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© 1997 Prentice-Hall, Inc. S2 - 1 Principles of Operations Management Forecasting Chapter S2

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© 1997 Prentice-Hall, Inc. S2 - 2 Learning Objectives n Define forecasting n Describe types of forecasts n Describe time series n Use time series forecasting methods n Use causal forecasting methods n Explain how to monitor & control forecasts

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© 1997 Prentice-Hall, Inc. S2 - 3 What Is Forecasting? n Process of predicting a future event n Underlying basis of all business decisions l Production l Inventory l Personnel l Facilities Sales will be $200 Million!

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© 1997 Prentice-Hall, Inc. S2 - 4 Types of Forecasts by Time Horizon n Short-range forecast l Up to 1 year; usually < 3 months l Job scheduling, worker assignments n Medium-range forecast l 3 months to 3 years l Sales & production planning, budgeting n Long-range forecast l 3+ years l New product planning, facility location

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© 1997 Prentice-Hall, Inc. S2 - 5 Types of Forecasts by Item Forecast n Economic forecasts l Address business cycle l e.g., inflation rate, money supply etc. n Technological forecasts l Predict technological change l Predict new product sales n Demand forecasts l Predict existing product sales

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© 1997 Prentice-Hall, Inc. S2 - 6 n Used when situation is ‘stable’ & historical data exist l Existing products l Current technology n Involves mathematical techniques n e.g., forecasting sales of color televisions Quantitative Methods Forecasting Approaches n Used when situation is vague & little data exist l New products l New technology n Involves intuition, experience n e.g., forecasting sales on Internet Qualitative Methods

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© 1997 Prentice-Hall, Inc. S2 - 7 Qualitative Forecasting Methods

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© 1997 Prentice-Hall, Inc. S2 - 8 Naive Approach n Assumes demand in next period is the same as demand in most recent period n e.g., If May sales were 48, then June sales will be 48 n Sometimes cost effective & efficient © 1995 Corel Corp.

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© 1997 Prentice-Hall, Inc. S2 - 9 Jury of Executive Opinion n Involves small group of high-level managers l Group estimates demand by working together n Combines managerial experience with statistical models n Relatively quick n ‘Group-think’ disadvantage © 1995 Corel Corp.

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© 1997 Prentice-Hall, Inc. S2 - 10 Delphi Method n Iterative group process n 3 types of people l Decision makers l Staff l Respondents n Reduces ‘group- think’ Decision Makers (Sales?) (Sales will be 50!) Respondents (Sales will be 45, 50, 55) Staff (What will sales be? survey)

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© 1997 Prentice-Hall, Inc. S2 - 11 Sales Force Composite n Each salesperson projects their sales n Combined at district & national levels n Sales rep’s know customers’ wants n Tends to be overly optimistic Sales © 1995 Corel Corp.

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© 1997 Prentice-Hall, Inc. S2 - 12 Consumer Market Survey n Ask customers about purchasing plans n What consumers say, & what they actually do are often different n Sometimes difficult to answer How many hours will you use the Internet next week? © 1995 Corel Corp.

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© 1997 Prentice-Hall, Inc. S2 - 13 Causal Models Quantitative Forecasting Methods Quantitative Forecasting Time Series Models Linear Regression Exponential Smoothing Trend Projection Moving Average

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© 1997 Prentice-Hall, Inc. S2 - 14 What’s a Time Series? n Set of evenly spaced numerical data l Obtained by observing response variable at regular time periods n Forecast based only on past values l Assumes that factors influencing past, present, & future will continue n Example Year:19931994199519961997 Sales:78.763.589.793.292.1

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© 1997 Prentice-Hall, Inc. S2 - 15 Trend Component n Persistent, overall upward or downward pattern n Due to population, technology etc. n Several years duration Mo., Qtr., Yr. Response © 1984-1994 T/Maker Co.

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© 1997 Prentice-Hall, Inc. S2 - 16 Cyclical Component n Repeating up & down movements n Due to interactions of factors influencing economy n Usually 2-10 years duration Mo., Qtr., Yr. Response Cycle B

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© 1997 Prentice-Hall, Inc. S2 - 17 Seasonal Component n Regular pattern of up & down fluctuations n Due to weather, customs etc. n Occurs within 1 year Mo., Qtr. Response Summer © 1984-1994 T/Maker Co.

