaches Jury of executive opinion Delphi method Sales force composite Consumer market survey

Quantitative Approaches Naïve approach Moving average Exponential smoothing Trend projection Linear regression Time-Series Models

Time Series Forecasting Set of evenly spaced numerical data  Obtained by observing response variable at regular time periods Forecast based only on past values, no other variables important  Assumes that factors influencing past and present will continue influence in future

Time Series Components Trend Seasonal Cycles Random

Components of Demand Demand for product or service |||| 1234 Year Average demand over four years Seasonal peaks Trend component Actual demand Random variation

Trend Component Overall upward or downward pattern Changes due to population, technology, age, culture, etc. Typically several years duration

Seasonal Component Regular pattern of up and down fluctuations Due to weather, customs, etc Occurs within a single year Number of PeriodLengthSeasons WeekDay7 MonthWeek4-4.5 MonthDay28-31 YearQuarter4 YearMonth12 YearWeek52

Cycles Component Repeating up and down movements Affected by business cycle, political, and economic factors Multiple years duration

Random Component Erratic, unsystematic, Due to random variation or unforeseen events Short duration and non-repeating MTWTFMTWTFMTWTFMTWTF

Naive Approach Assumes demand in next period is the same as demand in most recent period Uh, give me a minute.... We sold 250 wheels last week.... Now, next week we should sell....

Moving Average Method Use a number of historical actual data values to generate a forecast An average of the n most recent periods Useful if can assume that market demand will stay fairly steady over time ∑ demand in previous n periods n Moving average =

Moving Average Example January10 February12 March13 April16 May19 June23 July26 Actual3-Month MonthShed SalesMoving Average ( )/3 = 13 2 / 3 ( )/3 = 16 ( )/3 = 19 1 / ( )/3 = 11 2 / 3

Graph of Moving Average ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Shed Sales – – – – – – – – – – – Actual Sales Moving Average Forecast

Weighted Moving Average Used when trend or pattern is present Weights based on experience and intuition Weighted moving average = ∑ (weight for period n) x (demand in period n) ∑ weights

Weighted Moving Average Example January10 February12 March13 April16 May19 June23 July26 Actual3-Month Weighted MonthShed SalesMoving Average [(3 x 16) + (2 x 13) + (12)]/6 = 14 1 / 3 [(3 x 19) + (2 x 16) + (13)]/6 = 17 [(3 x 23) + (2 x 19) + (16)]/6 = 20 1 / [(3 x 13) + (2 x 12) + (10)]/6 = 12 1 / 6 Weights AppliedPeriod 3Last month 2Two months ago 1Three months ago 6Sum of weights

Potential Problems With Moving Average Increasing n smooths the forecast but makes it less sensitive to changes Do not forecast trends well Require extensive historical data

Moving Average And Weighted Moving Average – – – – – 5 5 – Sales demand ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Actual sales Moving average Weighted moving average

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  Weights decline exponentially  Most recent data weighted most Involves little record keeping of past data Requires smoothing constant (  )  Ranges from 0 to 1  Subjectively chosen

Exponential Smoothing New forecast =Last period’s forecast +  (Last period’s actual demand – Last period’s forecast) F t = F t – 1 +  (A t – 1 - F t – 1 ) whereF t =new forecast F t – 1 =previous forecast  =smoothing (or weighting) constant (0 ≤  ≤ 1)

Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20 New forecast= (153 – 142) = = = ≈ 144 cars

Selecting of Smoothing Constant Chose high values of  when actual demand display an increasing (or decreasing) trend Chose low values of  when demand is relatively stable without any trend Chose low values of  when demand is relatively stable without any trend

Exponential Smoothing with Trend Adjustment When a trend is present, exponential smoothing must be modified Forecast including (FIT t ) = trend ExponentiallyExponentially smoothed (F t ) +(T t )smoothed forecasttrend F t =  (A t - 1 ) + (1 -  )(F t T t - 1 ) T t =  (F t - F t - 1 ) + (1 -  )T t - 1

