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 6. Methods for Forecasting Stationary Series 7. Trend-Based Methods 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

2.6.Methods of Forecasting Stationary Series Exponential Smoothing-the current forecast is weighted average of the last forecast and the last value of demand. new forecast a(current observation of demand)+(1-a)(Last forecast) E,=aD,-1+(1-a)E,-1 where 0<a1 is the smoothing constant,which determines the relative weight placed on the last observation of demand, while 1-a is weight placed on the last forecast. F=aD,-1+(1-a)F,-=F-1-a(F-1-D-i)=F-1-Ce-l

Exponential Smoothing -the current forecast is weighted average of the last forecast and the last value of demand. 1 1 ( ) (1 )(Last forecast) (1 ) tt t new forecast current observation of demand FD F           where 0<1 is the smoothing constant, which determines the relative weight placed on the last observation of demand, while 1-  is weight placed on the last forecast. 1 1 FD F tt t      (1 )  2.6. Methods of Forecasting Stationary Series 1 11 ( )  F FD t tt       F e t t 1 1   

2.6.Methods of Forecasting Stationary Series Exponential Smoothing F,=aD,-1+(1-a)F-1 F-1=aD-2+(1-ax)E-2 E=aD,-1+a(1-)D,-2+(1-a)2E-2 F=aD-+a(I-a)D-2+(1-a)F-2=...=>a(I-a)D- i=0

Exponential Smoothing 1 1 (1 ) FD F tt t        12 2 (1 ) FD F tt t        2 1 22    (1 ) (1 ) FD D F tt t t        2.6. Methods of Forecasting Stationary Series 2 1 22 1 0 (1 ) (1 ) ... (1 )i t t t t ti i FD D F D                 

2.6.Methods of Forecasting Stationary Series a) 0.1 The older of a past data,the =018 0.09 smaller of its contribution to 0.08 the forecast for a future 0.07 period. 0.06 0.05 0.04 0.03 0.02 0.01 0 0 12345678910111213141516171819 Fig.2-5 Weights in Exponential Smoothing

Fig.2-5 Weights in Exponential Smoothing The older of a past data, the smaller of its contribution to the forecast for a future period. (1 ) 0.1 i      2.6. Methods of Forecasting Stationary Series

2.6.Methods of Forecasting Stationary Series Example 2.3 Consider Example 2.2,in which the observed number of failures over a two yrs period are 200,250,175,186,225,285,305,190.We will now forecast using exponential smoothing.We assume that the forecast for period 1 was 200,and suppose that a=0.1 F2=ES(0.1)2=0D+(1-0)F=0.1×200+(1-0.1)×200=200 F3=ES(0.1)3=0D2+(1-)F2=0.1×250+(1-0.1)×200=205 .Assume that the initial forecast is equal to the initial value of demand to get the method start.Drawback???

Example 2.3 • Consider Example 2.2, in which the observed number of failures over a two yrs period are 200, 250, 175, 186, 225, 285, 305, 190. We will now forecast using exponential smoothing. We assume that the forecast for period 1 was 200, and suppose that =0.1 F2= ES(0.1)2= D1+(1- )F1=0.1200+(1-0.1)  200=200 F3= ES(0.1)3= D2+(1- )F2=0.1250+(1-0.1)  200=205 •Assume that the initial forecast is equal to the initial value of demand to get the method start. Drawback??? 2.6. Methods of Forecasting Stationary Series

2.6.Methods of Forecasting Stationary Series 100 Smaller a turns out a 90 stable forecast,while 80 larger a results in better 70 track of series 60 8 0 10 0 12345678910111213141516171819202122232425 Time -Demand ES(.4) ES(.1) Fig.2-6 Exponential Smoothing for Different Values of Alpha

Fig.2-6 Exponential Smoothing for Different Values of Alpha Smaller  turns out a stable forecast, while larger  results in better track of series 2.6. Methods of Forecasting Stationary Series

2.6.Methods of Forecasting Stationary Series Comparing of ES and MA ④Similarities Both methods are based on assumption that underlying demand is stationary; Both methods depend on a single parameters; Both methods will lag behind a trend if one exits. ©Differences MA is better than EA in that it needs only past N data,while EA needs all the past data

Comparing of ES and MA Similarities • Both methods are based on assumption that underlying demand is stationary; • Both methods depend on a single parameters; • Both methods will lag behind a trend if one exits. Differences • MA is better than EA in that it needs only past N data, while EA needs all the past data. 2.6. Methods of Forecasting Stationary Series

圖 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 2.7.Trend-Based Methods Regression analysis .A method that fits a straight line to a set of Holt's Method data .Double exponential smoothing

2.7. Trend-Based Methods Holt’s Method Regression analysis •A method that fits a straight line to a set of data •Double exponential smoothing