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© 1997 Prentice-Hall, Inc. S2 - 18 Random Component n Erratic, unsystematic, ‘residual’ fluctuations n Due to random variation or unforeseen events l Union strike l Tornado n Short duration & nonrepeating © 1984-1994 T/Maker Co.

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© 1997 Prentice-Hall, Inc. S2 - 19 Moving Average Method n MA is a series of arithmetic means n Used if little or no trend n Used often for smoothing l Provides overall impression of data over time n Equation MA n n Demand in Previous Periods Periods

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© 1997 Prentice-Hall, Inc. S2 - 20 You’re manager of a museum store that sells historical replicas. You want to forecast sales (000) for 1998 using a 3-period moving average. 19934 1994 6 19955 19963 19977 Moving Average Example © 1995 Corel Corp.

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© 1997 Prentice-Hall, Inc. S2 - 21 Time Response Y i Moving Total (n = 3) Moving Avg. ( n = 3) 19934NANA 19946NANA 19955NANA 19963 4 + 6 + 5 = 15 15/3 = 5.0 19977 6 + 5 + 3 = 14 14/3 = 4.7 1998NA 5 + 3 + 7 = 15 15/3 = 5.0 Moving Average Solution

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© 1997 Prentice-Hall, Inc. S2 - 22 Moving Average Graph Year Sales 0 2 4 6 8 939495969798 Actual Forecast

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© 1997 Prentice-Hall, Inc. S2 - 23 Moving Average Thinking Challenge You work for Firestone Tire. You want to forecast sales using a 3-period moving average. 199320,000 1994 24,000 199522,000 199626,000 199725,000 AloneGroupClass

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© 1997 Prentice-Hall, Inc. S2 - 24 Moving Average Solution* YearSalesMA(3) YearSalesMA(3) 199320,000 1994 24,000 199522,000 199626,000 199725,000 1998NA

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© 1997 Prentice-Hall, Inc. S2 - 25 Disadvantages of Moving Averages n Increasing n makes forecast less sensitive to changes n Do not forecast trend well n Require much historical data © 1984-1994 T/Maker Co.

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© 1997 Prentice-Hall, Inc. S2 - 26 Exponential Smoothing Method n Form of weighted moving average l Weights decline exponentially l Most recent data weighted most Requires smoothing constant ( ) Requires smoothing constant ( ) l Ranges from 0 to 1 l Subjectively chosen n Involves little record keeping of past data

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© 1997 Prentice-Hall, Inc. S2 - 27 Exponential Smoothing Equations n F t = Forecast value next period n F t-1 = Forecast value last period n A t-1 = Actual value last period = Smoothing constant = Smoothing constant F t = F t-1 + ·(A t-1 - F t-1 ) F t = F t-1 + ·(A t-1 - F t-1 )

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© 1997 Prentice-Hall, Inc. S2 - 28 You’re organizing a Kwanza meeting. You want to forecast attendance for 1998 using exponential smoothing ( =.10). The 1993 forecast was 175. 1993180 1994 168 1995159 1996175 1997190 Exponential Smoothing Example © 1995 Corel Corp.

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© 1997 Prentice-Hall, Inc. S2 - 29 Exponential Smoothing Solution F t = F t-1 + · (A t-1 - F t-1 ) TimeActual Forecast,F t ( =.10) 1993180 175.00 (Given) 1994168 175.00 +.10(180 - 175.00) = 175.50 1995159 1996175 1997190 1998NA

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© 1997 Prentice-Hall, Inc. S2 - 30 Exponential Smoothing Solution F t = F t-1 + · (A t-1 - F t-1 ) TimeActual Forecast,F t ( =.10) 1993180 175.00 (Given) 1994168 175.00 +.10(180 - 175.00) = 175.50 1995159 175.50 +.10(168 - 175.50) = 174.75 1996175 174.75 +.10(159 - 174.75) = 173.18 1997190 173.18 +.10(175 - 173.18) = 173.36 1998NA 173.36 +.10(190 - 173.36) = 175.02

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© 1997 Prentice-Hall, Inc. S2 - 31 Exponential Smoothing Graph Year Sales 140 150 160 170 180 190 939495969798 Actual Forecast

