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菜篮子工程中的蔬菜种植问题

摘要

本文研究的是蔬菜基地为满足不同销售点需求条件的最优调配方案问题，用了Froyd算法、线性规划建立了一系列数学规划模型，并用MATLAB软件编程实现，图论绘图软件绘图。

关于问题一：线性规划问题中的单纯形法求解，为了使蔬菜短缺补偿和运费补贴的总补偿最小。运费用R表示。R为距离与送货量的积，因为与送货距离相关，我们必须先求出八个基地至各个销售点的最短距离。采用Froyd算法，结合MATLAB编程实现。其次考虑缺货损失Q，以题中要求为约束条件，损失最低为目标建立线性规划模型，用MATLAB编程求解。

目标函数总费用P来表示,总费用包括两部分: 蔬菜调运费R，各市场供给量小于需求量的短缺补偿Q，即：P=R+Q

在此种方案下，使政府的短缺补偿和运费补贴最少，求得最小金额为45509元。若规定各蔬菜销售点的短缺量一律不超过需求量的30%，此情况下最小金额为53160元。

关于问题二：本问采用的方法是表上作业法。题中无法确定8个新增蔬菜种植量，由于销售点的需求量不变，基地蔬菜种植量改变。由此逆向思考此问题。设AI’为由各个销售点逆向运往基地的蔬菜量。要使总短缺补偿和运费补贴最少，应当保证供销平衡。总补偿只考虑运费补偿：

P?R?Q???0.04DJ?1I?1358(I,J)X(J,I) 可用MATLAB编程求解。总短缺补偿和

运费补贴最少为：308.76元。

关于问题三：本问采用的是层次分析法。关键要解决销售点和基地的对应问题。通过第二题的结论得到的各个基地供应销售点的分配方式，通过统计可以看出，基地1，基地2，基地8供求平衡，于是不考虑这三个基地以及对应销售点，对剩下未平衡的基地与销售点重新设计运送方案。由于只有销售点11，销售点33，销售点34对应基地运送数量未知，我们对销售点——基地——运送量进行线性规划求解得到各基地蔬菜种植计划。蔬菜运送方案运费补贴：108.607+256.128=364.735元。

关于问题四：本题我们采用层次分析法解决。先定性，再定量分析。

关键字：蔬菜市场调配方案 Froyd算法线性规划逆向思维层次分析

一.问题重述

为缓解我国副食品供不应求的矛盾，农业部于1988年提出建设“菜篮子工程”。一些中小城市，蔬菜种植采取以郊区和农区种植为主，结合政府补贴的方式来保障城区蔬菜的供应。

JG市在郊区和农区建立了8个蔬菜种植基地，每天将蔬菜运送到市区的35个蔬菜销售点。市区有15个主要交通路口，运费补贴标准为0.04元/（1吨.1公里）。

需要解决的问题如下：

1.用数学模型方法制定运送方案，使政府的短缺补偿和运费补贴最少；重新制定方案，规定各蔬菜销售点的短缺量一律不超过需求量的30%。

2.建立问题的数学模型以确定8个蔬菜种植基地的新增蔬菜种植量，并重新设计蔬菜运送方案，使总短缺补偿和运费补贴最少。

3.在问题2结果的建立数学模型基础上，蔬菜种植基地可种植12种蔬菜。给出问题的求解算法，确定每个蔬菜种植基地的种植计划，并重新设计蔬菜运送方案，使总短缺补偿和运费补贴最少。

4.收集信息，形成问题的描述。并建立数学模型，给出数值结果使得计划更好的实行。

5.附件2中销售点17日需求量13.6吨/天，在附件4中17日需求量13.5元/吨.天。基于实践可行性考虑，小组将13.5吨/天作为真实值建模，特此声明。

二. 变量说明

AI (I=1,2??8） A代表基地，AI 代表基地的供应量（常数） BJ (J=1,2??35） B代表销售点，BJ 代表销售点J的需求量 X(I,J)(1≤I≤8; 1≤J≤35） I基地运往J销售点的运输量 SJ (J=1,2??35） J销售点短缺补偿单价

D(I,J) (1≤I≤8; 1≤J≤35） I基地到J销售点最短距离 P 总补偿 Q 短缺补偿

R 运费补偿

AI’(I=1,2??8）新增加蔬菜后各基地蔬菜量

X(J,I)(1≤I≤8; 1≤J≤35） J销售点到I基地运输量(逆向假设) B(J,K) (J=11,33,34) 销售点J对K类蔬菜的需求量

X(I,J,K) (3≤I≤7;J=11,33,34;1≤K≤12) J销售点K类蔬菜理想运往I基地的蔬菜量

三. 基本假设

1.只考虑运输费用和短缺费用，不考虑装卸等其他费用。 2.假设运输的蔬菜路途中没有损耗。 3.假设日需求量与缺货损失费用不变。

4.假设各基地供应蔬菜同质且可以种植任意的12种蔬菜。 5.假设在蔬菜调配的过程中无意外发生。 6.假设新增产的蔬菜能够满足缺货量。 7.假设道路双向通行，且运费相同。 8.假设车辆载重可以一次达到要求。

