4-1 Operations Management Forecasting Chapter 4

4-2 Learning Objectives When you complete this chapter, you should be able to : Identify or Define :  Forecasting  Types of forecasts  Time horizons  Approaches to forecasts

4-3 Learning Objectives - continued When you complete this chapter, you should be able to : Describe or Explain:  Moving averages  Exponential smoothing  Trend projections  Regression and correlation analysis  Measures of forecast accuracy

4-4 What is Forecasting?  Process of predicting a future event  Underlying basis of all business decisions  Production  Inventory  Personnel  Facilities

4-5  Short-range forecast  Up to 1 year; usually less than 3 months  Job scheduling, worker assignments  Medium-range forecast  3 months to 3 years  Sales & production planning, budgeting  Long-range forecast  3 + years  New product planning, facility location Types of Forecasts by Time Horizon

4-6 Short-term vs. Longer-term Forecasting  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.

4-7 Influence of Product Life Cycle  Stages of introduction and growth require longer forecasts than maturity and decline  Forecasts useful in projecting  staffing levels,  inventory levels, and  factory capacity as product passes through life cycle stages Introduction, Growth, Maturity, Decline

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J Types of Forecasts  Economic forecasts  Address business cycle, e.g., inflation rate, money supply etc.  Technological forecasts  Predict rate of technological progress  Predict acceptance of new product  Demand forecasts  Predict sales of existing product

4-9 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

4-10 Product Demand Charted over 4 Years with Trend and Seasonality Year 1 Year 2 Year 3 Year 4 Seasonal peaksTrend component Actual demand line Average demand over four years Demand for product or service Random variation

4-11 Actual Demand, Moving Average, Weighted Moving Average Actual sales Moving average Weighted moving average

4-12 Realities of Forecasting  Forecasts are seldom perfect  Most forecasting methods assume that there is some underlying stability in the system  Both product family and aggregated product forecasts are more accurate than individual product forecasts

4-13 Forecasting Approaches  Used when situation is ‘stable’ & historical data exist  Existing products  Current technology  Involves mathematical techniques  e.g., forecasting sales of color televisions Quantitative Methods  Used when situation is vague & little data exist  New products  New technology  Involves intuition, experience  e.g., forecasting sales on Internet Qualitative Methods

4-14 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  Sales force composite  Estimates from individual salespersons are reviewed for reasonableness, then aggregated  Consumer Market Survey  Ask the customer

4-15  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

4-16 Sales Force Composite  Each salesperson projects his or her sales  Combined at district & national levels  Sales reps know customers’ wants  Tends to be overly optimistic

4-17 Delphi Method  Iterative group process  3 types of people  Decision makers  Staff  Respondents  Reduces ‘group-think’ Respondents Staff Decision Makers (Sales?) ( What will sales be? survey) (Sales will be 45, 50, 55) (Sales will be 50!)

4-18 Consumer Market Survey  Ask customers about purchasing plans  What consumers say, and what they actually do are often different  Sometimes difficult to answer How many hours will you use the Internet next week?

4-19 Overview of Quantitative Approaches  Naïve approach  Moving averages  Exponential smoothing  Trend projection  Linear regression Time-series Models Associative models

4-20 Quantitative Forecasting Methods (Non-Naive) Quantitative Forecasting Linear Regression Associative Models Exponential Smoothing Moving Average Time Series Models Trend Projection

4-21  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  Example Year: Sales: What is a Time Series?

4-22 Trend Seasonal Cyclical Random Time Series Components

4-23  Persistent, overall upward or downward pattern  Due to population, technology etc.  Several years duration Mo., Qtr., Yr. Response Trend Component

4-24  Regular pattern of up & down fluctuations  Due to weather, customs etc.  Occurs within 1 year Mo., Qtr. Response Summer Seasonal Component

4-25 Common Seasonal Patterns Period of Pattern “Season” Length Number of “Seasons” in Pattern WeekDay7 MonthWeek4 – 4 ½ MonthDay28 – 31 YearQuarter4 YearMonth12 YearWeek52

