浅析需求量服从poisson分布的报童问题.doc

(1)%poisson分布图clf,clear,m=30;lambta1=60;lambta2=70;a=30;b=110; subplot(2,2,1)for k=1:m x=poissrnd(lambta1); y=poisspdf(x,lambta1);stem(x,y,LineWidth,2,. MarkerEdgeColor,k,. MarkerFaceColor,red,. MarkerSize,5) hold on axis(a b 0 0.06) grid on; title(lambta=60)endsubplot(2,2,3)t=a:3:b;f=poisspdf(t,lambta1);plot(t,f,-rs,LineWidth,2,. MarkerEdgeColor,k,. MarkerFaceColor,g,. MarkerSize,3)hold onaxis(a b 0 0.06)grid on;subplot(2,2,2)for k=1:m x=poissrnd(lambta2); y=poisspdf(x,lambta2); stem(x,y,LineWidth,2,. MarkerEdgeColor,k,. MarkerFaceColor,red,. MarkerSize,5) hold on axis(a b 0 0.06) grid on; title(lambta=70)endsubplot(2,2,4)t=a:3:b;f=poisspdf(t,lambta2);y0=max(f)+0.1;plot(t,f,-rs,LineWidth,2,. MarkerEdgeColor,k,. MarkerFaceColor,g,. MarkerSize,3)axis(a b 0 0.06)grid on;(2)%购进量随收益值变化的动画图线a=2;b=1.3;c=0.2;for lambta=40:110;x=0:200; y=poisspdf(x,lambta); %需求量的概率服从泊松分布for n=0:200 j=n+1; sy=0;for x=0:200 %用累加的方法计算收益值 i=x+1; if xn sy=sy+(a-b)*n*y(i); end end sy(j)=sy; plot(n,sy(j),-rs,LineWidth,1,. MarkerEdgeColor,r,. MarkerFaceColor,g,. MarkerSize,2); %画出购进量与收益值的函数图形 hold onend legend(lambta变化时收益的变化情况); temp1=num2str(floor(lambta); str=strcat(lambta=,temp1); text(20,90,str,FontSize,15); %在坐标轴（20，90）处标注hold offaxis(0 200 -10 100); set(gca,XTick,0:20:200); %设置x轴网格线 set(gca,YTick,-10:10:100); grid on; drawnow; end(3)%lambta取70时不同购进量对应的收益值a=2;b=1.3;c=0.2;lambta=70;x=40:10:110;y=poisscdf(x,lambta); %不同需求量所对应的概率值x1=rand(365,1);%随机产生一年内的概率，从而确定某一天的报纸的需求量for n=4:11 supply=n*10; sub(n)=0; for i=1:365 if x1(i)=y(1) need=40; elseif x1(i)=y(2) need=50; elseif x1(i)=y(3) need=60; elseif x1(i)=y(4) need=70; elseif x1(i)=y(5) need=80; elseif x1(i)=y(6) need=90; elseif x1(i)=need sale=need; remand=supply-need; else sale=supply; remand=0; end %确定剩余量 sub(n)=sub(n)+a*sale-b*supply+c*remand; end %求购进量为n时一年内报纸的收益值endoptneed=40;optmoney=sub(4);40,sub(4)/365%购进量为40时平均每天报纸的收益值for n=5:11 if sub(n)=optmoney optneed=n*10; optmoney=sub(n); end n,sub(n)/365endoptneed,optmoney,optmoney/365%求最优购进量和最大收益值(4)%lambta的取值对最大收益的影响cleara=2;b=1.3;c=0.2;j=0;m=zeros(73,1);for lambta=40:1:112 j=j+1;x=40:10:110;y=poisscdf(x,lambta);x1=rand(365,1);for n=4:11 supply=n*10; sub(n)=0; for i=1:365 if x1(i)=y(1) need=40; elseif x1(i)=y(2) need=50; elseif x1(i)=y(3) need=60; elseif x1(i)=y(4) need=70; elseif x1(i)=y(5) need=80; elseif x1(i)=y(6) need=90; elseif x1(i)=need sale=need; remand=supply-need; else sale=supply; remand=0; end sub(n)=sub(n)+a*sale-b*supply+c*remand; endendoptneed=40;optmoney=sub(4);%40,sub(4)/365;for n=5:11 if sub(n)=optmoney optneed=n*10; optmoney=sub(n); end %n,sub(n)/365endoptneed,optmoney,optmoney/365m(j)=optmoney;endla=40:1:112;plot(la,m)title(lambta取不同值时对最大收益的影响)（4）%在每增加0.1元卖价则降低d份需求量的条件下，价格与收益的关系clearb=1.3;c=0.2;d=4;lambta=70;x=40:10:110;y=poisscdf(x,lambta);x1=rand(365,1);m=zeros(16,1);j=0;for a=1.5:0.1:3 j=j+1;for n=4:11 supply=n*10; sub(n)=0; for i=1:365 if x1(i)=y(1) need=40-d*j; %每增加0.1元卖价，则降低d份需求量 elseif x1(i)=y(2) need=50-d*j; elseif x1(i)=y(3) need=60-d*j; elseif x1(i)=y(4) need=70-d*j; elseif x1(i)=y(5) need=80-d*j; elseif x1(i)=y(6) need=90-d*j; elseif x1(i)=y(7) need=100-d*j; else need=110-d*j; end if need=need sale=need; remand=supply-need; else sale=supply; remand=0; end sub(n)=sub(n)+a*sale-b*supply+c*remand; end endoptneed=40;optm