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1、物流管理定量分析方法重难点分析第二章 资源合理配置的线性规划法【重点与难点】重点：线性规划模型的建立，矩阵的加减法、数乘法、转置及乘法，矩阵的初等行变换，矩阵求逆，线性规划的标准形式，线性规划的矩阵形式难点：矩阵求逆，线性规划的单纯形法【重难点分析】1. 线性规划模型的建立，主要掌握主、辅教材中提到的几种情形。建立线性规划模型的步骤：(1)确定变量；(2)确定目标函数；(3)写出约束条件（含变量非负限制）；(4)写出线性规划模型。即变量目标函数约束条件线性规划模型变量就是待确定的未知数；目标函数就是使问题达到最大值或最小值的函数；约束条件就是各种资源的限制及变量非负限制；由目标函数和约束条件组
2、成的数学模型就是线性规划模型。2. 要熟悉矩阵的一些概念及矩阵的加减法、数乘法、矩阵转置等基本运算，重点掌握矩阵的初等行变换、矩阵的乘法和求逆。矩阵概念：由mn个数aij（i1，2，m；j1，2，n）排成一个m行、n列的矩形阵表称为mn矩阵，通常用大写字母A，B，C， 表示。单位矩阵：主对角线上元素全为1，其余元素均为0的方阵，称为单位矩阵，记为：I，即I本课程我们主要掌握二阶单位矩阵和三阶单位矩阵。矩阵加减法：若矩阵A与B是同型矩阵，且则ABC，其中C矩阵数乘法：设矩阵Aaijmn，l 是任意常数，则矩阵乘法：设Aaij 是一个ms矩阵，Bbij 是一个sn矩阵，则称mn矩阵Ccij 为A与
3、B的乘积，其中（i1，2，m；j1，2，n），记为：CAB。矩阵转置：把一个mn矩阵A的行、列互换得到的nm矩阵，称为A的转置矩阵，记为AT，即AT可逆矩阵与逆矩阵概念：设矩阵A，如果存在一个矩阵B，使得ABBAI则称矩阵A是可逆矩阵，并称B是A的逆矩阵，记为：BA1。矩阵的初等行变换：是指对矩阵进行下列三种变换：(1) 互换矩阵某两行的位置 记为：（，）；(2) 用非0常数遍乘矩阵的某一行 记为：k；(3) 将矩阵的某一行遍乘一个常数k加到另一行 记为：k。求逆矩阵：用初等行变换求逆矩阵，其方法是：以A为二阶矩阵为例，初等行变换求逆矩阵的过程中，一般是：先将第一列化为，再化第二列为，这实质是
4、将 (A，I ) 化为行简化阶梯形矩阵，这样右半部分便是逆矩阵。当然，也可以先将 (A，I ) 化为阶梯形矩阵，再化为行简化阶梯形矩阵，同样可得逆矩阵。或者将这两种方法综合，适当避开分数运算，只要最后得到行简化阶梯形矩阵，便可得到逆矩阵。3. 要熟悉阶梯形矩阵、行简化阶梯形矩阵、系数矩阵和增广矩阵等概念，以及线性方程组的解法，主要掌握其基本方法便可。矩阵中元素全为0的行，称为零行；至少有一个非0元素的行，称为非零行；非零行中从左到右的第一个非0元素，称为首非零元。阶梯形矩阵：满足下列条件的矩阵称为阶梯形矩阵（简称阶梯阵）：(1) 各个非零行的首非零元的列标随着行标的递增而严格增大；(2) 如果
5、矩阵有零行，零行在矩阵的最下方。行简化阶梯形矩阵：满足下列条件的阶梯形矩阵称为行简化阶梯形矩阵：(1) 各个非零行的首非零元都是1；(2) 所有首非零元所在列的其余元素都是0。方程组称为n元非齐次线性方程组，有时简称n元线性方程组。方程组 称为n元齐次线性方程组。系数矩阵：A称为n元线性方程组的系数矩阵。增广矩阵：由非齐次线性方程组的系数和常数项组成的矩阵称为n元线性方程组的增广矩阵，记为或 (A，b)。解线性方程组的一般方法：(1) 写出线性方程组的增广矩阵；(2) 对施行初等行变换，使化为行简化阶梯形矩阵；(3) 在化行简化阶梯形矩阵的过程中，若出现一行（0 0 0 c）（c0），则原方程
6、组无解。否则有解；(4) 有解时，写出惟一解或一般解。解齐次线性方程组的一般方法是：(1) 写出齐次线性方程组的系数矩阵A；(2) 对A施行初等行变换，使A化为行简化阶梯形矩阵；(3) 在行简化阶梯形矩阵中，当非零行行数未知量个数时，齐次线性方程组只有零解x1x2xn0；当非零行行数未知量个数时，齐次线性方程组有非零解，可由行简化阶梯形矩阵写出一般解。4. 要会写线性规划模型的标准形式和矩阵形式。线性规划模型的标准形式：(1) 目标函数求最大值；(2) 除变量非负限制外的约束条件均为等式；(3) 常数项非负。即 （2.5.1）其中bi0（i1，2，m）。线性规划的矩阵形式：如果把S也视为一个变
7、量，线性规划模型 (2.5.1) 可改写为 (2.5.2)方程组 (2.5.2) 是一个n1个未知量x1，x2，xn，S，m1个方程的线性方程组，开始时取S0，则 (2.5.2) 式的矩阵形式为：【例题讲解】例1 某企业生产甲、乙两种产品，要用A，B，C三种不同的原料，从工艺资料知道：每生产一件产品甲，需用三种原料分别为1，1，0单位；生产一件产品乙，需用三种原料分别为1，2，1单位。每天原料供应的能力分别为6，8，3单位。又知，销售一件产品甲，企业可得利润3万元；销售一件产品乙，企业可得利润4万元。试写出能使利润最大的线性规划模型。解：设生产甲、乙两种产品的产量分别为x1件和x2件。显然，x
8、1，x20线性规划模型为：例2 设，求：解：例3 写出线性规划问题的标准形式和矩阵形式。解：引入松驰变量x3，x4，将线性规划问题化为标准形式：写出矩阵形式：例4 某企业在一个生产周期内生产甲、乙两种产品，这两种产品分别需要A，B，C，D四种不同的机床来加工，这四种机床的可用工时分别为1500，1200，1800，1400。每件甲产品分别需要A，B，C机床加工4工时、2工时、5工时；每件乙产品分别需要A，B，D机床加工3工时、3工时、2工时。又知甲产品每件利润6元，乙产品每件利润8元。试建立在上述条件下，如何安排生产计划，使企业能获得利润最大的线性规划模型，并写出用MATLAB软件计算该线性规
9、划问题的命令语句。解：设生产甲、乙两种产品的产量分别为x1件和x2件。显然，x1，x20线性规划模型为：解上述线性规划问题的语句为：clear;C=-6 8;A=4 3;2 3;5 0;0 2;B=1500;1200;1800;1400;LB=0;0;X,fval,exitflag=linprog(C,A,B,LB)Winger Tuivasa-Sheck, who scored two tries in the Kiwis 20-18 semi-final win over England, has been passed fit after a lower-leg injury, whil
10、e Slater has been named at full-back but is still recovering from a knee injury aggravated against USA.Both sides boast 100% records heading into the encounter but Australia have not conceded a try since Josh Charnleys effort in their first pool match against England on the opening day.Aussie winger