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J  Repeating up & down movements  Due to interactions of factors influencing economy  Usually 2-10 years duration Mo., Qtr., Yr. Response Cycle  Cyclical Component

4-27  Erratic, unsystematic, ‘residual’ fluctuations  Due to random variation or unforeseen events  Union strike  Tornado  Short duration & nonrepeating Random Component

4-28  Any observed value in a time series is the product (or sum) of time series components  Multiplicative model  Y i = T i · S i · C i · R i (if quarterly or mo. data)  Additive model  Y i = T i + S i + C i + R i (if quarterly or mo. data) General Time Series Models

4-29 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 & efficient

4-30  MA is a series of arithmetic means  Used if little or no trend  Used often for smoothing  Provides overall impression of data over time  Equation MA n n  Demand in Previous Periods Periods Moving Average Method

4-31 You’re manager of a museum store that sells historical replicas. You want to forecast sales (000) for 2003 using a 3-period moving average Moving Average Example

4-32 Moving Average Solution

4-33 Moving Average Solution

4-34 Moving Average Solution

Year Sales Actual Forecast Moving Average Graph

4-36  Used when trend is present  Older data usually less important  Weights based on intuition  Often lay between 0 & 1, & sum to 1.0  Equation WMA = Σ(Weight for period n) (Demand in period n) ΣWeights Weighted Moving Average Method

4-37 Actual Demand, Moving Average, Weighted Moving Average Actual sales Moving average Weighted moving average

4-38  Increasing n makes forecast less sensitive to changes  Do not forecast trend well  Require much historical data Disadvantages of Moving Average Methods

4-39  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 Exponential Smoothing Method

4-40  F t =  A t  (1-  ) A t  (1-  ) 2 ·A t  (1-  ) 3 A t  (1-  ) t- 1 ·A 0  F t = Forecast value  A t = Actual value   = Smoothing constant  F t = F t -1 +  ( A t -1 - F t -1 )  Use for computing forecast Exponential Smoothing Equations

4-41 During the past 8 quarters, the Port of Baltimore has unloaded large quantities of grain. (  =.10). The first quarter forecast was QuarterActual ? Exponential Smoothing Example Find the forecast for the 9 th quarter.

4-42 F t = F t ( A t -1 - F t -1 ) QuarterActual Forecast, F t ( α =.10) (Given) Exponential Smoothing Solution

4-43 Quarter Actua Actual Forecast, F t ( α =.10) (Given) ( Exponential Smoothing Solution F t = F t ( A t -1 - F t -1 )

4-44 QuarterActual Forecast,F t ( α =.10) (Given) ( Exponential Smoothing Solution F t = F t ( A t -1 - F t -1 )

4-45 QuarterActual Forecast,F t ( α =.10) (Given) ( ) Exponential Smoothing Solution F t = F t ( A t -1 - F t -1 )

4-46 QuarterActual Forecast,F t ( αααα =.10) (Given) ( ) = Exponential Smoothing Solution F t = F t ( A t -1 - F t -1 )

4-47 F t = F t ( A t -1 - F t -1 ) QuarterActual Forecast, F t ( α =.10) (Given) ( ) = ( ) = Exponential Smoothing Solution

4-48 F t = F t ( A t -1 - F t -1 ) Quarter Actual Forecast, F t ( α =.10) (Given) ( ) = ( ) = ( )= Exponential Smoothing Solution

4-49 F t = F t ( A t -1 - F t -1 ) QuarterActual Forecast, F t ( α =.10) (Given) ( ) = ( ) = ( ) = ( ) = Exponential Smoothing Solution

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J F t = F t ( A t -1 - F t -1 ) QuarterActual Forecast, F t ( α =.10) (Given) ( ) = ( ) = ( ) = ( ) = ( ) = Exponential Smoothing Solution

4-51 F t = F t ( A t -1 - F t -1 ) TimeActual Forecast, F t ( α =.10) ( ) = ( ) = ( ) = Exponential Smoothing Solution ( ) =

4-52 F t = F t ( A t -1 - F t -1 ) TimeActual Forecast, F t ( α =.10) ( ) = ( ) = ( ) = Exponential Smoothing Solution ( ) = ( ) = ( ) = ?

