電大物流定量分析第二章重難點(diǎn)分析

1、物流管理定量分析方法重難點(diǎn)分析第二章 資源合理配置的線性規(guī)劃法【重點(diǎn)與難點(diǎn)】重點(diǎn)：線性規(guī)劃模型的建立，矩陣的加減法、數(shù)乘法、轉(zhuǎn)置及乘法，矩陣的初等行變換，矩陣求逆，線性規(guī)劃的標(biāo)準(zhǔn)形式，線性規(guī)劃的矩陣形式難點(diǎn)：矩陣求逆，線性規(guī)劃的單純形法【重難點(diǎn)分析】1. 線性規(guī)劃模型的建立，主要掌握主、輔教材中提到的幾種情形。建立線性規(guī)劃模型的步驟：(1)確定變量；(2)確定目標(biāo)函數(shù)；(3)寫出約束條件（含變量非負(fù)限制）；(4)寫出線性規(guī)劃模型。即變量目標(biāo)函數(shù)約束條件線性規(guī)劃模型變量就是待確定的未知數(shù)；目標(biāo)函數(shù)就是使問題達(dá)到最大值或最小值的函數(shù)；約束條件就是各種資源的限制及變量非負(fù)限制；由目標(biāo)函數(shù)和約束條件組

2、成的數(shù)學(xué)模型就是線性規(guī)劃模型。2. 要熟悉矩陣的一些概念及矩陣的加減法、數(shù)乘法、矩陣轉(zhuǎn)置等基本運(yùn)算，重點(diǎn)掌握矩陣的初等行變換、矩陣的乘法和求逆。矩陣概念：由mn個(gè)數(shù)aij（i1，2，m；j1，2，n）排成一個(gè)m行、n列的矩形陣表稱為mn矩陣，通常用大寫字母a，b，c， 表示。單位矩陣：主對(duì)角線上元素全為1，其余元素均為0的方陣，稱為單位矩陣，記為：i，即i本課程我們主要掌握二階單位矩陣和三階單位矩陣。矩陣加減法：若矩陣a與b是同型矩陣，且則abc，其中c矩陣數(shù)乘法：設(shè)矩陣aaijmn，l 是任意常數(shù)，則矩陣乘法：設(shè)aaij 是一個(gè)ms矩陣，bbij 是一個(gè)sn矩陣，則稱mn矩陣ccij 為a與

3、b的乘積，其中（i1，2，m；j1，2，n），記為：cab。矩陣轉(zhuǎn)置：把一個(gè)mn矩陣a的行、列互換得到的nm矩陣，稱為a的轉(zhuǎn)置矩陣，記為at，即at可逆矩陣與逆矩陣概念：設(shè)矩陣a，如果存在一個(gè)矩陣b，使得abbai則稱矩陣a是可逆矩陣，并稱b是a的逆矩陣，記為：ba1。矩陣的初等行變換：是指對(duì)矩陣進(jìn)行下列三種變換：(1) 互換矩陣某兩行的位置 記為：（，）；(2) 用非0常數(shù)遍乘矩陣的某一行 記為：k；(3) 將矩陣的某一行遍乘一個(gè)常數(shù)k加到另一行 記為：k。求逆矩陣：用初等行變換求逆矩陣，其方法是：以a為二階矩陣為例，初等行變換求逆矩陣的過程中，一般是：先將第一列化為，再化第二列為，這實(shí)質(zhì)是

4、將 (a，i ) 化為行簡(jiǎn)化階梯形矩陣，這樣右半部分便是逆矩陣。當(dāng)然，也可以先將 (a，i ) 化為階梯形矩陣，再化為行簡(jiǎn)化階梯形矩陣，同樣可得逆矩陣。或者將這兩種方法綜合，適當(dāng)避開分?jǐn)?shù)運(yùn)算，只要最后得到行簡(jiǎn)化階梯形矩陣，便可得到逆矩陣。3. 要熟悉階梯形矩陣、行簡(jiǎn)化階梯形矩陣、系數(shù)矩陣和增廣矩陣等概念，以及線性方程組的解法，主要掌握其基本方法便可。矩陣中元素全為0的行，稱為零行；至少有一個(gè)非0元素的行，稱為非零行；非零行中從左到右的第一個(gè)非0元素，稱為首非零元。階梯形矩陣：滿足下列條件的矩陣稱為階梯形矩陣（簡(jiǎn)稱階梯陣）：(1) 各個(gè)非零行的首非零元的列標(biāo)隨著行標(biāo)的遞增而嚴(yán)格增大；(2) 如果