四. 模型的建立与求解

第一题 ⑴：

问题分析：此题是线性规划问题中的单纯形法求解，为了使蔬菜短缺补偿和运费补贴的总补偿最小。运费用R表示。R为距离与送货量的积，因为与送货距离相关，我们必须先求出八个基地至各个销售点的最短距离。采用Froyd算法，结合MATLAB编程实现。其次考虑缺货损失Q，以题中要求为约束条件，损失最低为目标建立线性规划模型，用MATLAB编程求解。

目标函数总费用P来表示,总费用包括两部分: 蔬菜调运费R，各市场供给量小于需求量的短缺损失Q，即：P=R+Q 其中R??I?18?DJ?135(I,J)X(I,J)；市场j的短缺量为: BJ??X(I,J)；

I?1358所以目标函数为:P??I?18?DJ?1(I,J)X(I,J)8???Q?BJ??X(I,J)?；

JI?1??约束条件为： 1.变量非负性限制,即

X(I,J)?0 (I?1,2,?8;J?1,2,?35)

2.基地I的供应量等于基地I运往所有销售点的蔬菜数量，即

?XJ?I35(I,J)?A (I?1,2,3?8)

I83.从所有基地运送到销售点j的蔬菜量之和小于等于销售点j的需求数量，即 ?X(I,J)?BJ (J?1,2,3?35)

i?1模型的建立：

由图和表格的信息知，建立一个线性规划模型，使得蔬菜调运及预期的短缺损失为最小。

调运总费用P为：

P?R?Q??J?135?0.04DI?18(I,J)X(I,J)??(BJ??X(I,J))SJ

J?1I358 若使调运总费用最少，则应保证8个基地到35个销售点的路程最短，最短路线的求解过程如图一：

（图一）

图一是基于Froyd算法的图论绘图截图，AI,BJ,CX 分别是基地，销售点，路口的各个点，蓝色线段则表示各点间距。

分析上图可知，该路线为无向网络，就该图而言，该图权矩阵过为庞大。为58阶网络距离矩阵。现在给出网络最短路线的Froyd算法：（1） d1=w.(w为所给网络的n阶权矩阵) （2） dk=(dkij)n?n,k=2,3,…,p.

其中dkij=min[d(k?1)is+d(k?1)sj,i,j=1,2,…,n. Froyd算法计算次数的确定：当wij?0时，p由下式确定：

p?ln(n-1)/ln2，这样的dp就确定了网络各点间的最短距离。此处n=58,解出p?5.86

故只需要取p=6即可，即算到d6即可。按照Froyd算法：首先建立m文件，输入Froyd算法代码： function y=fld(n,x) for r=1:n for i=1:n for j=1:n

p(j)=x(i,j)+x(j,r); end

y(r,i)=min(p); end

End

在MATLAB命令窗输入下列代码：

d =[0 14 16 10 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 14 0 Inf 3 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 16 Inf 0 2 15 Inf Inf 2 Inf Inf Inf Inf Inf Inf Inf Inf Inf 10 3 2 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 15 Inf 0 5 9 7 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 5 0 4 2 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 9 4 0 Inf 19 6 Inf Inf Inf Inf Inf Inf Inf Inf Inf 2 Inf 7 2 Inf 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 19 Inf 0 11 12 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 6 Inf 11 0 6 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 12 6 0 Inf 5 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 25 10 15 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 5 25 0 Inf 5 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 10 Inf 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 15 5 Inf 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 3 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 3 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 9 Inf 14 9 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 26 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 30 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 9 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 7 Inf Inf Inf 15 Inf Inf Inf Inf Inf Inf Inf Inf Inf

Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 15 Inf 6 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 2 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 3 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 5 Inf Inf 3 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 7 Inf 11 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 6 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 8 6 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Columns 18 through 34

Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 30 Inf 9 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 9 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 14 26 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 9 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 Inf Inf Inf Inf 4 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 6 25 16 8 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 6 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 25 Inf 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 16 Inf Inf 0 10 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 4 8 Inf Inf 10 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 7 15 8 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 7 0 Inf Inf Inf Inf Inf 15 11 Inf Inf Inf Inf Inf Inf Inf Inf 15 Inf 0 Inf Inf Inf Inf Inf 12 Inf Inf Inf Inf Inf Inf Inf Inf 8 Inf Inf 0 17 6 Inf 6 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 17 0 15 20 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 6 15 0 4 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 20 4 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 15 Inf 6 Inf Inf Inf 0 Inf 13 Inf Inf Inf Inf Inf Inf Inf Inf 11 12 Inf Inf Inf Inf Inf 0 8 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 13 8 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 4 Inf 5 Inf 3 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 10 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 13

Inf Inf Inf Inf 3 5 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 14 Inf Inf Inf 4 7 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 5 Inf Inf Inf Inf 20 Inf Inf Inf Inf Inf 10 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 7 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 6 Inf Inf Inf 8 6 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 5 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 5 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 2 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Columns 35 through 51

Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 7 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 15 Inf Inf Inf Inf Inf Inf Inf Inf 2 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 5 Inf Inf 15 Inf 6 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 3 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 3 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 4 20 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 3 7 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 5 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 10 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 4 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 10 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 5 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 5 Inf Inf Inf Inf Inf Inf Inf Inf Inf 3 Inf Inf Inf Inf 13 14 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 Inf Inf Inf 10 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 13 8 4 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 13 0 11 Inf 7 Inf Inf Inf Inf 16 5 Inf Inf Inf Inf Inf Inf 8 11 0 Inf Inf Inf Inf Inf Inf Inf 8 11 Inf Inf Inf Inf 10 4 Inf Inf 0 17 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 7 Inf 17 0 Inf Inf Inf 5 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 Inf Inf 2 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 3 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 3 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 5 2 Inf Inf 0 11 Inf Inf Inf Inf Inf 9

Inf Inf 16 Inf Inf Inf Inf Inf Inf 11 0 10 Inf 3 Inf Inf 5 Inf Inf 5 8 Inf Inf Inf Inf Inf Inf 10 0 Inf 9 Inf Inf Inf Inf Inf Inf 11 Inf Inf Inf Inf Inf Inf Inf Inf 0 3 Inf 4 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 3 9 3 0 4 7 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 4 0 4 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 4 7 4 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 9 5 Inf Inf Inf Inf Inf 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 18 Inf Inf Inf 6 Inf 13 Inf Inf Inf Inf Inf Inf Inf Inf Inf 10 Inf Inf Inf Inf Inf Inf 4 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 8 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf

Columns 52 through 58

Inf Inf Inf 8

Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 6 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 13 4 Inf Inf 8 Inf Inf 0 Inf Inf Inf Inf 9 Inf Inf 0 4 Inf 6 Inf Inf Inf 4 0 7 Inf Inf Inf Inf Inf 7 0 Inf Inf Inf Inf 6 Inf Inf 0 7 Inf 9 Inf Inf Inf 7 0 Inf Inf Inf Inf Inf Inf Inf 0]

d1=d；d2=fld(58,d1)；d3=fld(58,d2)；d4=(fld(58,d3)；d5=(fld(58,d4)；d6=(fld(58,d5) 输出结果见附录。

模型结果：

1.根据上述矩阵和代码，分别找出各基地到各销售点的最短距离，见表一：基地1 基地2 基地3 基地4 基地5 基地6 基地7 基地8 销售点1 47 销售点2 35 销售点3 26 销售点4 13 销售点5 17 销售点6 33 销售点7 41 销售点8 49 销售点9 50 销售点10 40 销售点11 37 销售点12 30 销售点13 20 销售点14 12 销售点15 16 销售点16 21 销售点17 24 销售点18 35 销售点19 40 销售点20 43 销售点21 37 销售点22 33 销售点23 29 销售点24 31 销售点25 25 销售点26 22 销售点27 25 销售点28 28 销售点29 33 销售点30 40 销售点31 37 48 36 27 14 18 34 41 39 40 29 29 24 13 9 5 10 13 24 29 32 26 22 18 20 14 11 14 17 22 29 26 61 51 42 29 33 49 50 48 49 38 38 33 28 24 20 19 22 33 38 41 35 31 27 21 15 14 11 12 17 28 35 68 64 59 46 50 56 57 55 54 45 45 46 45 41 37 32 35 40 37 40 34 30 32 26 28 32 31 25 20 18 24 9

52 51 50 46 50 43 41 39 32 32 35 42 45 41 37 32 29 30 24 18 16 20 24 33 36 39 42 39 35 24 17 26 31 30 43 40 23 15 13 6 17 27 34 43 39 35 30 27 22 16 8 14 18 22 35 34 37 40 37 42 31 24 7 14 14 27 28 21 18 25 27 30 34 41 36 32 36 41 44 35 38 41 46 45 44 51 45 42 45 48 53 58 51 32 23 15 28 29 22 30 38 39 39 35 42 37 33 37 42 45 38 41 51 49 48 47 52 46 43 46 49 54 61 54 销售点32 44 33 40 34 销售点33 50 39 48 28 销售点34 42 31 40 19 销售点35 48 37 36 10 表（一）

9 3 12 21 17 23 29 38 50 56 56 65 56 62 59 68 2.根据MATLAB，各个基地到各销售点的运输量，见表二：基地一基地二基地三基地四基地五基地六基地七基地八基地一基地二基地三基地四基地五基地六基地七基地八基地一基地二基地三基地四基地五基地六基地七基地八基地一基地二基地三基地四基地五基地六基地七基地八

