4 – 1 PSM10 © 2006 Prentice Hall, Inc. PowerPoint presentation to accompany Heizer/Render Operations Management, 8e Chapter 4 – Forecasting

4 – 2 PSM10 What is Forecasting?  Process of predicting a future event  Underlying basis of all business decisions  Production  Inventory  Personnel  Facilities ??

4 – 3 PSM10 Forecasting Time Horizons  Short-range forecast  Up to 1 year, generally less than 3 months  Purchasing, job scheduling, workforce levels, job assignments, production levels  Medium-range forecast  3 months to 3 years  Sales and production planning, budgeting  Long-range forecast  3 + years  New product planning, facility location, research and development

4 – 4 PSM10 Distinguishing Differences  Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes  Short-term forecasting usually employs different methodologies than longer-term forecasting  Short-term forecasts tend to be more accurate than longer-term forecasts

4 – 5 PSM10 Influence of Product Life Cycle  Introduction and growth require longer forecasts than maturity and decline  As product passes through life cycle, forecasts are useful in projecting  Staffing levels  Inventory levels  Factory capacity Introduction – Growth – Maturity – Decline

4 – 6 PSM10 Types of Forecasts  Economic forecasts  Address business cycle – inflation rate, money supply, housing starts, etc.  Technological forecasts  Predict rate of technological progress  Impacts development of new products  Demand forecasts  Predict sales of existing product

4 – 7 PSM10 Strategic Importance of Forecasting  Human Resources – Hiring, training, laying off workers  Capacity – Capacity shortages can result in undependable delivery, loss of customers, loss of market share  Supply-Chain Management – Good supplier relations and price advance

4 – 8 PSM10 Seven Steps in Forecasting 1.Determine the use of the forecast 2.Select the items to be forecasted 3.Determine the time horizon of the forecast 4.Select the forecasting model(s) 5.Gather the data 6.Make the forecast 7.Validate and implement results

4 – 9 PSM10 The Realities!  Forecasts are seldom perfect  Most techniques assume an underlying stability in the system  Product family and aggregated forecasts are more accurate than individual product forecasts

4 – 10 PSM10 Forecasting Approaches  Used when situation is vague and little data exist  New products  New technology  Involves intuition, experience  e.g., forecasting sales on Internet Qualitative Methods

4 – 11 PSM10 Forecasting Approaches  Used when situation is ‘stable’ and historical data exist  Existing products  Current technology  Involves mathematical techniques  e.g., forecasting sales of color televisions Quantitative Methods

4 – 12 PSM10 Overview of Qualitative Methods  Jury of executive opinion  Pool opinions of high-level executives, sometimes augment by statistical models  Delphi method  Panel of experts, queried iteratively

4 – 13 PSM10 Overview of Qualitative Methods  Sales force composite  Estimates from individual salespersons are reviewed for reasonableness, then aggregated  Consumer Market Survey  Ask the customer

4 – 14 PSM10  Involves small group of high-level managers  Group estimates demand by working together  Combines managerial experience with statistical models  Relatively quick  ‘Group-think’ disadvantage Jury of Executive Opinion

4 – 15 PSM10 Sales Force Composite  Each salesperson projects his or her sales  Combined at district and national levels  Sales reps know customers’ wants  Tends to be overly optimistic

4 – 16 PSM10 Delphi Method  Iterative group process, continues until consensus is reached  3 types of participants  Decision makers  Staff  Respondents Staff (Administering survey) Decision Makers (Evaluate responses and make decisions) Respondents (People who can make valuable judgments)

4 – 17 PSM10 Consumer Market Survey  Ask customers about purchasing plans  What consumers say, and what they actually do are often different  Sometimes difficult to answer

4 – 18 PSM10 Overview of Quantitative Approaches 1.Naive approach 2.Moving averages 3.Exponential smoothing 4.Trend projection 5.Linear regression Time-Series Models Associative Model

4 – 19 PSM10 Time Series Forecasting  Set of evenly spaced numerical data  Obtained by observing response variable at regular time periods  Forecast based only on past values  Assumes that factors influencing past and present will continue influence in future

4 – 20 PSM10 Trend Seasonal Cyclical Random Time Series Components

4 – 21 PSM10 Components of Demand Demand for product or service |||| 1234 Year Average demand over four years Seasonal peaks Trend component Actual demand Random variation

4 – 22 PSM10 Trend Component  Persistent, overall upward or downward pattern  Changes due to population, technology, age, culture, etc.  Typically several years duration

4 – 23 PSM10 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

4 – 24 PSM10 Cyclical Component  Repeating up and down movements  Affected by business cycle, political, and economic factors  Multiple years duration  Often causal or associative relationships

4 – 25 PSM10 Random Component  Erratic, unsystematic, ‘residual’ fluctuations  Due to random variation or unforeseen events  Short duration and nonrepeating MTWTFMTWTFMTWTFMTWTF