11、 Jarryd Hayne is the competitions top try scorer with nine, closely followed by Tuivasa-Sheck with eight.But it is recently named Rugby League International Federation player of the year Sonny Bill Williams who has attracted the most interest in the tournament so far.The Kiwi - with a tournament hig
12、h 17 offloads - has the chance of becoming the first player to win the World Cup in both rugby league and rugby union after triumphing with the All Blacks in 2011.Id give every award back in a heartbeat just to get across the line this weekend, said Williams.The (lack of) air up there Watch mCayman
13、Islands-based Webb, the head of Fifas anti-racism taskforce, is in London for the Football Associations 150th anniversary celebrations and will attend Citys Premier League match at Chelsea on Sunday.I am going to be at the match tomorrow and I have asked to meet Yaya Toure, he told BBC Sport.For me
14、its about how he felt and I would like to speak to him first to find out what his experience was.Uefa hasopened disciplinary proceedings against CSKAfor the racist behaviour of their fans duringCitys 2-1 win.Michel Platini, president of European footballs governing body, has also ordered an immediat
15、e investigation into the referees actions.CSKA said they were surprised and disappointed by Toures complaint. In a statement the Russian side added: We found no racist insults from fans of CSKA. Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunda
16、.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere)
17、where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause),
18、e can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet ( Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.They blew it in 2008 when they got caught cold in the final and they will not make the same mistake
19、 against the Kiwis in Manchester.Five years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored by Englands Josh Charnley in the opening game of the tournament.That could be classed as a weakness, a team under-cooked - but I have
20、been impressed by the Kangaroos focus in their games since then.They have been concentrating on the sort of stuff that wins you tough, even contests - strong defence, especially on their own goal-line, completing sets and a good kick-chase. Theyve been great at all the unglamorous stuff that often g
21、oes unnoticed in the stands but not by your team-mates.It is as though their entire tournament has been preparation for the final.In Johnathan Thurston, Cooper Cronk, Cameron Smith and either Billy Slater or Greg Inglis at full-back they have a spine that is unmatched in rugby league. They have play
22、ed in so many high-pressure games - a priceless asset going into Saturday.The Kiwis are a lot less experienced but winning a dramatic match like their semi-final against England will do wonders for their confidence.They defeated Australia in the Four Nations final in 2010 and the last World Cup, and know they can rise to the big occasion.7
