What Is Forecasting? Chapter 11. How Famous People Feel About Forecasts? Learning Objectives. We Classify Forecasting Methods Into Three Types

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1 Chapter 11 Forecasting Demand for Services What Is Forecasting? Predicting the future How many people will buy dell dimension 8200 on December? Estimating/measuring the reliability of the prediction Forecasts are always wrong except by accident Learning Objectives Understand sources of demand variability. Able to pick the appropriate ing model. Exponential smoothing and moving average. Linear regression and time series. Seasonality. How Famous People Feel About Forecasts? "Prediction is very difficult, especially if it's about the future." --Nils Bohr, Nobel laureate in physics. "If you have to, often. " --A useful survival tactic for a consultant. I think there is a world market for maybe five computers. --Thomas Watson ( ), chairman of IBM, IBM alone produces over 1 million computers per year. We Classify Forecasting Methods Into Three Types Judgmental Uses subjective inputs Time series Assumes past is best predictor of future Associative Uses explanatory variables to predict the future Judgmental Forecasts Judgmental s are subjective, based on Executive opinions Sales force composite Consumer surveys Outside opinion Opinions of managers and staff Delphi method

2 Time Series Forecasts Time series s are often prepared by decomposing the data Trend Long-term movement in data Seasonality Short-term regular variations in data Irregular variations Caused by unusual circumstances Random variations Associative Forecasts Associative s assume a correlation with predictor variables Predictor variables Used to predict values of variable interest Regression Technique for fitting a line to a set Least squares line Minimizes sum of squared deviations around the line Caused by chance Judgmental Forecasts Pros Easy to prepare Can be used when no appropriate data exist for other methods Relatively easy to start with new items Cons Accuracy is poor More often represent the ers hopes rather than probable outcomes Next, Associative Forecasts Pros Some methods (e.g. Linear regression) are straight forward Use causal relationships Useful for sensitivity Produce measures of correlation Cons Data intensive Computation intensive Non-linear methods may not be easy Linear regression may not be feasible Difficult to start with new items Lastly, Time Series Forecasts Demand Patterns Pros Methods range from easy to complex Some methods are data and computation efficient Does not require causal variable identification Cons Some methods are data and/or computation intensive Cannot incorporate causal/co-relational relationships Very difficult to start with new items Quantity Time (a) Horizontal: Data cluster about a horizontal line.

3 Demand Patterns Demand Patterns Quantity Quantity Year 1 Year 2 Time (b) Trend: Data consistently increase or decrease. J F M A M J J A S O N D Months (c) Seasonal: Data consistently show peaks and valleys. Demand Patterns Demand Patterns Quantity Demand Years (d) Cyclical: Data reveal gradual increases and decreases over extended periods Period (E) seasonal multiplicative pattern Demand Patterns Demand Period (F) seasonal additive pattern Linear Regression Regression line Y = a + bx Least-squares regression line Prediction r 2 Causation and association

4 Prediction Choose the explanatory and response variables Plot the data Look for a straight-line relationship Fit the data for regression line Substitute the value of x and calculate y Causal Methods Linear Regression Dependent variable Y Estimate of Y from regression equation Deviation, or error { Actual value of Y Value of X used to estimate Y Independent variable Regression equation: Y = a + bx X Regression Line Summarizes the relationship between two variables. The variables must be explanatory and response variables. Describes how y changes as x takes different values. Use a regression line to predict the value of y for a given value of x. Regression Line: Equation Different people can draw different regression lines for a given graph A regression line that is the closest to the points in the vertical direction (y). A way to find an equation for the line. Least-squares regression line Minimizes the sum of squares of the vertical distances of the data points Y = a + bx A is the y-intercept B is the slope of the line Finding the LS Equation Sales Advertising Month (000 units) (000 $) a = Y bx b = ΣXY nxy ΣX 2 nx 2 Finding the LS Equation Sales, Y Advertising, X Month (000 units) (000 $) XY X 2 Y , , , , ,681 Total ,259 Y = 171 X = 1.64 a = Y bx b = (1.64)(171) (1.64) 2