1销售点 2销售点 3销售点 4销售点 5销售点 6销售点 7销售点 0.98 1.50 1.76 2.08 1.91 0.00 0.00 1.10 1.66 1.97 2.33 2.15 0.00 0.00 0.72 1.14 1.34 1.61 1.45 0.00 0.00 0.93 1.43 1.68 1.99 1.82 0.00 0.00 0.69 1.11 1.30 1.56 1.40 0.00 0.00 0.85 1.33 1.56 1.85 1.68 0.00 0.00 0.58 0.96 1.13 1.36 1.22 0.00 0.00 0.66 1.07 1.26 1.51 1.36 0.00 0.00 8销售点 9销售点 10销售点 11销售点 12销售点 13销售点 14销售点 1.40 0.00 1.25 1.54 1.04 1.26 0.00 1.55 0.00 1.39 1.71 1.16 1.40 0.00 1.07 0.00 0.94 1.18 0.78 0.95 0.00 1.33 0.00 1.19 1.47 0.99 1.20 0.00 1.03 0.00 0.90 1.14 0.75 0.92 0.00 1.24 0.00 1.10 1.36 0.91 1.11 0.00 0.89 0.00 0.77 0.99 0.64 0.79 0.00 1.00 0.00 0.87 1.11 0.72 0.88 0.00 15销售点 16销售点 17销售点 18销售点 19销售点 20销售点 21销售点 1.71 0.00 1.93 1.32 1.09 1.47 1.86 1.91 0.00 3.60 1.47 1.21 1.62 2.08 1.30 0.00 1.26 1.01 0.81 1.12 1.42 1.63 0.00 1.74 1.27 1.03 1.40 1.78 1.25 0.00 1.22 0.98 0.78 1.09 1.38 1.51 0.00 1.53 1.17 0.95 1.30 1.65 1.08 0.00 1.05 0.84 0.67 0.94 1.20 1.21 0.00 1.17 0.94 0.75 1.05 1.33 22销售点 23销售点 24销售点 25销售点 26销售点 27销售点 28销售点 1.10 1.00 1.85 1.41 0.00 1.34 1.31 1.23 1.13 2.08 1.56 0.00 0.44 1.45 0.82 0.74 1.39 1.08 0.00 0.86 1.00 1.05 0.95 1.76 1.35 0.00 1.22 1.25 0.79 0.71 1.34 1.04 0.00 0.82 0.96 0.97 0.87 1.62 1.25 0.00 1.07 1.16 0.68 0.60 1.16 0.90 0.00 0.68 0.83 0.76 0.69 1.30 1.01 0.00 0.78 0.93 29销售点 30销售点 31销售点 32销售点 33销售点 34销售点 35销售点 10

基地一 1.51 1.33 1.15 1.19 1.69 1.03 0.00 基地二 1.67 1.47 1.28 1.32 1.89 1.16 0.00 基地三 1.16 1.01 0.86 0.89 1.27 0.84 0.00 基地四 1.44 1.27 1.09 1.13 1.61 0.99 0.00 基地五 1.12 0.97 0.83 0.86 1.23 0.82 0.00 基地六 1.34 1.17 1.00 1.04 1.48 0.94 0.00 基地七 0.97 0.84 0.70 0.74 1.06 0.73 0.00 基地八 1.09 0.94 0.80 0.83 1.18 0.79 0.00 表（二）模型的评价与分析：

在此种方案下，使政府的短缺补偿和运费补贴最少，最小金额为45509元。

第一题⑵：

约束条件为:限制在每个销售点需供货70%以上，即在上一题的约束条件中增加

0.7BJ??X(I,J)?BJ

I?18模型结果：

根据新增条件，MATLAB求得各基地到各销售点的运输量，见表三（取两位小数） 1销售点 2销售点 3销售点 4销售点 5销售点 6销售点 7销售点基地一 1.01 1.54 1.23 1.45 1.32 1.13 1.42 基地二 1.17 1.77 1.36 1.60 1.47 1.26 1.57 基地三 0.69 1.11 0.95 1.14 1.03 0.86 1.11 基地四 0.95 1.45 1.17 1.39 1.26 1.08 1.36 基地五 0.66 1.07 0.92 1.10 1.00 0.83 1.08 基地六 0.85 1.32 1.09 1.29 1.18 1.00 1.27 基地七 0.54 0.91 0.80 0.98 0.88 0.73 0.95 基地八 0.63 1.03 0.89 1.07 0.97 0.81 1.05 8销售点 9销售点 10销售点 11销售点 12销售点 13销售点 14销售点基地一 0.98 1.03 1.28 1.08 0.74 0.89 1.23 基地二 1.10 1.16 1.47 1.21 0.84 1.00 1.37 基地三 0.74 0.78 0.91 0.82 0.54 0.66 0.94 基地四 0.94 0.98 1.21 1.03 0.70 0.84 1.17 基地五 0.72 0.75 0.87 0.80 0.51 0.63 0.92 基地六 0.86 0.91 1.09 0.95 0.64 0.77 1.09 基地七 0.62 0.65 0.73 0.69 0.43 0.54 0.80 基地八 0.69 0.73 0.84 0.77 0.49 0.61 0.89 15销售点 16销售点 17销售点 18销售点 19销售点 20销售点 21销售点基地一 1.19 1.28 1.37 0.93 0.77 1.03 1.29 基地二 1.32 1.42 1.52 1.05 0.87 1.14 1.44 基地三 0.91 0.99 1.07 0.70 0.56 0.79 1.00 基地四 1.13 1.22 1.31 0.89 0.73 0.98 1.24 基地五 0.88 0.96 1.04 0.68 0.54 0.76 0.97 基地六 1.05 1.13 1.22 0.82 0.67 0.91 1.15 基地七 0.77 0.84 0.91 0.58 0.46 0.66 0.85 基地八 0.86 0.93 1.01 0.65 0.52 0.74 0.94 11

