补充6 供应链中的需求预测(二)时序预测法(移动平均法、简单指数平滑法、Holt模型和Winter模型)的具体实现——基于java的实现

        本文主要说明如何使用Excel和Java建立上篇文章讨论的模型。包括移动平均法、简单指数平滑法、Holt模型和Winter模型，内附java源码。

目录

一、需求历史数据

 二、移动平均法

  1.基于EXCEL的实现

  2.基于java的实现

 三、简单指数平滑法

1.基于EXCEL的实现

2.基于java的实现

 四、趋势调整的指数平滑法(Holt模型)

1.基于EXCEL的实现

2.基于java的实现

 五、趋势和季节调整的指数平滑法(Winter模型)

1.基于EXCEL的实现

2.基于java的实现

一、需求历史数据

        下面有一段时期的需求历史数据。为了选择一种最合适的适应性预测方法对未来四个季度进行分析，需要用到前面文章提到的预测方法进行分析和预测。下面是MoonLight公司一段时期内的需求历史数据。

 二、移动平均法

  1.基于EXCEL的实现

        首先决定对四期的移动平均法的预测结果进行检验。EXCEL的实现过程在这里不再详述，结果如下:

         正如上图所示，TS很好地保持在±6的范围内，这说明该方法预测不存在任何显著的偏差，但是MAD在第12期相当大，MAPE也相当大。

        因此，使用四期的移动平均法，得到未来四期(13~16)的预测值如下：

         由于MAD在第12期为9719，因此预测的标准差为1.25*9719=12149。这相对于预测值来说，预测误差的标准差是非常大的。

  2.基于java的实现

public class HistoryData {//过去12期的历史需求double[] demands = {8000,13000,23000,34000,10000,18000,23000,38000,12000,13000,32000,41000};
}

import java.util.Arrays;public class MovingAverageMethod {private double[] demands;public MovingAverageMethod(double[] demands) {this.demands = demands;}public void calculation(Integer periods){if(periods>=demands.length){System.out.println("移动平均时期数大于需求时期数，不可计算！");return;}double[] level = new double[demands.length-periods+1];for (int i = 0; i < demands.length-periods+1; i++) {double periodSum = 0;for (int j = i; j < i+periods; j++) {periodSum+=demands[j];}level[i] = periodSum/periods;}System.out.println("level="+Arrays.toString(level));double[] forecast = new double[demands.length-periods];for (int i = 0; i < demands.length-periods; i++) {forecast[i] = level[i];}System.out.println("forecast="+Arrays.toString(forecast));double[] error = new double[demands.length-periods];for (int i = 0; i < demands.length-periods; i++) {error[i] = forecast[i]-demands[i+periods];}System.out.println("error="+Arrays.toString(error));double[] absoluteError = new double[demands.length-periods];for (int i = 0; i < demands.length - periods; i++) {absoluteError[i]=Math.abs(error[i]);}System.out.println("absoluteError="+Arrays.toString(absoluteError));double[] mse = new double[demands.length-periods];for (int i = 0; i <demands.length-periods; i++) {double sumSquares = 0;for (int j = 0; j < i+1; j++) {sumSquares = sumSquares + Math.pow(error[j],2);}mse[i] = sumSquares/(i+1);}System.out.println("mse="+Arrays.toString(mse));double[] mad = new double[demands.length-periods];for (int i = 0; i <demands.length-periods; i++) {double sumSquares = 0;for (int j = 0; j < i+1; j++) {sumSquares = sumSquares +absoluteError[j];}mad[i] = sumSquares/(i+1);}System.out.println("mad="+Arrays.toString(mad));double[] errorPercentage = new double[demands.length-periods];for (int i = 0; i < demands.length-periods; i++) {errorPercentage[i]=100*absoluteError[i]/demands[i+periods];}System.out.println("errorPercentage="+Arrays.toString(errorPercentage));double[] mape = new double[demands.length-periods];for (int i = 0; i < demands.length-periods; i++) {double sum = 0;for (int j = 0; j < i + 1; j++) {sum = sum + errorPercentage[j];}mape[i] = sum/(i+1);}System.out.println("mape="+Arrays.toString(mape));double[] ts = new double[demands.length-periods];for (int i = 0; i < demands.length-periods; i++) {double sum = 0;for (int j = 0; j < i + 1; j++) {sum = sum + error[j];}ts[i] = sum/mad[i];}System.out.println("ts="+Arrays.toString(ts));System.out.println("============================================");System.out.println("未来"+periods+"期的预测值="+level[level.length-1]);System.out.println("预测的标准差="+1.25*mad[mad.length-1]);}
}

public class Test {public static void main(String[] args) {MovingAverageMethod method = new MovingAverageMethod(new HistoryData().demands);method.calculation(4);}
}

