Forecasting MD707 Operations Management Professor Joy Field

Components of the Forecast 2

Forecasting using Judgment Methods Sales force estimates Executive opinion Market research Delphi method 3

Forecasting using Time Series Methods Naïve forecasts Moving averages Weighted moving averages Exponential smoothing Trend-adjusted exponential smoothing Multiplicative seasonal method 4

Moving Average Method Use a 3-month moving average, what is the forecast for month 5? If the actual demand for month 5 is 805 customers, what is the forecast for month 6? 5 MonthCustomers

Comparison of Three-Week and Six-Week Moving Average Forecasts 6

Weighted Moving Average Method Let Calculate the forecast for Month 5. If the actual number of customers in month 5 is 805, what is the forecast for month 6? 7 MonthCustomers

Exponential Smoothing Suppose What is the forecast for Month 5? If the actual number of customers in month 5 is 805, what is the forecast for month 6? 8 MonthCustomers

Trend-Adjusted Exponential Smoothing Using months 1-4, an initial estimate of the trend for Month 5 is 2 [(4-2+4)/3 = 2]. The starting forecast for month 5 is 54+2 = 56. Using and forecast the number of customers in month 6. 9 Month Customers

Trend-Adjusted Exponential Smoothing (cont.) If the actual number of customers in month 6 is 58, what is the forecast for month 7? 10

Multiplicative Seasonal Method Procedure  Calculate the trend line based on the available data using regression.  Calculate the centered moving average, with the number of periods equal to the number of seasons.  Calculate the seasonal relative for a period by dividing the actual demand for the period by the corresponding centered moving average.  Calculate the overall estimated seasonal relative by averaging the seasonal relatives from the same periods over the cycle.  Calculate the trend values for each of the periods to be forecast based on the trend line determined in Step 1.  To get a forecast for a given period in a future cycle, multiply the seasonal factor by the trend values. 11

Multiplicative Seasonal Method Example QuarterDemandCMA (4 seasons)MA (2 periods) Seasonal Relatives Normalized S.R. Year 1, Q1 100 Year 1, Q Year 1, Q Year 1, Q Year 2, Q Year 2, Q Year 2, Q3 384 Total3.924 Year 2, Q4 216 Year 3, Q1331(trend value*)227(forecast) Year 3, Q2344(trend value*)480(forecast) Year 3, Q3356(trend value*)417(forecast) Year 3, Q4369(trend value*)275(forecast) 12 * Using regression, the trend line is t.

Linear Regression where  y = dependent (predicted) variable  x = independent (predictor) variable  a = y-intercept of the line (i.e., value of y when x = 0)  b = slope of the line 13 y = a + bx

Linear Regression Line Relative to Actual Data 14

Regression Analysis Example Week x (Price) y (Appetizers) 1$ An analyst for a chain of seafood restaurants is interested in forecasting the number of crab cake appetizers sold each week. He believes that the number sold has a linear relationship to the price and uses linear regression to determine if this is the case.

Regression Analysis Example (cont.) Regression Statistics Multiple R0.843 R-Square0.711 Adjusted R-Square0.639 Standard Error Observations6 ANOVA dfSSMSFSignificance F Regression Residual Total CoefficientsStandard Errort StatP-value Intercept Price ($)

Least Squares Regression Line Appetizer Example 17

Interpretation of the Regression Intercept 18

Another Regression Analysis Example HoursScore A professor is interested in determining whether average study hours per week is a good predictor of test scores. The results of her study are: A student says: "Professor, what can I do to get a B or better on the next test. The professor asks, "On average, how many hours do you spend studying for this course per week?" The student responds, "About 2 hours." Use linear regression to forecast the student's test score.

Another Regression Analysis Example (cont.) 20 Regression Statistics Multiple R0.391 R-Square0.153 Adjusted R-Square Standard Error Observations8 ANOVA dfSSMSFSignificance F Regression Residual Total71300 CoefficientsStandard Errort StatP-value Intercept Study hours

Forecast Error Measures Bias  Average error Variability  Mean squared error (MSE)  Standard deviation (s)  Mean absolute error (MAD)  Mean percent absolute error (MAPE) Relative bias  Tracking signal (TS) 21

Summarizing Forecast Accuracy PeriodActual (A)Forecast (F)Error (E=A-F)Abs ErrorError Sq [(Abs E)/A] x Total MAD =23.9 MSE = s =34.8 MAPE =23.8% 22

Tracking and Analyzing Forecast Errors PeriodActual (A)Forecast (F)Error (E=A-F)Assessing bias: Cumulative forecast error (periods 1-9) = MAD (periods 1-9) = Tracking signal (periods 1-9) = Cumulative forecast error (periods 1-18) = MAD (periods 1-18) = Tracking signal (periods 1-18) = Assessing error variability/size: Total4 Standard deviation (periods 1-9) = 2s control limits for errors: 0 +/- 2(34.8) = / s Control Chart for Errors UCL = 69.6 LCL = -69.6

Forecast Performance of Various Forecasting Methods for a Medical Clinic Method Cumulative Sum of Forecast Errors (CFE – bias) Mean Absolute Deviation (MAD - variability) Simple moving average Three-week (n = 3) Six-week (n = 6) period weighted moving average w = 0.70, 0.20, Exponential smoothing = =