基地一基地二基地三基地四基地五基地六基地七基地八基地一基地二基地三基地四基地五基地六基地七 22销售点 23销售点 24销售点 25销售点 26销售点 27销售点 28销售点 1.15 1.04 1.28 0.99 1.52 0.76 0.93 1.33 1.21 1.42 1.10 1.68 0.87 1.04 0.79 0.71 0.99 0.75 1.19 0.55 0.69 1.07 0.98 1.22 0.94 1.45 0.72 0.88 0.75 0.68 0.96 0.73 1.16 0.53 0.67 0.96 0.88 1.13 0.87 1.35 0.66 0.81 0.62 0.55 0.84 0.63 1.03 0.45 0.57 0.72 0.65 0.93 0.71 1.13 0.51 0.64 29销售点 30销售点 31销售点 32销售点 33销售点 34销售点 35销售点 1.06 1.18 1.18 1.23 1.17 1.24 1.10 1.18 1.34 1.37 1.42 1.30 1.38 1.23 0.81 0.86 0.83 0.86 0.90 0.95 0.84 1.01 1.11 1.11 1.15 1.11 1.18 1.05 0.78 0.83 0.79 0.82 0.87 0.92 0.81 0.93 1.02 1.00 1.04 1.03 1.10 0.97 0.68 0.70 0.66 0.68 0.76 0.81 0.70 表（三）

模型的评价与分析：

若规定各蔬菜销售点的短缺量一律不超过需求量的30%，此情况下最小金额为53160元。

第二题：

问题分析：本问采用的方法是表上作业法。题中无法确定8个新增蔬菜种植量，由于销售点的需求量不变，基地蔬菜种植量改变。由此逆向思考此问题。设AI’为由各个销售点逆向运往基地的蔬菜量。要使总短缺补偿和运费补贴最少，应当保证供销平衡。总补偿只考虑运费补偿：

P?R?Q???0.04DJ?1I?1358(I,J)X(J,I) 可用MATLAB编程求解。

约束条件为：

1.?X(J,I)?BJ (J?1,2,3?35)

I?13582.?X(J,I)?J?1AI,AI?'A (I?1,2,3?8)

I3.X(J,I)?0

模型的建立:

MATLAB 建模求得各基地运往各销售点新增的蔬菜种植量如表四： 1销2销3销4销5销6销7销8销9销10销11销12销13销14销售点售点售点售点售点售点售点售点售点售点售点售点售点售点 12

12.012.0基地一 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 8.50 0 0 14.314.010.0基地二 0.00 0.00 0.00 0.00 0.00 0.00 8.40 0.00 0.00 0.00 0.00 0 0 0 基地三 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 基地四 6.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 基地五 0.00 0.00 0.00 0.00 0.00 0.00 0.00 9.50 0.00 0.00 4.80 0.00 0.00 0.00 10.2基地六 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 5.70 0.00 0.00 0.00 0 13.0基地七 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 11.0基地八 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 7.00 0.00 0.00 0 15销16销17销18销19销20销21销22销23销24销25销26销27销28销售点售点售点售点售点售点售点售点售点售点售点售点售点售点 12.712.5基地一 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 8.90 0 0 基地二 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 基地三 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 9.60 0.00 7.20 0.00 基地四 0.00 0.00 0.00 9.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 基地五 0.00 0.00 0.00 0.00 7.30 0.00 0.00 7.40 0.00 0.00 0.00 0.00 0.00 0.00 13.5基地六 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 12.515.0基地七 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 0 11.610.0基地八 0.00 0.00 0.00 0.00 0.00 0.00 6.70 0.00 0.00 0.00 0.00 0.00 0 0 新增29销30销31销32销33销34销35销种植原种种植售点售点售点售点售点售点售点量植量量 10.777.3基地一 0.00 0.00 0.00 0.00 0.00 0.00 40 37.3 0 0 46.7基地二 0.00 0.00 0.00 0.00 0.00 0.00 0.00 45 1.7 0 34.6基地三 0.00 0.00 0.00 8.00 9.86 0.00 0.00 30 4.66 6 10.338.0基地四 9.00 0.00 0.00 1.54 1.66 0.00 38 0 0 0 29.0基地五 0.00 0.00 0.00 0.00 0.00 0.00 0.00 29 0 0 基地六 0.00 0.00 0.00 0.00 0.00 5.60 0.00 35.035 0 13

