Supply Chain Management SYST 4050 Slides Supply Chain Management Lecture 13 Chapter 1

Outline Today Thursday Friday Chapter 7 SYST 4050 Slides Outline Today Chapter 7 Thursday Network design simulation assignment Chapter 8 Friday Homework 3 due before 5:00pm Chapter 1

Outline February 23 (Today) February 25 March 2 March 4 March 9 SYST 4050 Slides Outline February 23 (Today) Chapter 7 February 25 Network design simulation description Chapter 8 Homework 4 (short) March 2 Chapter 8, 9 Network design simulation due before 5:00pm March 4 Simulation results Midterm overview Homework 4 due March 9 Midterm Chapter 1

Summary: Static Forecasting Method SYST 4050 Slides Summary: Static Forecasting Method Estimate level and trend Deseasonalize the demand data Estimate level L and trend T using linear regression Obtain deasonalized demand Dt Estimate seasonal factors Estimate seasonal factors for each period St = Dt /Dt Obtain seasonal factors Si = AVG(St) such that t is the same season as i Forecast Forecast for future periods is Ft+n = (L + nT)*St+n Forecast Ft+n = (L + nT)St+n Chapter 1

Ethical Dilemma? How can this model be abused? SYST 4050 Slides Ethical Dilemma? In 2009, the board of regents for all public higher education in a large Midwestern state hired a consultant to develop a series of enrollment forecasting models, one for each college. These models used historical data and exponential smoothing to forecast the following year’s enrollments. Each college’s budget was set by the board based on the model, which included a smoothing constant () for each school. The head of the board personally selected each smoothing constant based on “gut reactions and political acumen.” How can this model be abused? What can be done to remove any biases? Can a regression model be used to bias results? Chapter 1

Time Series Forecasting SYST 4050 Slides Time Series Forecasting Observed demand = Systematic component + Random component Forecast Forecast error L Level (current deseasonalized demand) T Trend (growth or decline in demand) S Seasonality (predictable seasonal fluctuation) The goal of any forecasting method is to predict the systematic component of demand The goal of any forecasting method is to predict the systematic component (Forecast) of demand and measure the size and variability of the random component (Forecast error) Chapter 1

1) Characteristics of Forecasts SYST 4050 Slides 1) Characteristics of Forecasts Forecasts are always wrong! Forecasts should include an expected value and a measure of error (or demand uncertainty) Forecast 1: sales are expected to range between 100 and 1,900 units Forecast 2: sales are expected to range between 900 and 1,100 units Chapter 1

SYST 4050 Slides Examples Chapter 1

Measures of Forecast Error SYST 4050 Slides Measures of Forecast Error Measure Description Error Absolute Error Forecast – Actual Demand Absolute deviation Mean Squared Error (MSE) Squared deviation of forecast from demand Mean Absolute Deviation (MAD) Absolute deviation of forecast from demand Mean Absolute Percentage Error (MAPE) Absolute deviation of forecast from demand as a percentage of the demand Tracking signal (TS) Ratio of bias and MAD Chapter 1

Forecast Error Error (E) SYST 4050 Slides Forecast Error Error (E) Measures the difference between the forecast and the actual demand in period t Want error to be relatively small Et = Ft – Dt Chapter 1

SYST 4050 Slides Forecast Error Chapter 1

Forecast Error Bias Measures the bias in the forecast error SYST 4050 Slides Forecast Error Bias Measures the bias in the forecast error Want bias to be as close to zero as possible A large positive (negative) bias means that the forecast is overshooting (undershooting) the actual observations Zero bias does not imply that the forecast is perfect (no error) -- only that the mean of the forecast is “on target” biast = ∑n ∑t=1 Et Chapter 1

Forecast mean “on target” but not perfect SYST 4050 Slides Forecast Error Forecast mean “on target” but not perfect Undershooting Chapter 1

Forecast Error Absolute deviation (A) SYST 4050 Slides Forecast Error Absolute deviation (A) Measures the absolute value of error in period t Want absolute deviation to be relatively small At = |Et| Chapter 1