  运行结果如下：

 三、简单指数平滑法

1.基于EXCEL的实现

        接着，决定对α=0.1的简单指数平湖法的预测结果进行检验。根据上文，估计第0期的初始需求水平为第1~12期的实际需求的平均值(L0=22083),结果如下：

         正如上图所示，TS在合理范围内，表示没有发生显著的偏差。但是MAD却相当大，为10208；MAPE为59%。

        因此，使用四期的移动平均法，得到未来四期(13~16)的预测值如下：

         在这种情况下，MAD在第12期为10208，而MAPE在第12期为59%，因此该方法预测误差的标准差估计为1.25*10208=12760，这个值是相当大的。

2.基于java的实现

public class HistoryData {//过去12期的历史需求double[] demands = {8000,13000,23000,34000,10000,18000,23000,38000,12000,13000,32000,41000};
}

import java.util.Arrays;public class SimpleExponentialSmoothingMethod {private double[] demands;private double a;public SimpleExponentialSmoothingMethod(double[] demands, double a) {this.demands = demands;this.a = a;}public void calculation(){if(a<=0||a>=1){System.out.println("a小于0或大于1，无法计算!");return;}double[] level = new double[demands.length+1];for (int i = 0; i < demands.length; i++) {level[0] += demands[i] / demands.length;}for (int i = 1; i < demands.length+1; i++) {level[i]=a*demands[i-1]+(1-a)*level[i-1];}System.out.println("level="+ Arrays.toString(level));double[] forecast = new double[demands.length];for (int i = 0; i < demands.length; i++) {forecast[i] = level[i];}System.out.println("forecast="+Arrays.toString(forecast));double[] error = new double[demands.length];for (int i = 0; i < demands.length; i++) {error[i] = forecast[i]-demands[i];}System.out.println("error="+Arrays.toString(error));double[] absoluteError = new double[demands.length];for (int i = 0; i < demands.length; i++) {absoluteError[i]=Math.abs(error[i]);}System.out.println("absoluteError="+Arrays.toString(absoluteError));double[] mse = new double[demands.length];for (int i = 0; i <demands.length; i++) {double sumSquares = 0;for (int j = 0; j < i+1; j++) {sumSquares = sumSquares + Math.pow(error[j],2);}mse[i] = sumSquares/(i+1);}System.out.println("mse="+Arrays.toString(mse));double[] mad = new double[demands.length];for (int i = 0; i <demands.length; i++) {double sumSquares = 0;for (int j = 0; j < i+1; j++) {sumSquares = sumSquares +absoluteError[j];}mad[i] = sumSquares/(i+1);}System.out.println("mad="+Arrays.toString(mad));double[] errorPercentage = new double[demands.length];for (int i = 0; i < demands.length; i++) {errorPercentage[i]=100*absoluteError[i]/demands[i];}System.out.println("errorPercentage="+Arrays.toString(errorPercentage));double[] mape = new double[demands.length];for (int i = 0; i < demands.length; i++) {double sum = 0;for (int j = 0; j < i + 1; j++) {sum = sum + errorPercentage[j];}mape[i] = sum/(i+1);}System.out.println("mape="+Arrays.toString(mape));double[] ts = new double[demands.length];for (int i = 0; i < demands.length; i++) {double sum = 0;for (int j = 0; j < i + 1; j++) {sum = sum + error[j];}ts[i] = sum/mad[i];}System.out.println("ts="+Arrays.toString(ts));System.out.println("============================================");System.out.println("未来4期的预测值="+level[level.length-1]);System.out.println("预测的标准差="+1.25*mad[mad.length-1]);}
}

public class Test {public static void main(String[] args) {SimpleExponentialSmoothingMethod method = new SimpleExponentialSmoothingMethod(new HistoryData().demands,0.1);method.calculation();}
}

运行结果如下：

 四、趋势调整的指数平滑法(Holt模型)