5 Finding the LS Equation Sales, Y Advertising, X Month (000 units) (000 $) XY X 2 Y , , , , ,681 Total ,259 Y = 171 X = 1.64 a = b = Y = (X) Forecasting/prediction Y = (x) Forecast for month 6: Advertising expenditure = $1750 Y = (1.75) = Prediction: More Given the equation of the regression line Y = (x) What is the value for the intercept? What does the intercept mean here? What is the value for the slope? What does the slope mean in this example? Understanding Prediction Prediction works best when the model fits the data closely. Prediction outside the range of data of available data is risky (extrapolation). Check for outliers What is r 2 The square of the correlation is the fraction of the variation in the values of y that is explained by x The variation that occurs in y can be attributed to the changing x values variation in predicted y as x pulls it along the line r 2 = total variation in observed values of y Using r 2 Correlation tells how close the points are to the line r 2 is the measure of how successful the regression was in explaining the response

6 Finding r and r 2 Sales, Y Advertising, X Month (000 units) (000 $) XY X 2 Y , , , , ,681 Total ,259 Y = 171 X = 1.64 r = nσxy ΣX ΣY [nσx 2 (ΣX) 2 ][nσy 2 (ΣY) 2 ] Finding r and r 2 Sales, Y Advertising, X Month (000 units) (000 $) XY X 2 Y , , , , ,681 Total ,259 Y = 171 X = 1.64 r = 0.98 r 2 = 0.96 σ YX = r2: Example Given the numerical value of the correlation for the sales/advertising data r = 0.98 What percent of variation in sales is explained by how much the advertising expenditure is? The Question of Causation A strong relationship between two variables does not always mean that changes in one variable cause changes in the other. The relationship between two variables is often influenced by other variables in the background. The best evidence for causation comes form randomized comparative experiments. Association and Causation A high association can mean one of the following scenarios: Causation Common response Confounding Now We re Going to Focus on Time Series Methods Quantitative ing methods Forecasts are not based on predictive variables Inherent assumption: the past is the best predictor of the future

7 Time Series Forecasts Time series s can address all of these components Trend Seasonality Cycles Random variations Time Series Forecasts Most time series methods involve some form of averaging Moving average (MA) Weighted moving average (WMA) Exponential smoothing (ES) Basic Notations D 1,D 2, D t : the demand of values observed during periods 1,2,...,t. F t : the made for period t in period t-1 before D t is observed Naive Forecast Method What is the for month 5? Month Customer Simple Moving Averages The procedure F t +1 = D t + D t D t n +1 n D t : actual demand in period t n: number of periods in the average Moving Averages The main idea behind a MA is to smooth random variations Uses a number of the most recent data values Each data value has equal weight

8 Simple Moving Averages Simple Moving Averages Simple Moving Averages Simple Moving Averages Patient Arrivals Patient Arrivals F 4 = Simple Moving Averages Patient Arrivals F 4 = Simple Moving Averages Patient Arrivals F 5 = 3

9 Simple Moving Averages Patient Arrivals F 5 = Implications of Increasing N differences in responsiveness 3-week MA 6-week MA Simple Moving Average Month Customer Weighted Moving Average F t+ 1 = WD 1 t + WD 2 t Wn Dt n+ 1 n W 1 i = Weighted Moving Average 3-week MA 6-week MA Weighted Moving Average Assigned weights t 0.70 t t Weighted Moving Average 3-week MA 6-week MA Weighted Moving Average Assigned weights t 0.70 t t F 4 = 0.70(411) (380) (400)

10 Weighted Moving Average 3-week MA 6-week MA Weighted Moving Average Assigned weights t 0.70 t t F 4 = Weighted Moving Average 3-week MA 6-week MA Weighted Moving Average Assigned weights t 0.70 t t F 4 = 404 F 5 = Weighted Moving Average Month Customer Moving Averages (MA & WMA) Let s review what we know about moving averages (MA & WMA) We need n data values for an n-period moving average We need n weighting factors for an n- period weighted moving average The responsiveness of the is determined by n (ES) Now let s look at exponential smoothing (ES) Requires only three parameters Previous Current data value Smoothing factor (often referred to as a smoothing constant) Smoothing controls responsiveness F t + 1 α : = F + α( D F ) t t t a smoothingparameter with a valuebetween 0 and1