Exponential Smoothing with Trend Adjustment ExampleForecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t

Exponential Smoothing with Trend Adjustment ExampleForecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t F 2 =  A 1 + (1 -  )(F 1 + T 1 ) F 2 = (.2)(12) + (1 -.2)(11 + 2) = = 12.8 units Step 1: Forecast for Month 2

Exponential Smoothing with Trend Adjustment ExampleForecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t T 2 =  (F 2 - F 1 ) + (1 -  )T 1 T 2 = (.4)( ) + (1 -.4)(2) = = 1.92 units Step 2: Trend for Month 2

Exponential Smoothing with Trend Adjustment ExampleForecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t FIT 2 = F 2 + T 1 FIT 2 = = units Step 3: Calculate FIT for Month 2

Exponential Smoothing with Trend Adjustment ExampleForecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t

Exponential Smoothing with Trend Adjustment Example ||||||||| ||||||||| Time (month) Product demand – – – – – – 5 5 – 0 0 – Actual demand (A t ) Forecast including trend (FIT t ) with  =.2 and  =.4

Seasonal Variations In Data Regularly repeating movements (upward or downward) in a time series that can be tie to recurring events.  Multiplicative seasonal method a method whereby seasonal factors are multiplied by an estimate of average demand to arrive at a seasonal forecast.

Seasonal Variations In Data 1.Find average historical demand for each season 2.Compute the average demand over all seasons 3.Compute a seasonal index for each season 4.Estimate next year’s total demand 5.Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for that season Steps in the process:

Seasonal Index Example Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec DemandAverageAverage Seasonal Month MonthlyIndex

Seasonal Index Example Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec DemandAverageAverage Seasonal Month MonthlyIndex Seasonal index = average monthly demand average monthly demand = 90/94 =.957

Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec DemandAverageAverage Seasonal Month MonthlyIndex Seasonal Index Example

Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec DemandAverageAverage Seasonal Month MonthlyIndex Expected annual demand = 1,200 Janx.957 = 96 1, Febx.851 = 85 1, Forecast for 2008 Seasonal Index Example

– – – – – – – – ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Time Demand 2008 Forecast 2007 Demand 2006 Demand 2005 Demand Seasonal Index Example

Associative Forecasting Used when changes in one or more independent variables can be used to predict the changes in the dependent variable Most common technique is linear regression analysis

Regression Analysis Forecasting an outcome based on predictor variables using the least squares technique y = a + bx ^ where y= computed value of the variable to be predicted (dependent variable) a= y-axis intercept b= slope of the regression line x= the independent variable though to predict the value of the dependent variable ^

Least Squares Method Time period Values of Dependent Variable Figure 4.4 Deviation 1 (error) Deviation 5 Deviation 7 Deviation 2 Deviation 6 Deviation 4 Deviation 3 Actual observation (y value) Trend line, y = a + bx ^

Time period Values of Dependent Variable Figure 4.4 Deviation 1 Deviation 5 Deviation 7 Deviation 2 Deviation 6 Deviation 4 Deviation 3 Actual observation (y value) Trend line, y = a + bx ^ Least squares method minimizes the sum of the squared errors (deviations) Least Squares Method

Equations to calculate the regression variables b =  xy - nxy  x 2 - nx 2 y = a + bx ^ a = y - bx Least Squares Method

Least Squares Requirements 1.We always plot the data to insure a linear relationship 2.We do not predict time periods far beyond the database 3.Deviations around the least squares line are assumed to be random

Associative Forecasting Example SalesLocal Payroll ($ millions), y($ billions), x – 3.0 – 2.0 – 1.0 – ||||||| ||||||| Sales Area payroll

Sales, y Payroll, xx 2 xy ∑y = 15.0∑x = 18∑x 2 = 80∑xy = 51.5 x = ∑x/6 = 18/6 = 3 y = ∑y/6 = 15/6 = 2.5 b = = =.25 ∑xy - nxy ∑x 2 - nx (6)(3)(2.5) 80 - (6)(3 2 ) a = y - bx = (.25)(3) = 1.75 Associative Forecasting Example

