上海交通大学：《生产计划与控制 Production Planning and Control》课程教学资源（课件讲稿）chap02 Forecasting 8. Methods for Seasonal Series

© Production Planning and Control Dr.GENG Na Department of Industrial Engineering Logistics Management Shanghai Jiao Tong University

Production Planning and Control Dr. GENG Na Department of Industrial Engineering & Logistics Management Shanghai Jiao Tong University

© Chapter 2 Forecasting Contents 1.Introduction 2.The Time Horizon in Forecasting 3.Classification of Forecasts 4.Evaluating Forecast 5.Notation Conventions 6.Methods for Forecasting Stationary Series 7.Trend-Based Methods 8.Methods for Seasonal Series

Chapter 2 Forecasting Contents 1. Introduction 2. The Time Horizon in Forecasting 3. Classification of Forecasts 4. Evaluating Forecast 5. Notation Conventions 6. Methods for Forecasting Stationary Series 7. Trend-Based Methods 8. Methods for Seasonal Series

图 2.8.Methods of Forecasting Trend Seasonal Series more complex time series:Trend Seasonality 0 35 30 20 15 10 5 0 Time Seasonal Decomposition Using Moving Averages Winter's Method(triple exponential smoothing)

2.8. Methods of Forecasting Trend Seasonal Series Seasonal Decomposition Using Moving Averages A more complex time series: Trend + Seasonality Winter’s Method (triple exponential smoothing)

2.8.Methods of Forecasting Trend Seasonal Series A more complex time series:Trend Seasonality Seasonal Decomposition Using Moving Averages 40 .Deseaonalized-Get 30 seasonality away; 250 .Make forecast on deseaonalized data; 10 .Get seasonality 5 back 0 Time

2.8. Methods of Forecasting Trend Seasonal Series •Deseaonalized- Get seasonality away; •Make forecast on deseaonalized data; •Get seasonality back Seasonal Decomposition Using Moving Averages A more complex time series: Trend + Seasonality

2.8.Methods of Forecasting Trend Seasonal Series Procedures: Draw the demand curves and estimate the season length N; Computer the moving average MA(N): Centralize the moving averages; Get the centralized MA values back on period; Calculate seasonal factors,and make sure of >c,=N Divide each observation by the appropriate seasonal factor to obtain the deseasonalized demand Forecast is made based on deseasonalized demand. Final forecast is obtained by multiplying the forecast(with no seasonality)with seasonal factors

2.8. Methods of Forecasting Trend Seasonal Series Procedures: • Draw the demand curves and estimate the season length N; • Computer the moving average MA(N); • Centralize the moving averages; • Get the centralized MA values back on period; • Calculate seasonal factors, and make sure of  ct=N. • Divide each observation by the appropriate seasonal factor to obtain the deseasonalized demand • Forecast is made based on deseasonalized demand. • Final forecast is obtained by multiplying the forecast (with no seasonality) with seasonal factors

图 2.8.Methods of Forecasting Trend Seasonal Series Summation Deseasonalized Period Demand MA(4) CMA BCMA Ratio SF Demand 10 18.8125 0.532 0.558 17.91 2 20 18.8125 1.063 1.062 18.84 18.25 3 26 18.5 1.405 1.413 18.40 18.75 4 17 19.125 0.889 0.967 17.59 19.5 5 12 18.25 20 0.600 0.558 21.49 20.5 6 23 18.75 21.125 1.089 1.062 21.66 21.75 7 30 19.5 20.5625 1.459 1.413 21.23 8 22 20.5 20.5625 1.070 0.967 22.76 21.75

Period Demand MA(4) CMA BCMA Ratio SF Deseasonalized Demand 1 10 18.8125 0.532 0.558 17.91 2 20 18.8125 1.063 1.062 18.84 18.25 3 26 18.5 1.405 1.413 18.40 18.75 4 17 19.125 0.889 0.967 17.59 19.5 5 12 18.25 20 0.600 0.558 21.49 20.5 6 23 18.75 21.125 1.089 1.062 21.66 21.75 7 30 19.5 20.5625 1.459 1.413 21.23 8 22 20.5 20.5625 1.070 0.967 22.76 21.75 2.8. Methods of Forecasting Trend Seasonal Series Summation