11 Is just a weighted average between the old (old ES average) and the new data value Efficiently incorporates more distant data values through the old α = 0.10 F t +1 = F t + α (D t F t ) α = 0.10 α = 0.10 F t +1 = F t + α (D t F t ) F 3 = ( )/2 D 3 = 411 F 4 = 0.10(411) (390) F t +1 = F t + α (D t F t ) F 3 = ( )/2 D 3 = 411 F 4 = α = 0.10 F t +1 = F t + α (D t F t ) F 4 = D 4 = 415 F 4 = F 5 = 394.4

12 3-week MA 6-week MA Exponential smoothing α = 0.10 Exponential smoothing α = 0.10 Month Customer Advantages. Simplicity. Minimal data requirements compared to moving average. Inexpensive. Disadvantages. Lags behind changes in underlying average. Does not account for any factors other than the series past performance. Require only three parameters. Are controlled by the smoothing factor on interval [0,1]. Values close to 0 (large n) provide very stable (unresponsive) s. Values close to 1 (small n) provide very aggressive (responsive) s. Moving Average and ES We can approximate moving average with ES! 2 α n + 1 n 2 α α

13 Smooth estimates for the series average as well as the trend Actual blood test requests Trend-adjusted Trend-adjusted Actual blood test requests Number of time periods Demand smoothing coefficient (α ) 0.20 Initial demand value Trend-smoothing coefficient (β ) 0.20 Actual blood Estimate of trend 3.00 test requests Smoothed Trend Forecast Trend-adjusted Arrivals Average Average Forecast Error Actual blood test requests Smoothed Trend Forecast 80 Arrivals Average Trend-adjusted Average Forecast Error SUMMARY Average 44 demand Mean 37square error Mean absolute deviation Forecast 38 for week Actual blood 7 Forecast 57 for week test requests 8 Forecast 61 for week

14 The er for Canine Gourmet dog breath fresheners estimated (in March) the series average to be 300,000 cases sold per month and the trend to be +8,000 per month. The actual sales for April were 330,000 cases. What are the s for May and July, assuming alpha 0.2 and beta 0.1? Seasonal Patterns (a) Multiplicative pattern Seasonal Patterns (b) Additive pattern Demand Demand Period Period Seasonal Influences Multiplicative seasonal method Seasonal Influences Quarter Year 1 Year 2 Year 3 Year Total Average

15 Seasonal Patterns Forecast Error Forecast error is the difference between the actual demand and. Et = Dt Ft Cumulative sum of errors (CFE). Useful for bias measurement. Used in tracking signals. Average error equals CFE divided by the number of data points. Forecast Error Mean absolute deviation (MAD) Measures dispersion of errors Easier for managers to understand than standard deviation Standard deviation (σ) Measures dispersion of errors Want to have small values of σ MAD = 0.8 σ σ = 1.25MAD Forecast Error Mean squared error (MSE). Measures dispersion of errors. Places greater weight than MAD on large errors. Mean absolute percent error (MAPE) Relates error to level of demand Puts the size of a error in proper perspective Forecast Error Forecast Error Absolute Error Absolute Percent Month, Demand, Forecast, Error, Squared, Error, Error, t D t F t E t E 2 t E t ( E t /D t )(100) % Total %

16 Forecast Error Measures of Error Absolute CFE = 15 Error Absolute 15 Percent E Month, = Demand, = Forecast, Error, Squared, Error, Error, 8 t D t F t E t E 2 t E t 5275 ( E t /D t )(100) MSE 1= 200 = % σ = MAD = = % MAPE = = 10.2% 8 Total % Criteria for Selecting Time Series Methods Statistical criteria Minimize bias. Minimize MAD or MSE. Meet managerial expectations of changes. Minimize the error last period. Use a holdout set (data from more recent periods) as a final test, after constructing model from data from earlier periods.