4.0 – 3.0 – 2.0 – 1.0 – ||||||| ||||||| Sales Area payroll y = x ^ Sales = (payroll) If payroll next year is estimated to be $6 billion, then: Sales = (6) Sales = $3,250, Associative Forecasting Example

Standard Error of the Estimate  A forecast is just a point estimate of a future value  This point is actually the mean of a probability distribution 4.0 – 3.0 – 2.0 – 1.0 – ||||||| ||||||| Sales Area payroll 3.25

wherey=y-value of each data point y c =computed value of the dependent variable, from the regression equation n=number of data points S y,x = ∑(y - y c ) 2 n - 2 Standard Error of the Estimate

Computationally, this equation is considerably easier to use We use the standard error to set up prediction intervals around the point estimate S y,x = ∑y 2 - a∑y - b∑xy n - 2 Standard Error of the Estimate

4.0 – 3.0 – 2.0 – 1.0 – ||||||| ||||||| Sales Area payroll 3.25 S y,x = = ∑y 2 - a∑y - b∑xy n (15) -.25(51.5) S y,x =.306 The standard error of the estimate is $306,000 in sales Standard Error of the Estimate

 How strong is the linear relationship between the variables?  Coefficient of correlation, r, measures degree of association  Values range from -1 to +1 Correlation r = n  xy -  x  y [n  x 2 - (  x) 2 ][n  y 2 - (  y) 2 ]

y x (a)Perfect positive correlation: r = +1 y x (b)Positive correlation: 0 < r < 1 y x (c)No correlation: r = 0 y x (d)Perfect negative correlation: r = -1

Measuring Forecast Error Mean Absolute Deviation (MAD) MAD = ∑ |Actual - Forecast| n Mean Squared Error (MSE) MSE = ∑ (Forecast Errors) 2 n

Mean Absolute Percent Error (MAPE) MAPE = ∑ 100|Actual i - Forecast i |/Actual i n n i = 1 Measuring Forecast Error

Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =

RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD = ∑ |deviations| n = 82.45/8 = For  =.10 = 98.62/8 = For  =.50 Comparison of Forecast Error

RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD = 1,526.54/8 = For  =.10 = 1,561.91/8 = For  =.50 MSE = ∑ (forecast errors) 2 n Comparison of Forecast Error

RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD MSE = 44.75/8 = 5.59% For  =.10 = 54.05/8 = 6.76% For  =.50 MAPE = ∑ 100|deviation i |/actual i n i = 1 Comparison of Forecast Error

RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD MSE MAPE5.59%6.76% Comparison of Forecast Error

 Measures how well the forecast is predicting actual values  Good tracking signal has low values  If forecasts are continually high or low, the forecast has a bias error  +ve signal : demand greater then forecast Monitoring and Controlling Forecasts Tracking Signal

Tracking signal RSFEMAD= = ∑(Actual demand in period i - Forecast demand in period i)  ∑|Actual - Forecast|/n) Monitoring and Controlling Forecasts Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD)

Tracking Signal Tracking signal + 0 MADs – Upper control limit Lower control limit Time Signal exceeding limit Acceptable range

Tracking Signal ExampleCumulative AbsoluteAbsolute ActualForecastForecastForecast QtrDemandDemandErrorRSFEErrorErrorMAD

Cumulative AbsoluteAbsolute ActualForecastForecastForecast QtrDemandDemandErrorRSFEErrorErrorMAD Tracking Signal (RSFE/MAD) -10/10 = /7.5 = -2 0/10 = 0 -10/10 = -1 +5/11 = /14.2 = +2.5 The variation of the tracking signal between -2.0 and +2.5 is within acceptable limits Tracking Signal Example

Forecasting in the Service Sector  Presents unusual challenges  Special need for short term records  Holidays and other calendar events  Unusual events

Fast Food Restaurant Forecast 20% 20% – 15% 15% – 10% 10% – 5% 5% – (Lunchtime)(Dinnertime) Hour of day Percentage of sales Figure 4.12

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