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 3. Classification of Forecasts 4. Evaluating Forecast 5. Notation Conventions 6. Methods for Forecasting Stationary 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

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

2.3.Classification of Forecasts .Sales force composites; Customer surveys; Subjective-based on human Jury of executive opinion; judgment .The Delphi method. .Causal Models -the forecast for a phenomenon is some function Objective-derived of some variables from analysis of .Time Series Methods -forecast data of future values of some economic or physical phenomenon is derived from a collection of their past observations

Subjective-based on human judgment Objective-derived from analysis of data •Sales force composites; •Customer surveys; •Jury of executive opinion; •The Delphi method. •Causal Models -the forecast for a phenomenon is some function of some variables •Time Series Methods -forecast of future values of some economic or physical phenomenon is derived from a collection of their past observations 2.3. Classification of Forecasts

2.3.Classification of Forecasts -Objective Causal Model ·Let Y-the phenomenon needed to be forecasted;(numbers of house sales) X1,X2,...,X (interest rate of mortgage)are variables supposed to be related to Y Then,the general casual model is as follows: Y=f(X1,X2...,X). Econometric models are lineal casual models: Y=0+01X+02X2+..+0nXn, where a;(i=1~n)are constants

Causal Model • Let Y-the phenomenon needed to be forecasted; (numbers of house sales) X1, X2, …, Xn (interest rate of mortgage) are variables supposed to be related to Y • Then, the general casual model is as follows: Y=f(X1, X2, …, Xn). • Econometric models are lineal casual models: Y=0+ 1X1+ 2X2+…+ nXn,, where i (i=1~n) are constants. 2.3. Classification of Forecasts - Objective

2.3.Classification of Forecasts -Objective Causal Model The method of least squares is most commonly used for finding estimators of these constants. Assume we have the past data (xi,y),i=1~n;and the causal model is simplified as Y=a+bX.Define g(a,b)=∑y-(a+bx,)P i=l as the sum of the squares of the distances from line a+bX to data points yi

Causal Model The method of least squares is most commonly used for finding estimators of these constants. Assume we have the past data (xi, yi), i=1~n; and the causal model is simplified as Y=a+bX. Define 2 1 ( , ) [ ( )] n i i i g a b y a bx     as the sum of the squares of the distances from line a+bX to data points yi. 2.3. Classification of Forecasts - Objective

2.3.Classification of Forecasts -Objective Causal Model We may choose a and b to minimize(y(+ by letting 0g =0 Ba →22[y-(a+bx】-0a=2y-bx]=-饭 n i=1 .- 6 =0 →2[y-a+x小()-0 →b=L i=1 x-x∑x i=1 i=1

Causal Model 2 1 ( , ) [ ( )] n i i i g a b y a bx  We may choose a and b to minimize    by letting 0 g a      1 2 0         n i i i y a bx    1 0         n i ii i 0 y a bx x gb   2.3. Classification of Forecasts - Objective 1 1 2 1 1             n n ii i i i n n i i i i x yyx b x x x   1 1      n i i i a y bx y bx n

2.3.Classification of Forecasts-Objective Causal Model g(a,b)=∑y-(a+bx i=l og=0 a=y-bx Ba ag =0 ∑xy-∑xn∑xy-∑x ab b=i i=l i=1 i=1 x-x2x2x-2x i= i=1 i=1 S,=2y-2%:S=2x- 之x:-∑%

Causal Model 2 1 ( , ) [ ( )] n i i i g a b y a bx     0 g a    a  y  bx 1 11 1 2 2 11 1 1 n nn n ii i ii i i ii i xy nn n n xx ii i i ii i i x y y x n x y ny x S b S x x x n x nx x                   0 g b    2 2 ; () n nn n n xy i i i i xx i i i ii i i S n xy x y S n x x        1 1 ; ; n n i i i i x xy y n n     2.3. Classification of Forecasts - Objective

2.3.Classification of Forecasts -Objective Time Series Methods The idea is that information can be inferred from the pattern of past observations and can be used to forecast future values of the series. Try to isolate the following patterns that arise most often. -Trend-the tendency of a time series,usually a stable growth or decline,either linear (a line)or nonlinear(described as nonlinear function,e.g.a quadratic or exponential curve) -Seasonality-Variation of a series related to seasonal changes and repeated every season. -Cycles-Cyclic variation similar to seasonality,except that the length and the magnitude may change,usually associated with economic variation. Randomness-No recognizable pattern to the data

Time Series Methods • The idea is that information can be inferred from the pattern of past observations and can be used to forecast future values of the series. • Try to isolate the following patterns that arise most often. Trend-the tendency of a time series, usually a stable growth or decline, either linear (a line) or nonlinear (described as nonlinear function, e. g. a quadratic or exponential curve) Seasonality-Variation of a series related to seasonal changes and repeated every season. Cycles-Cyclic variation similar to seasonality, except that the length and the magnitude may change, usually associated with economic variation. Randomness-No recognizable pattern to the data. 2.3. Classification of Forecasts - Objective

2.3.Classification of Forecasts -Objective Purely random- Increasing No recognizable linear trend pattern ● ● ● ● ● ● Time Time Curvilinear Seasonal trend (quadratic, pattern plus exponential) linear growth ● ● pupwe Time Time Fig.2-2 Time Series Patterns

Fig. 2-2 Time Series Patterns 2.3. Classification of Forecasts - Objective

@ 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

2.4.Evaluating Forecast The forecast error e,in period t is the difference between the forecast value for that period and the actual demand for that period. e,=F-D The three measures for evaluating forecasting accuracy during n period MD=∑Ie,l MsE=∑e MAPE=[∑1e,/D,IxI00 n i=l n i=1 n i=l MAD:The mean absolute deviation,preferred method; MSE:The mean squared error; MAPE:The mean absolute percentage error(MAPE)

 The forecast error et in period t is the difference between the forecast value for that period and the actual demand for that period. ttt e FD    The three measures for evaluating forecasting accuracy during n period 2 1 1 n i i MSE e n    • MAD: The mean absolute deviation, preferred method; • MSE: The mean squared error; • MAPE: The mean absolute percentage error (MAPE) 1 1 | | n i i MAD e n    1 1[ | / |] 100 n i i i MAPE e D n     2.4. Evaluating Forecast