0 45.320.3基地七 0.00 0.00 0.00 0.00 0.00 4.84 0.00 25 4 4 54.0基地八 0.00 0.00 7.70 0.00 0.00 0.00 0.00 28 26 0 360 270 90 表（四）

模型的评价与分析：

表四中行表示35个销售点，列表示八个基地。每个方格中的数字表示对应基地运往对应销售点的蔬菜量，经MATLAB和简单计算。求得新增如下：

基地一：新增37.3；基地二：新增1.7；基地三：新增4.66；基地四：新增0；基地五：新增0；基地六：新增0；基地七：新增20.34；基地八：新增26；总增加：90，符合题意。

同理，用MATLAB编程求解(源程序及完整运行结果见附录)，部分运行结果如下: Optimization terminated. x =

0.0000 0.0000 0.0000 6.5000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 10.2000 0.0000 0.0000 12.0000 0.0000 0.0000 0.0000 0.0000 0.0000 fval =

308.7640

故按照以上方案运送，可使总短缺补偿和运费补贴最少，最少为：308.76元。

第三题：

问题分析：本问采用的是层次分析法。关键要解决销售点和基地的对应问题。通过第二题的结论得到的各个基地供应销售点的分配方式，通过统计可以看出，基地1，基地2，基地8供求平衡，于是不考虑这三个基地以及对应销售点，对剩下未平衡的基地与销售点重新设计运送方案。由于只有销售点11，销售点33，销售点34对应基地运送数量未知，我们对销售点——基地——运送量进行线性规划求解得到各基地蔬菜种植计划。销售与基地对应关系及部分运输量图二：

图（二）

在第二问基础上我们单独拿出需要分析的基地和销售点，其他不变。由第二问结果表示所有的最少费用308.76元，减去我们单独需要分析的各销售点运往各基地的运费总共52.132元。等于其他费用256.1288元。通过算出我们需要分析的情况最小费用，就可得到整个过程的最小费用。约束条件为：

1.P?R?Q??I?312711,33,34?J?12???X(J,K,I)?D(I,J) ?K?1?122.?X(11,K,5)?4.8 ?X(11,K,6)?5.7

K?112K?1123.?X(33,K,3)?9.86 ?X(33,K,4)?1.54

K?112K?1124.?X(34,K,4)?1.66 ?X(34,K,6)?5.6 ?X(34,K,7)?4.84

K?16K?1K?1125.?X(11,K,1)?B(11,K)?K?1,2,?12?

I?515

7.?X(34,K,I)?B(34,K)?K?1,2,?12?

I4,6,7模型的建立：

针对问题分析分别对销售点11，销售点33，销售点34对应基地的种植蔬菜种类进行MATLAB编程求解(源程序及完整运行结果见附录)，部分运行结果如下: f=DD4/12; A=[] b=[]

Aeq=[aeq1;aeq2;aeq3;aeq4;aeq5;aeq6;aeq7;aeq8_19;aeq20_31;aeq32_43]; beq=[4.8;5.7;9.86;1.54;1.66;5.6;4.84;

1.35;1;1.1;0.85;0.7;1.2;0.65;0.8;0.5;0.9;0.75;0.7; 2.5;2.05;1.7;0.9;0.7;1;0.85;0.75;0.6;0.35;0;0;

2.25;2.1;1.6;1;0.9;0.8;0.75;0.85;0.7;0.5;0.35;0.3]; lb=zeros(180,1); ub=[];

[x,fval,exitflag]=linprog(f,A,b,Aeq,beq,lb,ub)

%-----分别输出销售点11，33，34与蔬菜种类和生产基地的数量关系 x1ki=reshape( x(1:60,1),5,12)' x2ki=reshape( x(61:120,1),5,12)' x3ki=reshape( x(121:180,1),5,12)'

fval =

108.607

故销售点11，销售点33，销售点34运费补偿为108.607。

根据分析，各基地与销售点蔬菜运送方式如图三所示：

图（三）

模型的评价与分析：经过分析整理，重新设计蔬菜运送方案如表四所示：种类种类种类种类种类种类种类种类种类种类种类种类 1 2 3 4 5 6 7 8 9 10 11 12 基地13.69.90 77.38.25 7.30 5.15 5.30 4.55 6.00 5.45 4.50 3.85 3.40 一 5 0 基地8.70 46.74.55 4.05 4.65 2.80 3.85 2.85 4.05 2.80 2.75 3.35 2.30 二 0 基地5.80 34.64.32 3.73 3.04 3.26 3.37 2.29 2.70 2.21 1.48 1.25 1.20 三 6 基地38.05.36 4.57 4.24 3.40 2.91 3.63 2.56 3.06 1.93 2.59 2.46 1.30 四 0 基地29.03.96 2.76 2.75 2.79 2.82 2.85 1.85 2.27 1.78 2.11 1.49 1.57 五 0 基地35.06.52 4.55 3.40 3.02 1.94 3.12 1.89 2.57 2.13 2.06 2.35 1.45 六 0 基地10.145.36.01 3.48 5.21 2.77 2.68 2.36 3.20 2.59 2.46 2.65 1.78 七 6 4 基地54.07.95 5.85 4.60 5.40 3.70 4.70 3.70 4.10 4.15 3.35 3.80 2.70 八 0 表（四）蔬菜运送方案运费补贴：108.607+256.128=364.735元。

