1. Supply Chain Management Lecture 12

2. Outline Today –Chapter 7 Homework 3 –Online tomorrow –Due Friday February 26 before 5:00pm Next week Thursday –Finish Chapter 7 (forecast error measures) –Start with Chapter 8 –Network design simulation assignment

3. Announcements What? –Tour the Staples Fulfillment Center in Brighton, CO –Informal Lunch-and-Learn –Up to 20 students with a Operations Management major When? –Weeks of March 15 or March 29 –There is a fair amount of time involved in the activity Transit is close to an hour in each direction Probably 2 hours onsite Interested? –Let me know (email) by the end of this week

4. Time Series Forecasting Observed demand = Systematic component + Random component LLevel (current deseasonalized demand) TTrend (growth or decline in demand) SSeasonality (predictable seasonal fluctuation) 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)

5. Summary: N-Period Moving Average Method 1.Estimate level Take the average demand over the most recent N periods L t = (D t + D t-1 + … + D t-N+1 ) / N 2.Forecast Forecast for all future periods is based on the current estimate of level L t F t+n = L t Forecast F t+n = L t

6. Summary: Simple Exponential Smoothing Method 1.Estimate level The initial estimate of level L 0 is the average of all historical data L 0 = (∑ i D i )/ n Revise the estimate of level for all periods using smoothing constant  L t+1 =  D t+1 + (1 –  )*L t 2.Forecast Forecast for future periods is F t+n = L t Forecast F t+n = L t

7. Summary: Holt’s Method (Trend Corrected Exponential Smoothing) 1.Estimate level and trend The initial estimate of level L 0 and trend T 0 are obtained using linear regression =INTERCEPT(known_y’s, known_x’s) =LINEST(known_y’s, known_x’s) Revise the estimates for all periods using smoothing constants  and  L t+1 =  D t+1 + (1 –  )*(L t + T t ) T t+1 =  (L t+1 – L t ) + (1 –  )*T t 2.Forecast Forecast for future periods is F t+n = L t + nT t Forecast F t+n = L t + nT t

8. Summary: Winter’s Model (Trend and Seasonality Corrected Exp. Smoothing) 1.Estimate level, trend, and seasonality The initial estimates of L 0, T 0, S 1, S 2, S 3, and S 4 are obtained from static forecasting procedure Revise the estimates for all periods using smoothing constants ,  and  L t+1 =  (D t+1 /S t+1 ) + (1 –  )*(L t + T t ) T t+1 =  (L t+1 – L t ) + (1 –  )*T t S t+p+1 =  (D t+1 /L t+1 ) + (1 –  )S t+1 2.Forecast Forecast for future periods is F t+n = (L t + nT t )*S t+n Forecast F t+n = (L t + nT t )S t+n

9. Components of an Observation Trend (T) Forecast(F) F t+n = L t + nT t Holt’s method is appropriate when demand is assumed to have a level and a trend

10. Example: Holt’s Method An electronics manufacturer has seen demand for its latest MP3 player increase over the last six months –8415, 8732, 9014, 9808, 10413, 11961 Determine initial level L 0 = INTERCEPT(y’s, x’s) T 0 = LINEST(y’s, x’s)

11. Example: Holt’s Method An electronics manufacturer has seen demand for its latest MP3 player increase over the last six months –8415, 8732, 9014, 9808, 10413, 11961 Determine initial level L 0 = INTERCEPT(y’s, x’s) T 0 = LINEST(y’s, x’s) Determine levels L t+1 =  D t+1 + (1 –  )*(L t + T t ) T t+1 =  (L t+1 – L t ) + (1 –  )*T t Forecast F t+n = L t + nT t  = 0.1,  = 0.2

12. Example: Tahoe Salt

13. Demand forecasting using Holt’s method

14. Components of an Observation Seasonality (S) Forecast(F) F t+n = (L t + T t )S t+n

15. Example: Winter’s Model A theme park has seen the following attendance over the last eight quarters (in thousands) –54, 87, 192, 130, 80, 124, 265, 171 Determine initial levels L 0 = From static forecast T 0 = From static forecast S i,0 = From static forecast Forecast F t+1 = (L t + T t )S t+1 Determine levels L t+1 =  (D t+1 /S t+1 )+ (1 –  )*(L t + T t ) T t+1 =  (L t+1 – L t ) + (1 –  )*T t S t+p+1 =  (D t+1 /L t+1 ) + (1 –  )*S t+1

16. Example: Tahoe Salt

17. Demand forecast using Winter’s method

18. Static Versus Adaptive Forecasting Methods Static –D t : Actual demand –L: Level –T: Trend –S: Seasonal factor –F t : Forecast Adaptive –D t : Actual demand –L t : Level –T t : Trend –S t : Seasonal factor –F t : Forecast

19. Components of an Observation Seasonality (S) Forecast(F) F t+n = (L t + T t )S t+n

20. Example: Static Method A theme park has seen the following attendance over the last eight quarters (in thousands) –54, 87, 192, 130, 80, 124, 265, 171 Determine initial level L = INTERCEPT(y’s, x’s) T = LINEST(y’s, x’s) Determine deason. demand D t = L + Tt Determine seasonal factors S t = D t / D t Determine seasonal factors S i =AVG(S t ) Forecast F t = (L + T)S i

21. Example: Tahoe Salt

22. Static Forecasting Method

23. Deseasonalize demand –Demand that would have been observed in the absence of seasonal fluctuations Periodicity p –The number of periods after which the seasonal cycle repeats itself 12 months in a year 7 days in a week 4 quarters in a year 3 months in a quarter

24. Deseasonalize demand

25. Periodicity p is oddPeriodicity p is even

26. Example: Tahoe Salt

27. Static Forecasting Method

28. Example: Tahoe Salt Demand forecast using Static forecasting method

29. Summary: Static Forecasting Method 1.Estimate level and trend Deseasonalize the demand data Estimate level L and trend T using linear regression Obtain deasonalized demand D t 2.Estimate seasonal factors Estimate seasonal factors for each period S t = D t /D t Obtain seasonal factors S i = AVG(S t ) such that t is the same season as i 3.Forecast Forecast for future periods is F t+n = (L + nT)*S t+n Forecast F t+n = (L + nT)S t+n

30. ForecastForecast error Time Series Forecasting Observed demand = Systematic component + Random component LLevel (current deseasonalized demand) TTrend (growth or decline in demand) SSeasonality (predictable seasonal fluctuation) 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)

31. 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

32. Examples

33. Measures of Forecast Error MeasureDescription ErrorForecast – Actual Demand Mean Square Error (MSE)Estimate of the variance Mean Absolute Deviation (MAD) Estimate of the standard deviation of the random component Mean Absolute Percentage Error (MAPE) Absolute error as a percentage of the demand Tracking signalRatio of bias and MAD