chap2- PRODUCTION PLANNING AND CONTROL

1、1-1Production Planning and Control1-2Chapter TwoContentsvThe Time Horizon in Forecasting;vCharacteristics of Forecasts;vSubjective Foresting Methods;vObjective Forecasting Methods;vNotation Conventions;vEvaluating Forecast;vMethods for Forecasting Stationary Series;vTrend-Based Methods;vMethods for

2、Seasonal Series;1-3Introduction(1)vForecasting is the process of predicting the future;vAll business planning is based on a forecast;vFactors affecting the future success of a firm-Sales of existing productsCustomer demand patterns for new products;Needs and availabilities of raw materials;Changing

3、skills of workers;Interest rates;Capacity requirements;International policies;vMarketing and production make the most use of forecasting methods.Marketing needs to forecast for both new products and existing products;Sales forecasts are used for production planning1-4Introduction(2)Examples of benef

4、iting from good forecasting and paying price from poor one:Slow respond of Detroit to customer tastes in automobiles from heavy gas guzzlers to smaller and more fuel efficient ones during 1960s makes it suffered when OPEC oil embargoing in late 1970 speed up the trend of shifting to smaller cars.Com

5、paq Computer became a market leader in the early 1980s by properly predicating consumer demand for portable version of the IBM PC;Ford Motors early success and later demise;1-5The Time Horizon in ForecastingFig.2-1 Forecast Horizons in Operation PlanningvThe Short-term forecasting is required for da

6、y-to-day planning;vMeasured usually in day or weeks;vRequired for inventory management, production plan, and resource requirement planning, and shift schedulingvThe Intermediate term is measured in weeks or months;vTypical intermediate term forecasting problems include sales pattern of product famil

7、ies, requirements and availabilities of workers, and resource requirements.vThe long term is measured in months or years;vIt is one part of the overall firms manufacturing strategy;vProblems for long term forecasting include long term capacity planning; long term sales patters, and growth trend. vOn

8、e of example is long term planning of capacity;1-6Classification of Forecasts-based on human judgment-derived from analysis of datavSales force composites;vCustomer surveysvJury of executive opinion;vThe Delphi method;vCausal Models-the forecast for a phenomenon is some function of some variablesvTi

9、me Series Methods-forecast of future values of some economic or physical phenomenon is derived from a collection of their past observationsSale force is in a good position to see changes in their preferences;Numbers of the sale force submit sales estimates of the products they sell in the next year;

10、Sales manager aggregate individual estimates It can signal the future trends an shifting preference patterns;Survey and sampling plans must ensure statistically unbiased resulting data and representative of the customer base;Experts opinion is the only source of information for forecasting,when no p

11、ast history, as with new products;The approach is to combine the opinions of experts to derive a forecast;Two ways for the combinationNamed for the Delphic oracle of ancient Greece who had power to predicate the future;Based on soliciting the opinion of experts like jury of executive opinion;however

12、, in different manner in which individual opinions are combined in order to overcome some of the inherent shortcoming of group dynamics;Procedures for the Delphi method:A group of experts express their opinions;The opinions are then compiled and a summary of results are returned to the expert, with

13、special attention to those significant different opinions;The experts are asked if they wish to reconsider their original opinions in light of the group response;The process is repeated until an overall group consensus is reached;1-7Objective Forecasting MethodspLetY-the phenomenon needed to be fore

14、casted;X1, X2, , Xn-n variables supposed to be related to YpThen, the general casual model is as follows: Y=f(X1, X2, , Xn).pEconometric models are lineal casual models: Y=0+ 1X1+ 2X2+ nXn, where i (i=1-n) are constants.pThe method of least squares is most commonly used for finding estimators of the

15、se constants.1-8Objective Forecasting MethodsAssume we have the past data (xi, yi), i=1-n; and the the causal model is simply as Y=a+bX. Define21( , )()niiig a byabxAs the sum of the squares of the distances from line a+bX to data points yi. We may choose a and b to minimize g, by letting0ggab;xyxxS

16、baybxS22;()nnnnnxyiiiixxiiiiiiiSnx yxySnxx 11;nniiiixxyynn1-9Objective Forecasting MethodsIf the past data are in form of (i, Di), i=1n, where Di is the observed value of demand in period i; and the the causal model is simply astDabt2211(1)(1)(21)12.,14.26nniiiin nn nnxnxn 222(1);21)(21(1)64nnxyiiii