第四题：

问题的描述：由题目要使菜农种植蔬菜的积极性提高，并且得到质优价低的新鲜蔬菜，可以采取给每个基地配车的扶持政策。一来可以让菜农解决了买车上的经济负担，二来可以保证蔬菜的新鲜度。数学模型和解决方案：本题我们采用层次分析法解决。由第三题得到的结果知，只有销售点11，33，34由多个基地供应蔬菜，通过层次分析法，我们定性分析，为使减少政府补贴。一个基地完全负责某几个销售点可以。通过综合分析表格数据，为使运费最少，我们将销售点33的蔬菜需求全部由基地5供应。销售点11的蔬菜需求全部由基地6供应。销售点34的蔬菜需求全部由基地7供应。通过第三题的结果，结合假设，重新分配各基地的种植量。如下表五：

种植基地供应量 1 77.3 2 46.7 3 24.8 4 46.9 5 35.6 6 34.2 7 40.5 8 54 表（五）

由第三问结果，如果不考虑销售点11，销售点33，销售点34，我们知道最少运费是256.13，根据假设条件算出销售点11，销售点33，销售点34所需要的总运费为：

0.04*（11.4*3+11.5*27+12.1*19)=21.904元

（注:11.4，10.5，12.1分别是销售点33，销售点11，销售点34的需求量；3，27，19分别是基地5到销售点33的距离，基地6到销售点11的距离，基地4到销售点34的距离。）

根据附件3和各基地与销售点的路程关系，发现销售点19和22都由基地5供应，且是直达的；销售点16和销售点26是由基地7供应且直达，直达距离分别为7，7。由此我们想到，蔬菜运送汽车由

基地5到销售点22，终到销售点19行驶总路程最短，基地7到销售点26终到销售点16同理，如此，基地5可以省掉运费7.3*（30-7）*0.04=6.716元，同理基地6省掉运费（45-7）*15*0.04=22.2元。最终，总运费是256.128+21.904-22.2=255.832元。

五. 模型的及评价与改进

5.1模型的评价 5.1.1模型的优点：

模型简单易懂，主要用了图论，Froyd算法与线性规划，使问题的求解变得十分方便，能适应更重新的要求。 5.1.2模型的缺点：

上述模型只考虑了运输费用最小，假设条件较多，在理想条件下建模，没有考虑到供过于求造成的货物积压问题等变化条件。 5.2模型的改进:

由于上述模型只考虑了运输费用最小，却没有考虑到供过于求造成的货物积压问题。可将存货损失计算进去，这样会使这个模型更加完善。

六. 参考文献

[1]姜启源，数学模型，北京，高等教育出版社，2003

[2]黄雍检、赖明勇，MATLAB语言在运筹学中的应用，长沙，湖南大学出版社，2005

附录一：弗洛伊德结果D6 d6 =

Columns 1 through 30

0 13 12 10 21 16 20 14 36 25 28 53 33 48 38 53 50 42 43 51 50 40 40 43 40 47 53 32 41 26

13 0 5 3 14 9 13 7 29 18 21 46 26 41 31 46 43 35 36 40 19 28 13

12 5 0 2 9 4 36 26 41 38 30 31 45 24 33 18

10 3 2 0 11 6 38 28 43 40 32 33 43 22 31 16

21 14 9 11 0 5 37 27 42 39 31 32 49 33 42 27

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0 14

46 47 40 39 42 41 35 36 45 28 25 35 38 23 20 30 26 23 27 30 15 23 13 17 17 7 14 0

第一问（1）matlab

BB=[6.5 10.2 12 14.3 13 11 14 9.5 10 8.4 10.5 7 8.5 12 11.6 12.5 13.5 9 7.3 10 12.7 7.4 6.7 12.5 9.6 15 7.2 8.9 10.3 9 7.7 8 11.4 12.1 10.7]; SS=[710 700 580 600 570 480 500 610 440 705 610 630 590 490 570 460 530 640 665 650 580 680 685 560 660 430 540 620 630 680 695 690 560 520 500]; SS_for_add=[710 700 580 600 570 480 500 610 440 705 610 630 590 490 570 460 530 640 665 650 580 680 685 560 660 430 540 620 630 680 695 690 560 520 500