2.8.Winter's Method for Seasonal Problems Winter's Method The moving-average method requires that all seasonal factors be recalculated from scratch as new data become available. Winter's method is a type of triple exponential smoothing. Easy to update as new data become available Assumptions: Model of the form:D=(u+G)c,+ The length of the season is exactly N periods and the seasonal factors are the same each season and have the property that ∑c,=N

2.8. Winter’s Method for Seasonal Problems Winter’s Method • The moving-average method requires that all seasonal factors be recalculated from scratch as new data become available. • Winter’s method is a type of triple exponential smoothing. • Easy to update as new data become available. Assumptions: ► Model of the form: ► The length of the season is exactly N periods and the seasonal factors are the same each season and have the property that D Gc t tt t        t c N

2.8.Winter's Method for Seasonal Problems Winter's Method (triple exponential smoothing) The series.The current level of deseasonalized series S, S,=(D,/c-N)+(1-)(S-1+G-) The trend G,=B(S,-S-1)+(1-B)G1 The seasonal factors c,=y(D,/S,)+(1-Y)c-N The forecast made in period t for any future period t+t is given by (assume that t <=N) F=(S,+G)C+-N If N<T<=2N,the seasonal factor would be cr2N If 2N<T <=3N,the seasonal factor would be crw and so on

2.8. Winter’s Method for Seasonal Problems Winter’s Method (triple exponential smoothing) ► The series. The current level of deseasonalized series St ► The trend. ► The seasonal factors ► The forecast made in period t for any future period t+ τ is given by (assume that τ <= N) If N < τ <= 2 N, the seasonal factor would be ct+ τ-2N If 2 N < τ <= 3 N, the seasonal factor would be ct+ τ-3N and so on      1 1 1 t t tN t t S Dc S G        G SS G t tt t       1 1   1   c DS c t t t tN        1   F S Gc tt t t t N ,         

2.8.Winter's Method for Seasonal Problems Initialization Procedure Assume that exactly two seasons of data are available;that is,2N data points.Suppose that the current period is t=0,so that the past observations are labeled Da,D.N2,...,Do Step 1:Calculate the sample means for the two seasons Step 2:Define the initial slope estimate G。=('-)/N Step 3:Set the initial value of the series S,=V+G[(N-1)/2]

2.8. Winter’s Method for Seasonal Problems Initialization Procedure Assume that exactly two seasons of data are available; that is, 2N data points. Suppose that the current period is t = 0, so that the past observations are labeled D-2N+1, D-2N+2 , … , D 0 ► Step 1: Calculate the sample means for the two seasons ► Step 2: Define the initial slope estimate ► Step 3: Set the initial value of the series 0 1 2 21 1 1 1 , N j j j N jN V DV D N N          G VVN 0 21     SVG N 020     1 2    

2.8.Winter's Method for Seasonal Problems Initialization Procedure Step 4(a):Calculate the initial seasonal factors D for-2W+1≤t≤0 V-[(N+1)/2-]G。 where i=1 for the first season,i=2 for the second season,j is the period of the season.That is,j=1 for 1=-2N+1 and t=-N+1;j=2 for t=-2N+2 and t=-N+2,and so on. Step 4(b):Average the seasonal factors C1=C21C,,G=C _N+Co 2 2 Step 4(c):Normalize the seasonal factors ys小w for-N+1≤j≤0

2.8. Winter’s Method for Seasonal Problems Initialization Procedure ► Step 4(a): Calculate the initial seasonal factors where i=1 for the first season, i=2 for the second season, j is the period of the season. That is, j=1 for t=-2 N+1 and t=- N+1; j=2 for t=-2 N+2 and t=- N+2, and so on. ► Step 4(b): Average the seasonal factors ► Step 4(c): Normalize the seasonal factors   0 for 2 1 0 1 2 t t i D c Nt V N jG         21 1 0 1 0 , ... , 2 2 NN N N c c cc c c           0 1 for 1 0 jj i i N c c cN N j              