Forecast Error  = 1.25*MAD Mean absolute deviation (MAD) SYST 4050 Slides Forecast Error Mean absolute deviation (MAD) Measures absolute error Positive and negative errors do not cancel out (as with bias) Want MAD to be as small as possible No way to know if MAD error is large or small in relation to the actual data 1 n MADn = ∑t=1 At ∑n  = 1.25*MAD Chapter 1

Not all that large relative to data SYST 4050 Slides Forecast Error Not all that large relative to data Chapter 1

Forecast Error Tracking signal (TS) SYST 4050 Slides Forecast Error Tracking signal (TS) Want tracking signal to stay within (–6, +6) If at any period the tracking signal is outside the range (–6, 6) then the forecast is biased TSt = biast / MADt Chapter 1

Biased (underforecasting) SYST 4050 Slides Forecast Error Biased (underforecasting) Chapter 1

Forecast Error Mean absolute percentage error (MAPE) SYST 4050 Slides Forecast Error Mean absolute percentage error (MAPE) Same as MAD, except ... Measures absolute deviation as a percentage of actual demand Want MAPE to be less than 10 (though values under 30 are common) Et Dt 100 ∑n ∑t=1 n MAPEn = Chapter 1

Forecast Error Smallest absolute deviation relative to demand SYST 4050 Slides Forecast Error Smallest absolute deviation relative to demand MAPE < 10 is considered very good Chapter 1

Forecast Error VAR = MSE Mean squared error (MSE) SYST 4050 Slides Forecast Error Mean squared error (MSE) Measures squared forecast error Recognizes that large errors are disproportionately more “expensive” than small errors Not as easily interpreted as MAD, MAPE -- not as intuitive 1 n MSEn = ∑t=1 ∑n Et2 VAR = MSE Chapter 1

Measures of Forecast Error SYST 4050 Slides Measures of Forecast Error Measure Description Error Absolute Error Et = Ft – Dt At = |Et| Mean Squared Error (MSE) MSEn = ∑t=1Et2 Mean Absolute Deviation (MAD) MADn = ∑t=1At Mean Absolute Percentage Error (MAPE) MAPEn = Tracking signal (TS) TSt = biast / MADt 1 n ∑n 1 n ∑n Et Dt 100 ∑n ∑t=1 n Chapter 1

Summary What information does the bias and TS provide to a manager? SYST 4050 Slides Summary What information does the bias and TS provide to a manager? The bias and TS are used to estimate if the forecast consistently over- or underforecasts What information does the MSE and MAD provide to a manager? MSE estimates the variance of the forecast error VAR(Forecast Error) = MSEn MAD estimates the standard deviation of the forecast error STDEV(Forecast Error) = 1.25 MADn Chapter 1

Forecast Error in Excel SYST 4050 Slides Forecast Error in Excel Calculate absolute error At =ABS(Et) Calculate mean absolute deviation MADn =SUM(A1:An)/n =AVERAGE(A1:An) Calculate mean absolute percentage error MAPEn =AVERAGE(…) Calculate tracking signal TSt =biast / MADt Calculate mean squared error MSEn =SUMSQ(E1:En)/n Chapter 1

Forecast Error in Excel SYST 4050 Slides Forecast Error in Excel Et = Ft – Dt Forecast Error Chapter 1

Forecast Error in Excel SYST 4050 Slides Forecast Error in Excel biasn = ∑t=1 ∑n Et Bias Chapter 1

Forecast Error in Excel SYST 4050 Slides Forecast Error in Excel At = |Et| Absolute Error Chapter 1

Forecast Error in Excel SYST 4050 Slides Forecast Error in Excel 1 n MADn = ∑t=1 At ∑n Mean Absolute Deviation Chapter 1

Forecast Error in Excel SYST 4050 Slides Forecast Error in Excel TSt = biast / MADt Tracking Signal Chapter 1

Forecast Error in Excel SYST 4050 Slides Forecast Error in Excel Et Dt 100 |%Error|t = |%Error| Chapter 1

Forecast Error in Excel SYST 4050 Slides Forecast Error in Excel ∑n ∑t=1 |%Error|t MAPEn = n Mean Absolute Percentage Error Chapter 1

Forecast Error in Excel SYST 4050 Slides Forecast Error in Excel 1 n MSEn = ∑t=1 ∑n Et2 Mean Squared Error Chapter 1