1.基于EXCEL的实现

    接着，决定对α=0.1，β=0.2的Holt模型的预测结果进行检验。根据上文，对需求和时间进行线性回归,得到L0=12015，T0=1549。结果如下：

      正如上图所示，TS在合理范围内，表示没有发生显著的偏差。但是MAD却相当大，为8836；MAPE为52%。

        因此，使用Holt模型，得到未来四期(13~16)的预测值如下：

         在这种情况下，MAD在第12期为8836，因此该方法预测误差的标准差估计为1.25*10208=11045，这个值是仍然偏大。

2.基于java的实现

public class HistoryData {//过去12期的历史需求double[] demands = {8000,13000,23000,34000,10000,18000,23000,38000,12000,13000,32000,41000};//时期tdouble[] time = {1,2,3,4,5,6,7,8,9,10,11,12};
}

import java.util.Random;public class SimpleRegression {public static double[] calculate(double[] xData, double[] yData){double sumX = 0;double sumY = 0;double sumXY = 0;double sumx2 = 0;double pjX,pjY;double b;double a;for(int i=0 ; i<xData.length ;  i++){double X = xData[i];double Y  = yData[i];sumX = sumX +X;sumY = sumY + Y;sumXY = sumXY + X*Y;sumx2 = sumx2 + X*X;}pjX = sumX / xData.length;pjY = sumY / xData.length;b = (sumXY - xData.length*pjX*pjY)/(sumx2 - xData.length*pjX*pjX);a = pjY - b*pjX;System.out.println("斜率："+b);System.out.println("截距："+a);double[] data = new double[2];data[0]=a;data[1]=b;return data;}
}

import java.util.Arrays;public class HoltMethod {private HistoryData historyData;private double a;private double b;public HoltMethod(HistoryData historyData, double a, double b) {this.historyData = historyData;this.a = a;this.b = b;}public void calculation(){if(a<=0||a>=1){System.out.println("a小于0或大于1，无法计算!");return;}if(b<=0||b>=1){System.out.println("b小于0或大于1，无法计算!");return;}double[] regressionData = SimpleRegression.calculate(historyData.time, historyData.demands);double[] level = new double[historyData.demands.length + 1];double[] trend = new double[historyData.demands.length + 1];level[0]=regressionData[0];trend[0]=regressionData[1];for (int i = 1; i < historyData.demands.length + 1; i++) {level[i]=a*historyData.demands[i-1]+(1-a)*(level[i-1]+trend[i-1]);trend[i]=b*(level[i]-level[i-1])+(1-b)*trend[i-1];}double[] forecast = new double[historyData.demands.length];for (int i = 0; i < historyData.demands.length; i++) {forecast[i] = level[i]+trend[i];}System.out.println("forecast="+Arrays.toString(forecast));double[] error = new double[historyData.demands.length];for (int i = 0; i < historyData.demands.length; i++) {error[i] = forecast[i]-historyData.demands[i];}System.out.println("error="+Arrays.toString(error));double[] absoluteError = new double[historyData.demands.length];for (int i = 0; i < historyData.demands.length; i++) {absoluteError[i]=Math.abs(error[i]);}System.out.println("absoluteError="+Arrays.toString(absoluteError));double[] mse = new double[historyData.demands.length];for (int i = 0; i <historyData.demands.length; i++) {double sumSquares = 0;for (int j = 0; j < i+1; j++) {sumSquares = sumSquares + Math.pow(error[j],2);}mse[i] = sumSquares/(i+1);}System.out.println("mse="+Arrays.toString(mse));double[] mad = new double[historyData.demands.length];for (int i = 0; i <historyData.demands.length; i++) {double sumSquares = 0;for (int j = 0; j < i+1; j++) {sumSquares = sumSquares +absoluteError[j];}mad[i] = sumSquares/(i+1);}System.out.println("mad="+Arrays.toString(mad));double[] errorPercentage = new double[historyData.demands.length];for (int i = 0; i < historyData.demands.length; i++) {errorPercentage[i]=100*absoluteError[i]/historyData.demands[i];}System.out.println("errorPercentage="+Arrays.toString(errorPercentage));double[] mape = new double[historyData.demands.length];for (int i = 0; i < historyData.demands.length; i++) {double sum = 0;for (int j = 0; j < i + 1; j++) {sum = sum + errorPercentage[j];}mape[i] = sum/(i+1);}System.out.println("mape="+Arrays.toString(mape));double[] ts = new double[historyData.demands.length];for (int i = 0; i < historyData.demands.length; i++) {double sum = 0;for (int j = 0; j < i + 1; j++) {sum = sum + error[j];}ts[i] = sum/mad[i];}System.out.println("ts="+Arrays.toString(ts));System.out.println("============================================");for (int i = 1; i < 5; i++) {double result = level[level.length-1]+i*trend[trend.length-1];System.out.println("未来"+i+"期的预测值="+result);}System.out.println("预测的标准差="+1.25*mad[mad.length-1]);}
}

public class Test {public static void main(String[] args) {HoltMethod method = new HoltMethod(new HistoryData(),0.1,0.2);method.calculation();}
}