4 – 26 PSM10 Naive Approach  Assumes demand in next period is the same as demand in most recent period  e.g., If May sales were 48, then June sales will be 48  Sometimes cost effective and efficient

4 – 27 PSM10 Moving Average Method  MA is a series of arithmetic means  Used if little or no trend  Used often for smoothing  Provides overall impression of data over time Moving average = ∑ demand in previous n periods n

4 – 28 PSM10 January10 February12 March13 April16 May19 June23 July26 Actual3-Month MonthShed SalesMoving Average ( )/3 = 13 2 / 3 ( )/3 = 16 ( )/3 = 19 1 / 3 Moving Average Example ( )/3 = 11 2 / 3

4 – 29 PSM10 Graph of Moving Average ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Shed Sales – – – – – – – – – – – Actual Sales Moving Average Forecast

4 – 30 PSM10 Weighted Moving Average  Used when trend is present  Older data usually less important  Weights based on experience and intuition Weighted moving average = ∑ (weight for period n) x (demand in period n) ∑ weights

4 – 31 PSM10 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 / 2 Weighted Moving Average [(3 x 13) + (2 x 12) + (10)]/6 = 12 1 / 6 Weights AppliedPeriod 3Last month 2Two months ago 1Three months ago 6Sum of weights

4 – 32 PSM10 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

4 – 33 PSM10 Moving Average And Weighted Moving Average – – – – – 5 5 – Sales demand ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Actual sales Moving average Weighted moving average

4 – 34 PSM10 Exponential Smoothing  Form of weighted moving average  Weights decline exponentially  Most recent data weighted most  Requires smoothing constant (  )  Ranges from 0 to 1  Subjectively chosen  Involves little record keeping of past data

4 – 35 PSM10 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)

4 – 36 PSM10 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20

4 – 37 PSM10 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20 New forecast= (153 – 142)

4 – 38 PSM10 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20 New forecast= (153 – 142) = = ≈ 144 cars

4 – 39 PSM10 Effect of Smoothing Constants Weight Assigned to Most2nd Most3rd Most4th Most5th Most RecentRecentRecentRecentRecent SmoothingPeriodPeriodPeriodPeriodPeriod Constant(  )  (1 -  )  (1 -  ) 2  (1 -  ) 3  (1 -  ) 4  =  =

4 – 40 PSM10 Impact of Different  – – – – ||||||||| ||||||||| Quarter Demand  =.1 Actual demand  =.5

4 – 41 PSM10 Choosing  The objective is to obtain the most accurate forecast no matter the technique We generally do this by selecting the model that gives us the lowest forecast error Forecast error= Actual demand - Forecast value = A t - F t

4 – 42 PSM10 Other interpretation F t = F t – 1 +  (A t - F t – 1 ) – forecast for the t+1st period, A t – demand of the t-th period Exponential smoothing is the weighted average of the complete historic demand. The weights are decreasing exponentially from period to period.

4 – 43 PSM10 Common Measures of Error Mean Absolute Deviation (MAD) MAD = ∑ |actual - forecast| n Mean Squared Error (MSE) MSE = ∑ (forecast errors) 2 n

4 – 44 PSM10 Common Measures of Error Mean Absolute Percent Error (MAPE) MAPE = 100 ∑ |actual i - forecast i |/actual i n n i = 1

4 – 45 PSM10 Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =

4 – 46 PSM10 Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD = ∑ |deviations| n = 84/8 = For  =.10 = 100/8 = For  =.50

4 – 47 PSM10 Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD = 1,558/8 = For  =.10 = 1,612/8 = For  =.50 MSE = ∑ (forecast errors) 2 n

4 – 48 PSM10 Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD MSE = 45.62/8 = 5.70% For  =.10 = 54.8/8 = 6.85% For  =.50 MAPE = 100 ∑ |deviation i |/actual i n i = 1

4 – 49 PSM10 Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD MSE MAPE5.70%6.85%

4 – 50 PSM10 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

4 – 51 PSM10 Exponential Smoothing with Trend Adjustment Step 1: Compute F t Step 2: Compute T t Step 3: Calculate the forecast FIT t = F t + T t

4 – 52 PSM10 Exponential Smoothing with Trend Adjustment Example Forecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t

4 – 53 PSM10 Exponential Smoothing with Trend Adjustment Example Forecast 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

4 – 54 PSM10 Exponential Smoothing with Trend Adjustment Example Forecast 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

4 – 55 PSM10 Exponential Smoothing with Trend Adjustment Example Forecast 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

4 – 56 PSM10 Exponential Smoothing with Trend Adjustment Example Forecast ActualSmoothedSmoothedIncluding Month(t)Demand (A t )Forecast, F t Trend, T t Trend, FIT t

4 – 57 PSM10 Exponential Smoothing with Trend Adjustment Example ||||||||| ||||||||| Time (month) Product demand – – – – – – 5 5 – 0 0 – Actual demand (A t ) Forecast including trend (FIT t )