17、xxn nSniDDnnnn nS1-10Objective Forecasting MethodsvThe idea is that information can be inferred from the pattern of past observations and can be used to forecast future values of the series.vAttempt to isolate the following patterns that arise most often.Trend-the tendency of a time series, usually

18、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 year.Cycles-Cyclic variation similar to seasonality, except that the length and t

19、he magnitude may change, usually associated with economic variation.Randomness-No recognizable pattern to the data.1-11Objective Forecasting MethodsFig. 2-2 Time Series Patterns1-12Notation ConventionvDefine D1, D2, , Dt, , as the observed values of demand during periods 1, 2, , t, vAssume Dt, t1 as

20、 the time series we need to predicate;vAssume if we are predicating in period t, we have already observed Dt, Dt-1, , but have no Dt+1.vDefine Ft as the forecast for period t that is made at the end of period t-1;vThe above is one-step-ahead forecast-they are made for the demand in the next period.

21、vA time series forecast is actually obtained by weighting the past data11120,mtt nt nttnFDfor some set of weights L1-13Evaluating ForecastvThe forecast error et in period t is the difference between the forecast value for that period and the actual demand for that period. For one-step-ahead forecast

22、ttteFDFor multiple-step-ahead forecast,tttteFDwhere Ft-,t is the forecast for period t which is made ahead of period t.vThe three measures for evaluating forecasting accuracy during n period211niiMSEenMAD: The mean absolute deviation, preferred method;MSE: The mean squared error;MAPE: The mean absol

23、ute percentage error (MAPE)11|niiMADen11|/| 100niiiMAPEeDn1-14Evaluating ForecastMAD1=2.83MAD2=3.00Plant 1 better 2MSE1=13.17MSE2=11.67Plant 2 better 1MAPE1=0.0325MAPE2=0.0336Plant 1 better 2vBoth MAD1 and MAPE1 are less than MAD2 and MAPE2, however MSE1 is larger than MSE2. ?vMSE is more sensitive

24、to one large error than is the MAD. Plant 1 has got a large error 7.1-15Evaluating ForecastFig2-3 Forecast Errors Over TimevA desirable forecast should be unbiased. Mathematically, E(ei)=0.vThe forecast error ei over time should fluctuate randomly above and below zero. 1-16Methods of Forecasting Sta

25、tionary Series: each observation can be represented by a constant plus a random fluctuation.ttDwhere = an unknown constant corresponding to mean of the series;= the random error with mean zero and variation 2.vMethods:Moving average;Exponential Smoothing;1-17Methods of Forecasting Stationary SeriesA

26、 moving average of order N is simply the arithmetic average of the most recent N observations (one-step-ahead), denoted ad MA(N).12111()Ntt ittt NiFDDDDNNLvExample 2.2 Engine failure forecasting;11121111111()()NttitttttNt NiNtt Nt ittiNt NFDDDNNDDDFDDNDDDND LvCalculate Ft+1 based on Ft-simplify the

27、calculation Only need to calculate the difference between the most recent demands and the demand N period ahead for updating the forecast.1-18Methods of Forecasting Stationary Series Fig.2-4 Moving-Average Forecasts Lag Behind a TrendImplication: the use of simple moving averages is not proper forec

28、asting method when there is a trend in the series.Forecasts lag behind the demand1-19Methods of Forecasting Stationary Seriesthe current forecast is weighted average of the last forecast and the last value of demand.11(1)tttFDFwhere 01 is the smoothing constant, which determines the relative weight

29、placed on the last observation of demand, while 1- is weight placed on the last forecast.1111111(1)()ttttttttFDFFFDFeThe forecast in any period t is the forecast in period t-1 minus some fraction of the observed forecast error in period t-1122(1)tttFDF212210(1)(1).(1)ittttt iiFDDFD 1-20Methods of Fo

30、recasting Stationary SeriesFig.2-5 Weights in Exponential SmoothingExponential smoothing apples declining set of weights t all past data1-21Example 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 forecas