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© 1997 Prentice-Hall, Inc. S2 - 32 Exponential Smoothing Thinking Challenge You’re an economist for GM. You want to forecast next year’s car sales. You decide to use exponential smoothing with =.25. Yearly sales (million units) in order are 2, 4, 1, 3. Assume that the first year’s forecast was 1. © 1995 Corel Corp. AloneGroupClass

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© 1997 Prentice-Hall, Inc. S2 - 33 1.F 1 = 1.00 2.F 2 = 3.F 3 = 4.F 4 = 5.F 5 = Exponential Smoothing Solution*

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© 1997 Prentice-Hall, Inc. S2 - 34 Linear Trend Projection n Used for forecasting linear trend line n Assumes relationship between response variable Y & time X is a linear function n Estimated by least squares method l Minimizes sum of squared errors

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© 1997 Prentice-Hall, Inc. S2 - 35 Y X Linear Regression Model Observed value YabX ii YabX ii Error Error Regression line

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© 1997 Prentice-Hall, Inc. S2 - 36 CorrelationCorrelation n Answers ‘how strong is the linear relationship between 2 variables?’ n Coefficient of correlation used l Sample correlation coefficient denoted r l Values range from -1 to +1 l Measures degree of association n Used mainly for understanding

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© 1997 Prentice-Hall, Inc. S2 - 37 Coefficient of Correlation Values +1.00 Perfect Positive Correlation Increasing degree of negative correlation -.5+.5 Perfect Negative Correlation No Correlation Increasing degree of positive correlation

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© 1997 Prentice-Hall, Inc. S2 - 38 Guidelines for Selecting Forecasting Model n No pattern or direction in forecast error l Error = (Y i - Y i ) = (Actual - Forecast) l Seen in plots of errors over time n Smallest forecast error l Mean square error (MSE) l Mean absolute deviation (MAD) ^^

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© 1997 Prentice-Hall, Inc. S2 - 39 Pattern of Forecast Error Trend Not Fully Accounted for Desired Pattern Time (Years) ErrorError 00 Error 0

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© 1997 Prentice-Hall, Inc. S2 - 40 Forecast Error Equations n Mean Square Error (MSE) n Mean Absolute Deviation (MAD)

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© 1997 Prentice-Hall, Inc. S2 - 41 Selecting Forecasting Model Example You’re a marketing analyst for Hasbro Toys. You’ve forecast sales with a linear model & expo. smoothing. Which model do you use? ActualLinear ModelExpo Smooth YearSalesForecastForecast (.9) 199210.61.0 199311.31.0 199422.01.9 199522.72.0 199643.43.8

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© 1997 Prentice-Hall, Inc. S2 - 42 Year ^ Y i Y i ^ 199210.6 0.4 0.40.160.4 199311.3-0.30.090.3 199422.0 0.0 0.00.000.0 199522.7-0.70.490.7 199643.4 0.6 0.60.360.6 Total0.01.102.0 Linear Model Evaluation MSE = Error 2 / n = 1.10 / 5 =.220 MAD = |Error| / n = 2.0 / 5 =.400 Error Error 2 |Error|

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© 1997 Prentice-Hall, Inc. S2 - 43 Exponential Smoothing Model Evaluation Year Y i Y i 199211.00.00.000.0 199311.00.00.000.0 199421.90.10.010.1 199522.00.00.000.0 199643.80.20.040.2 Total0.30.050.3 ^ MSE = Error 2 / n = 0.05 / 5 = 0.01 MAD = |Error| / n = 0.3 / 5 = 0.06 Error Error 2 |Error|

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© 1997 Prentice-Hall, Inc. S2 - 44 Tracking Signal n Measures how well forecast is predicting actual values n Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD) l Good tracking signal has low values n Should be within upper & lower control limits

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© 1997 Prentice-Hall, Inc. S2 - 45 Tracking Signal Equation

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© 1997 Prentice-Hall, Inc. S2 - 46 Tracking Signal Computation*

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© 1997 Prentice-Hall, Inc. S2 - 47 Tracking Signal Plot

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© 1997 Prentice-Hall, Inc. S2 - 48 ConclusionConclusion n Defined forecasting n Described types of forecasts n Described time series n Used time series forecasting methods n Used causal forecasting methods n Explained how to monitor & control forecasts

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