运行结果如下：

 五、趋势和季节调整的指数平滑法(Winter模型)

1.基于EXCEL的实现

接着，决定对α=0.05，β=0.1，γ=0.05的Holt模型的预测结果进行检验。根据上文，进行线性回归和求季节性因素,得到L0=12015，T0=1549,S1=0.47,S2=0.68,S3=1.17,S4=1.67。结果如下：

         正如上图所示，TS在合理范围内，表示没有发生显著的偏差。但是MAD(1469)和MAPE(8%)都明显小于其他方法。

        因此，使用Winter模型，得到未来四期(13~16)的预测值如下：

         在这种情况下，MAD在第12期为1469，因此该方法预测误差的标准差估计为1.25*1469=1836，这个值是最小的。

2.基于java的实现

public class HistoryData {//过去12期的历史需求double[] demands = {8000,13000,23000,34000,10000,18000,23000,38000,12000,13000,32000,41000};//时期tdouble[] time = {1,2,3,4,5,6,7,8,9,10,11,12};
}

import java.util.ArrayList;
import java.util.Arrays;public class ExcludingSeasonality {public static ArrayList<double[]> calculate(int period,HistoryData data){if((period&1)!=1){int first = 1+period/2;int last = data.demands.length-period/2;double[] series = new double[last-first+1];double[] pureDemand = new double[last-first+1];for (int i = 0; i < last-first+1; i++) {series[i]=data.time[first-1+i];double sum = 0;for (int j = first+i-period/2; j <first+i+period/2-1; j++) {sum+=data.demands[j];}pureDemand[i] = (data.demands[first-3+i]+data.demands[first+i+1]+2*sum)/(last-first+1);}System.out.println(Arrays.toString(series));System.out.println(Arrays.toString(pureDemand));ArrayList<double[]> objects = new ArrayList<>();objects.add(series);objects.add(pureDemand);return objects;} else {int first = 1 + (period-1)/2;int last = data.demands.length-(period-1)/2;System.out.println(first);System.out.println(last);double[] series = new double[last-first+1];double[] pureDemand = new double[last-first+1];for (int i = 0; i < last-first+1; i++) {series[i]=data.time[first-1+i];double sum = 0;for (int j = first+i-(period-1)/2; j <first+i+(period-1)/2-1; j++) {sum+=data.demands[j];}pureDemand[i] = sum/(last-first+1);}System.out.println(Arrays.toString(series));System.out.println(Arrays.toString(pureDemand));ArrayList<double[]> objects = new ArrayList<>();objects.add(series);objects.add(pureDemand);return objects;}}
}

import java.util.Random;public class SimpleRegression {public static double[] calculate(double[] xData, double[] yData){double sumX = 0;double sumY = 0;double sumXY = 0;double sumx2 = 0;double pjX,pjY;double b;double a;for(int i=0 ; i<xData.length ;  i++){double X = xData[i];double Y  = yData[i];sumX = sumX +X;sumY = sumY + Y;sumXY = sumXY + X*Y;sumx2 = sumx2 + X*X;}pjX = sumX / xData.length;pjY = sumY / xData.length;b = (sumXY - xData.length*pjX*pjY)/(sumx2 - xData.length*pjX*pjX);a = pjY - b*pjX;System.out.println("斜率："+b);System.out.println("截距："+a);double[] data = new double[2];data[0]=a;data[1]=b;return data;}
}