4 – 58 PSM10 Trend Projections Fitting a trend line to historical data points to project into the medium-to-long-range Linear trends can be found using the least squares technique (regression analysis) 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 ^

4 – 59 PSM10 Least Squares Method Time period Values of Dependent Variable Deviation 1 Deviation 5 Deviation 7 Deviation 2 Deviation 6 Deviation 4 Deviation 3 Actual observation (y value) Trend line, y = a + bx ^

4 – 60 PSM10 Least Squares Method Time period Values of Dependent Variable 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)

4 – 61 PSM10 Least Squares Method Equations to calculate the regression variables b =  xy - nxy  x 2 - nx 2 y = a + bx ^ a = y - bx

4 – 62 PSM10 Least Squares Example b = = = ∑xy - nxy ∑x 2 - nx 2 3,063 - (7)(4)(98.86) (7)(4 2 ) a = y - bx = (4) = TimeElectrical Power YearPeriod (x)Demandx 2 xy ∑x = 28∑y = 692∑x 2 = 140∑xy = 3,063 x = 4y = 98.86

4 – 63 PSM10 Least Squares Example b = = =  xy - nxy  x 2 - nx 2 3,063 - (7)(4)(98.86) (7)(4 2 ) a = y - bx = (4) = TimeElectrical Power YearPeriod (x)Demandx 2 xy  x = 28  y = 692  x 2 = 140  xy = 3,063 x = 4y = The trend line is y = x ^

4 – 64 PSM10 Least Squares Example ||||||||| – – – – – – – – – – – – Year Power demand Trend line, y = x ^ 141=56.7+8*10.54

4 – 65 PSM10 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

4 – 66 PSM10 Seasonal Variations In Data The multiplicative seasonal model can modify trend data to accommodate seasonal variations in demand 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

4 – 67 PSM10 Seasonal Index Example Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec DemandAverageAverage Seasonal Month MonthlyIndex

4 – 68 PSM10 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

4 – 69 PSM10 Seasonal Index Example Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec DemandAverageAverage Seasonal Month MonthlyIndex 1,128

4 – 70 PSM10 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 2006

4 – 71 PSM10 Seasonal Index Example Jan 95,70 Feb 85,10 Mar 90,40 Apr 106,40 May 130,90 Jun 122,30 Jul 111,70 Aug 106,40 Sept 95,70 Oct 85,10 Nov Dec

4 – 72 PSM10 Seasonal Index Example – – – – – – – – ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Time Demand 2006 Forecast 2005 Demand 2004 Demand 2003 Demand

4 – 73 PSM10 Monitoring and Controlling Forecasts  Measures how well the forecast is predicting actual values  Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD)  Good tracking signal has low values  If forecasts are continually high or low, the forecast has a bias error Tracking Signal

4 – 74 PSM10 Monitoring and Controlling Forecasts Tracking signal RSFEMAD= = ∑(actual demand in period i - forecast demand in period i)  ∑|actual - forecast|/n)

4 – 75 PSM10 Tracking Signal Tracking signal + 0 MADs – Upper control limit Lower control limit Time Signal exceeding limit Acceptable range

4 – 76 PSM10 Tracking Signal Example Cumulative AbsoluteAbsolute ActualForecastForecastForecast QtrDemandDemandErrorRSFEErrorErrorMAD

4 – 77 PSM10Cumulative AbsoluteAbsolute ActualForecastForecastForecast QtrDemandDemandErrorRSFEErrorErrorMAD Tracking Signal Example 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

4 – 78 PSM10 Forecasting in the Service Sector  Presents unusual challenges  Special need for short term records  Needs differ greatly as function of industry and product  Holidays and other calendar events  Unusual events

4 – 79 PSM10Questions Answer the following questions How would you rate the time horizon for long range forecast in the field of mobile information technologies? Which of the Seven Steps in Forecasting is the most interesting for you? Did you ever use the method of “Jury of Executive Opinion” when discussing family affairs at home? Which week sides if the Delphi method would you identify? Under which circumstances do the Weighted Moving Average method and the method of exponential smoothing coincide? Can the two methods of exponential smoothing ever coincide? Look for the various opportunities of using forecast methods by Excel. Let the demand follow the function d(t) = t and apply the simple weighted average forecast method with n = 2. What can you say about the tracking signal?

4 – 80 PSM10Questions Homework No. 3: Create an Excel Spreadsheet to solve the following problem! Sales of music stands at Johnny Ho’s music store, in Columbus, Ohio, over the past 10 weeks are shown in the table below. WeekDemandWeekDemand ? a)Forecast demand for each week, including week 10, using exponential smoothing with α = 0.3 (initial forecast F 1 = 20) b)Compute the MAD. c)Compute the tracking signal. Submit your solution file via to (term: ). Don’t forget to indicate your university ID card number. Put here the last digit of your university ID card number.