710 700 580 600 570 480 500 610 440 705 610 630 590 490 570 460 530 640 665 650 580 680 685 560 660 430 540 620 630 680 695 690 560 520 500 710 700 580 600 570 480 500 610 440 705 610 630 590 490 570 460 530 640 665 650 580 680 685 560 660 430 540 620 630 680 695 690 560 520 500 710 700 580 600 570 480 500 610 440 705 610 630 590 490 570 460 530 640 665 650 580 680 685 560 660 430 540 620 630 680 695 690 560 520 500 710 700 580 600 570 480 500 610 440 705 610 630 590 490 570 460 530 640 665 650 580 680 685 560 660 430 540 620 630 680 695 690 560 520 500 710 700 580 600 570 480 500 610 440 705 610 630 590 490 570 460 530 640 665 650 580 680 685 560 660 430 540 620 630 680 695 690 560 520 500 710 700 580 600 570 480 500 610 440 705 610 630 590 490 570 460 530 640 665 650 580 680 685 560 660 430 540 620 630 680 695 690 560 520 500 %销售点短缺补偿

710 700 580 600 570 480 500 610 440 705 610 630 590 490 570 460 530 640 665 650 580 680 685 560 660 430 540 620 630 680 695 690 560 520 500];%写成8行是为了计算方便 BS=BB.*SS; sum(BS,2)

Y=35*8;所以，要使用DD' DD_use_0=DD'*0.04

%%xishu=DD_use_0-SS_for_add xishu=sum(DD_use_0)-SS

f=[xishu';xishu';xishu';xishu';xishu';xishu';xishu';xishu'];

%%xishu_use= reshape(xishu',[],1); % f使用的系数，将35*8的变成240*1的矩阵 %%f=xishu_use

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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ]; beq=[40;45;30;38;29;35;25;28] lb=zeros(280,1) ub=[]

[x,fval,exitflag]=linprog(f,A,b,Aeq,beq,lb,ub) fval+sum(BS,2) %= 4.5509e+04 xx=reshape(x,35,8) x_output=xx'

第一题（2）matlab

710 700 580 600 570 480 500 610 440 705 610 630 590 490 570 460 530 640 665 650 580 680 685 560 660 430 540 620 630 680 695 690 560 520 500];%写成8行是为了计算方便 BS=BB.*SS; BS_sum=sum(BS,2) Y=35*8;所以，要使用DD' DD_use_0=DD'*0.04

%%xishu=DD_use_0-SS_for_add xishu=sum(DD_use_0)-SS

f=[xishu';xishu';xishu';xishu';xishu';xishu';xishu';xishu'];

%%xishu_use= reshape(xishu',[],1); % f使用的系数，将35*8的变成240*1的矩阵 %%f=xishu_use

A1=[ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;

0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;

0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]; A2=-A1; A=[A1;A2];

b1=[6.5;10.2;12;14.3;13;11;14;9.5;10;8.4;10.5;7;8.5;12;11.6;12.5;13.5;9;7.3;10;12.7;7.4;6.7;12.5;9.6;15;7.2;8.9;10.3;9;7.7;8;11.4;12.1;10.7];

b2=b1*(-0.7) b=[b1;b2]

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ]; beq=[40;45;30;38;29;35;25;28] lb=zeros(280,1) ub=[]

[x,fval,exitflag]=linprog(f,A,b,Aeq,beq,lb,ub) fval+sum(BS,2) xx=reshape(x,35,8) x_output=xx'

%xlswrite('a.xls',a) target=5.3160e+04

第二题matlab：

m=zeros(35,280) for i=1:35 for j=1:280

if (j>=((i-1)*8+1))&&(j<=8*i) m(i,j)=1; else m(i,j)=0; end end end

710 700 580 600 570 480 500 610 440 705 610 630 590 490 570 460 530 640 665 650 580 680 685 560 660 430 540 620 630 680 695 690 560 520 500];%写成8行是为了计算方便 BS=BB.*SS; sum(BS,2)

Y=35*8;所以，要使用DD' DD_use_0=DD'*0.04;

xishu=reshape(DD_use_0',280,1); f=xishu; A0=eye(8) A1=eye(8)

for i=1:34 A1=[A1,A0]; end A=-A1;

b=[-40;-45;-30;-38;-29;-35;-25;-28]; Aeq=m;

beq=[6.5;10.2;12;14.3;13;11;14;9.5;10;8.4;10.5;7;8.5;12;11.6;12.5;13.5;9;7.3;10;12.7;7.4;6.7;12.5;9.6;15;7.2;8.9;10.3;9;7.7;8;11.4;12.1;10.7];

lb=zeros(280,1) ub=[]

[x,fval,exitflag]=linprog(f,A,b,Aeq,beq,lb,ub) xx2=reshape(x,8,35)

第三题matlab：

DD1=[38 45 35 27 34] DD2=[48 28 3 23 56] DD3=[40 19 12 29 56] DD4=DD1; for i= 2:36

if (i>=2)&&(i<=12) DD4=[DD4,DD1];

else if (i>=13)&&(i<=24) DD4=[DD4,DD2]; else DD4=[DD4,DD3]; end end end f=DD4/12;

%%%%%%%%%%%%%%%%%%%%%%% —————— Aeq前7行系数————————%%%%%%%%%%%%%%%%%%%%%% aeq1=zeros(1,180); for i=1:60