import java.util.ArrayList;
import java.util.Arrays;public class WinterMethod {private HistoryData historyData;private double a;private double b;private double c;private int period;public WinterMethod(HistoryData historyData, double a, double b,double c,int period) {this.historyData = historyData;this.a = a;this.b = b;this.c = c;this.period=period;}public void calculation(){ArrayList<double[]> excludeData = ExcludingSeasonality.calculate(period, historyData);double[] regressionData = SimpleRegression.calculate(excludeData.get(0), excludeData.get(1));System.out.println("回归结果:"+Arrays.toString(regressionData));//剔除季节性因素后的需求double[] pureDemands=new double[historyData.demands.length];double[] seasonalFactors=new double[historyData.demands.length];for (int i = 0; i < pureDemands.length; i++) {pureDemands[i] = regressionData[0]+regressionData[1]*historyData.time[i];seasonalFactors[i]=historyData.demands[i]/pureDemands[i];}double[] seasonalFactor = new double[period];for (int i = 0; i <period; i++) {double sum = 0;for (int j = 0; j < historyData.demands.length/period; j++) {sum+=seasonalFactors[i+period*j];}seasonalFactor[i]=sum/(historyData.demands.length/period);}System.out.println("季节因素:"+Arrays.toString(seasonalFactor));//求解double[] level = new double[historyData.demands.length + 1];double[] trend = new double[historyData.demands.length + 1];double[] season = new double[historyData.demands.length+period];level[0]=regressionData[0];trend[0]=regressionData[1];for (int i = 0; i < period; i++) {season[i]=seasonalFactor[i];}for (int i = 1; i < historyData.demands.length + 1; i++) {level[i]=a*(historyData.demands[i-1]/season[i-1])+(1-a)*(level[i-1]+trend[i-1]);trend[i]=b*(level[i]-level[i-1])+(1-b)*trend[i-1];if(i<=12){season[i+period-1]=c*(historyData.demands[i-1]/level[i])+(1-c)*season[i-1];}}System.out.println("level:"+Arrays.toString(level));System.out.println("trend:"+Arrays.toString(trend));System.out.println("season:"+Arrays.toString(season));double[] forecast = new double[historyData.demands.length];for (int i = 0; i < historyData.demands.length; i++) {forecast[i] = (level[i]+trend[i])*season[i];}System.out.println("forecast="+Arrays.toString(forecast));double[] error = new double[historyData.demands.length];for (int i = 0; i < historyData.demands.length; i++) {error[i] = forecast[i]-historyData.demands[i];}System.out.println("error="+Arrays.toString(error));double[] absoluteError = new double[historyData.demands.length];for (int i = 0; i < historyData.demands.length; i++) {absoluteError[i]=Math.abs(error[i]);}System.out.println("absoluteError="+Arrays.toString(absoluteError));double[] mse = new double[historyData.demands.length];for (int i = 0; i <historyData.demands.length; i++) {double sumSquares = 0;for (int j = 0; j < i+1; j++) {sumSquares = sumSquares + Math.pow(error[j],2);}mse[i] = sumSquares/(i+1);}System.out.println("mse="+Arrays.toString(mse));double[] mad = new double[historyData.demands.length];for (int i = 0; i <historyData.demands.length; i++) {double sumSquares = 0;for (int j = 0; j < i+1; j++) {sumSquares = sumSquares +absoluteError[j];}mad[i] = sumSquares/(i+1);}System.out.println("mad="+Arrays.toString(mad));double[] errorPercentage = new double[historyData.demands.length];for (int i = 0; i < historyData.demands.length; i++) {errorPercentage[i]=100*absoluteError[i]/historyData.demands[i];}System.out.println("errorPercentage="+Arrays.toString(errorPercentage));double[] mape = new double[historyData.demands.length];for (int i = 0; i < historyData.demands.length; i++) {double sum = 0;for (int j = 0; j < i + 1; j++) {sum = sum + errorPercentage[j];}mape[i] = sum/(i+1);}System.out.println("mape="+Arrays.toString(mape));double[] ts = new double[historyData.demands.length];for (int i = 0; i < historyData.demands.length; i++) {double sum = 0;for (int j = 0; j < i + 1; j++) {sum = sum + error[j];}ts[i] = sum/mad[i];}System.out.println("ts="+Arrays.toString(ts));System.out.println("============================================");for (int i = 1; i < 5; i++) {double result = (level[level.length-1]+i*trend[trend.length-1])*season[historyData.demands.length+period-5+i];System.out.println("未来"+i+"期的预测值="+result);}System.out.println("预测的标准差="+1.25*mad[mad.length-1]);}
}

public class Test {public static void main(String[] args) {WinterMethod method = new WinterMethod(new HistoryData(),0.05,0.1,0.1,4);method.calculation();}
}

运行结果如下：