4-53 F t =  A t  (1-  ) A t  (1-  ) 2 A t Forecast Effects of Smoothing Constant  Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2 ==  = 0.10  = %

4-54 F t =  A t  (1-  ) A t  (1-  ) 2 A t Forecast Effects of Smoothing Constant  Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2 ==  = 0.10  = % 9%

4-55 F t =  A t  (1-  ) A t  (1-  ) 2 A t Forecast Effects of Smoothing Constant  Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2 ==  = 0.10  = % 9% 8.1%

4-56 F t =  A t  (1-  ) A t  (1-  ) 2 A t Forecast Effects of Smoothing Constant  Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2 ==  = 0.10  = % 9% 8.1% 90%

4-57 F t =  A t  (1-  ) A t  (1-  ) 2 A t Forecast Effects of Smoothing Constant  Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2 ==  = 0.10  = % 9% 8.1% 90%9%

4-58 F t =  A t  (1-  ) A t  (1-  ) 2 A t Forecast Effects of Smoothing Constant  Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2 ==  = 0.10  = % 9% 8.1% 90%9%0.9%

4-59 Choosing  Seek to minimize the Mean Absolute Deviation (MAD) If:Forecast error = demand - forecast Then:

4-60 Exponential Smoothing with Trend Adjustment Forecast including trend (FIT t ) = exponentially smoothed forecast (F t ) + exponentially smoothed trend (T t )

4-61 F t = Last period’s forecast +  (Last period’s actual – Last period’s forecast) F t = F t-1 +  (A t-1 – F t-1 ) or T t =  (Forecast this period - Forecast last period) + (1-  )(Trend estimate last period T t =  (F t - F t-1 ) + (1-  )T t-1 or Exponential Smoothing with Trend Adjustment - continued

4-62  F t = exponentially smoothed forecast of the data series in period t  T t = exponentially smoothed trend in period t  A t = actual demand in period t  = smoothing constant for the average  = smoothing constant for the trend Exponential Smoothing with Trend Adjustment - continued

4-63 Comparing Actual and Forecasts

4-64 Regression

4-65 Least Squares Deviation Time Values of Dependent Variable Actual observation Point on regression line

4-66  Used for forecasting linear trend line  Assumes relationship between response variable, Y, and time, X, is a linear function  Estimated by least squares method  Minimizes sum of squared errors i YabX i  Linear Trend Projection

4-67 b > 0 b < 0 a a Y Time, X Linear Trend Projection Model

4-68 Least Squares Equations Equation: Slope: Y-Intercept:

4-69 Computation Table

4-70 Using a Trend Line YearDemand The demand for electrical power at N.Y.Edison over the years 1997 – 2003 is given at the left. Find the overall trend.

4-71 Finding a Trend Line YearTime Period Power Demand x2x2 xy  x=28  y=692  x 2 =140  xy=3,063

4-72 The Trend Line Equation

4-73 Multiplicative Seasonal Model  Find average historical demand for each “season” by summing the demand for that season in each year, and dividing by the number of years for which you have data.  Compute the average demand over all seasons by dividing the total average annual demand by the number of seasons.  Compute a seasonal index by dividing that season’s historical demand (from step 1) by the average demand over all seasons.  Estimate next year’s total demand  Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for that season. This provides the seasonal forecast.

4-74 YX ii = a b  Shows linear relationship between dependent & explanatory variables  Example: Sales & advertising ( not time) Dependent (response) variable Independent (explanatory) variable Slope Y-intercept ^ Linear Regression Model +

4-75 Y X Y a i  ^ ii bX i = ++ + Error Observed value YabX = ++ Regression line Linear Regression Model

4-76 Linear Regression Equations Equation: Slope: Y-Intercept:

4-77 Computation Table

4-78  Slope ( b )  Estimated Y changes by b for each 1 unit increase in X  If b = 2, then sales ( Y ) is expected to increase by 2 for each 1 unit increase in advertising ( X )  Y-intercept ( a )  Average value of Y when X = 0  If a = 4, then average sales ( Y ) is expected to be 4 when advertising ( X ) is 0 Interpretation of Coefficients