31、t using exponential smoothing. We assume that the forecast for period 1 was 200, and suppose that =0.1F2= ES(0.1)2= D1+(1- 1)F1=0.1200+(1-0.1) 200=200F3= ES(0.1)3= D2+(1- 1)F2=0.1250+(1-0.1) 200=205vSince ES requires that at each stage we need the previous forecast, it is not obvious how to get the

32、method started.vWe may assume that the initial forecast is equal to the initial value of demand.vHowever, this approach has a serious drawback.?1-22Methods of Forecasting Stationary SeriesFig.2-6 Exponential Smoothing for Different Values of AlphaSmaller turns out a stable forecast, while larger res

33、ults in better track of series1-23Methods of Forecasting Stationary SeriesComparing of ES and MAvSimilaritiesBoth 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.vDifferencesMA is bette

34、r than EA in that it needs only past N data, while EA needs all the past data;It is significant advantage of EA over MA that it only needs to save the last forecast, while MA needs to store N past data.1-24Trend Based MethodsvTwo methods that account for a trend in the data: regression analysis and

35、Holts method.vRegression AnalysisLet (x1, y1), (x2, y2), , (xn, yn) are n paired data points for the two variables X and Y; andAssume that yi is the observed value of Y when xi is the observed value of X.It is believed that there is a relationship between X and Y as followsYabXqRepresents the predic

36、ated value of Y;qa and b are chosen to minimize the sum of squared distance between regression line and the data point;xyxxSbaybxSLeast square method1-25Methods of Forecasting Stationary SeriesFig 2-7 An Example of a Regression LineYabX(i, Di)1-26Methods for Seasonal Seriesv A seasonal series is one

37、 that has a pattern that repeats every N periods (at least 3).Fig. 2-8 A Seasonal Demand SeriesLength of season-the number of periods before the pattern begins to repeat1-27Methods of Forecasting Stationary SeriesHow to represent seasonality?vSeasonal factor-A set of multipliers ct, 1 t N, ct=N;vct

38、represents the average amount that the demand in tth period of the season is above or below the overage.vFor example: if c3=1.25 and c5=0.6, then the demand in the 3rd period is 25 percent above the average demand; while demand in the 5th period is 40 percent below the average demand.Seasonal Factor

39、s for Stationary Seasonal Series (No trend)Computer the sample mean of all data(A minimum of two seasons of date is required): mDivide each observation by sample meanthe seasonal factors for each period of observed data: SFj,j=Dij/m （Dij-the jth observed dada in period i)Average the factors for the

40、same periods within each season the seasonal factorMultiplying the sample mean by a seasonal factor the forecast of demand in the corresponding period of the season.1-28Methods of Forecasting Stationary SeriesWk1Wk2Wk3Wk4Monday16.217.314.616.1Tuesday12.211.513.111.8Wednesday14.2151312.9Thursday17.31

41、7.616.916.6Friday22.523.521.924.3Monday0.977169Tuesday0.739726Wednesday 0.838661Thursday 1.041096Friday1.403349Wk1Wk2Wk3Wk4Monday0.986301 1.053272 0.888889 0.980213Tuesday0.74277 0.700152 0.797565 0.718417Wednesday 0.864536 0.913242 0.791476 0.785388Thursday 1.053272 1.071537 1.028919 1.010654Friday

42、1.369863 1.430746 1.333333 1.479452Monday16.05Tuesday12.15Wednesday13.775Thursday17.1Friday23.05Avg=16.42516.425*0.9771691-29Methods of Forecasting Stationary SeriesSeasonal Decomposition Using Moving Averages-Example 2.7 Draw the demand curves and estimate the season length N; Computer the moving a

43、verage 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 Deseasonalized series contain all components of the signal of

44、the original series except for seasonality. Forecast is made based on deseasonalized demand. Final forecast is obtained by multiplying the forecast (with no seasonality) with seasonal factors. Note: the forecast (with no seasonality) may be made by MA or regression methods.1-30Methods of Forecasting Stationary SeriesPeriodDemandMA(4) CMABOCMARatioFactorD. D.11018.810.5320.5660.588 17.921.522018.811.0631.0761.061 18.852.518.2532618.51.4051.4341.415 18.393.518.7541718.2519.1250.8880.9790.966 17.604.519.