4-79  Variation of actual Y from predicted Y  Measured by standard error of estimate  Sample standard deviation of errors  Denoted S Y,X  Affects several factors  Parameter significance  Prediction accuracy Random Error Variation

4-80 Least Squares Assumptions  Relationship is assumed to be linear. Plot the data first - if curve appears to be present, use curvilinear analysis.  Relationship is assumed to hold only within or slightly outside data range. Do not attempt to predict time periods far beyond the range of the data base.  Deviations around least squares line are assumed to be random.

4-81 Standard Error of the Estimate

4-82  Answers: ‘ how strong is the linear relationship between the variables?’  Coefficient of correlation Sample correlation coefficient denoted r  Values range from -1 to +1  Measures degree of association  Used mainly for understanding Correlation

4-83 Sample Coefficient of Correlation

Perfect Positive Correlation Increasing degree of negative correlation Perfect Negative Correlation No Correlation Increasing degree of positive correlation Coefficient of Correlation Values

4-85 Coefficient of Correlation and Regression Model r 2 = square of correlation coefficient (r), is the percent of the variation in y that is explained by the regression equation

4-86  You want to achieve:  No pattern or direction in forecast error  Error = ( Y i - Y i ) = (Actual - Forecast)  Seen in plots of errors over time  Smallest forecast error  Mean square error (MSE)  Mean absolute deviation (MAD) Guidelines for Selecting Forecasting Model ^

4-87 Time (Years) Error 0 0 Desired Pattern Time (Years) Error 0 Trend Not Fully Accounted for Pattern of Forecast Error

4-88  Mean Square Error (MSE)  Mean Absolute Deviation (MAD)  Mean Absolute Percent Error (MAPE) Forecast Error Equations

4-89 You’re a marketing analyst for Hasbro Toys. You’ve forecast sales with a linear model & exponential smoothing. Which model do you use? ActualLinear ModelExponential Smoothing YearSalesForecastForecast (.9) Selecting Forecasting Model Example

4-90 MSE = Σ Error 2 / n = 1.10 / 5 = MAD = Σ |Error| / n = 2.0 / 5 = MAPE = 100 Σ|absolute percent errors|/ n = 1.20/5 = Linear Model Evaluation Y i ^ Y i ^ Year Total Error Error |Error| Actual

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J MSE = Σ Error 2 / n = 0.05 / 5 = 0.01 MAD = Σ |Error| / n = 0.3 / 5 = 0.06 MAPE = 100 Σ |Absolute percent errors|/ n = 0.10/5 = 0.02 Exponential Smoothing Model Evaluation

4-92 Exponential Smoothing Model Evaluation Linear Model: MSE = Σ Error 2 / n = 1.10 / 5 =.220 MAD = Σ |Error| / n = 2.0 / 5 =.400 MAPE = 100 Σ|absolute percent errors|/ n = 1.20/5 = Exponential Smoothing Model: MSE = Σ Error 2 / n = 0.05 / 5 = 0.01 MAD = Σ |Error| / n = 0.3 / 5 = 0.06 MAPE = 100 Σ |Absolute percent errors|/ n = 0.10/5 = 0.02

4-93  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  Should be within upper and lower control limits Tracking Signal

4-94 Tracking Signal Equation

4-95 Tracking Signal Computation

4-96 Tracking Signal Computation

4-97 Tracking Signal Computation

4-98 Tracking Signal Computation

4-99 Tracking Signal Computation

4-100 Tracking Signal Computation

4-101 Tracking Signal Computation

4-102 Tracking Signal Computation

4-103 Tracking Signal Computation

4-104 Tracking Signal Computation

4-105 Tracking Signal Computation

4-106 Tracking Signal Computation

4-107 Tracking Signal Computation

4-108 Forecasting in the Service Sector  Presents unusual challenges  special need for short term records  needs differ greatly as function of industry and product  issues of holidays and calendar  unusual events