5、矩陣有零行，零行在矩陣的最下方。行簡(jiǎn)化階梯形矩陣：滿足下列條件的階梯形矩陣稱為行簡(jiǎn)化階梯形矩陣：(1) 各個(gè)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。方程組稱為n元非齊次線性方程組，有時(shí)簡(jiǎn)稱n元線性方程組。方程組 稱為n元齊次線性方程組。系數(shù)矩陣：a稱為n元線性方程組的系數(shù)矩陣。增廣矩陣：由非齊次線性方程組的系數(shù)和常數(shù)項(xiàng)組成的矩陣稱為n元線性方程組的增廣矩陣，記為或 (a，b)。解線性方程組的一般方法：(1) 寫出線性方程組的增廣矩陣；(2) 對(duì)施行初等行變換，使化為行簡(jiǎn)化階梯形矩陣；(3) 在化行簡(jiǎn)化階梯形矩陣的過程中，若出現(xiàn)一行（0 0 0 c）（c0），則原方程

6、組無解。否則有解；(4) 有解時(shí)，寫出惟一解或一般解。解齊次線性方程組的一般方法是：(1) 寫出齊次線性方程組的系數(shù)矩陣a；(2) 對(duì)a施行初等行變換，使a化為行簡(jiǎn)化階梯形矩陣；(3) 在行簡(jiǎn)化階梯形矩陣中，當(dāng)非零行行數(shù)未知量個(gè)數(shù)時(shí)，齊次線性方程組只有零解x1x2xn0；當(dāng)非零行行數(shù)未知量個(gè)數(shù)時(shí)，齊次線性方程組有非零解，可由行簡(jiǎn)化階梯形矩陣寫出一般解。4. 要會(huì)寫線性規(guī)劃模型的標(biāo)準(zhǔn)形式和矩陣形式。線性規(guī)劃模型的標(biāo)準(zhǔn)形式：(1) 目標(biāo)函數(shù)求最大值；(2) 除變量非負(fù)限制外的約束條件均為等式；(3) 常數(shù)項(xiàng)非負(fù)。即 （2.5.1）其中bi0（i1，2，m）。線性規(guī)劃的矩陣形式：如果把s也視為一個(gè)變

7、量，線性規(guī)劃模型 (2.5.1) 可改寫為 (2.5.2)方程組 (2.5.2) 是一個(gè)n1個(gè)未知量x1，x2，xn，s，m1個(gè)方程的線性方程組，開始時(shí)取s0，則 (2.5.2) 式的矩陣形式為：【例題講解】例1 某企業(yè)生產(chǎn)甲、乙兩種產(chǎn)品，要用a，b，c三種不同的原料，從工藝資料知道：每生產(chǎn)一件產(chǎn)品甲，需用三種原料分別為1，1，0單位；生產(chǎn)一件產(chǎn)品乙，需用三種原料分別為1，2，1單位。每天原料供應(yīng)的能力分別為6，8，3單位。又知，銷售一件產(chǎn)品甲，企業(yè)可得利潤(rùn)3萬元；銷售一件產(chǎn)品乙，企業(yè)可得利潤(rùn)4萬元。試寫出能使利潤(rùn)最大的線性規(guī)劃模型。解：設(shè)生產(chǎn)甲、乙兩種產(chǎn)品的產(chǎn)量分別為x1件和x2件。顯然，x

8、1，x20線性規(guī)劃模型為：例2 設(shè)，求：解：例3 寫出線性規(guī)劃問題的標(biāo)準(zhǔn)形式和矩陣形式。解：引入松馳變量x3，x4，將線性規(guī)劃問題化為標(biāo)準(zhǔn)形式：寫出矩陣形式：例4 某企業(yè)在一個(gè)生產(chǎn)周期內(nèi)生產(chǎn)甲、乙兩種產(chǎn)品，這兩種產(chǎn)品分別需要a，b，c，d四種不同的機(jī)床來加工，這四種機(jī)床的可用工時(shí)分別為1500，1200，1800，1400。每件甲產(chǎn)品分別需要a，b，c機(jī)床加工4工時(shí)、2工時(shí)、5工時(shí)；每件乙產(chǎn)品分別需要a，b，d機(jī)床加工3工時(shí)、3工時(shí)、2工時(shí)。又知甲產(chǎn)品每件利潤(rùn)6元，乙產(chǎn)品每件利潤(rùn)8元。試建立在上述條件下，如何安排生產(chǎn)計(jì)劃，使企業(yè)能獲得利潤(rùn)最大的線性規(guī)劃模型，并寫出用matlab軟件計(jì)算該線性規(guī)

9、劃問題的命令語句。解：設(shè)生產(chǎn)甲、乙兩種產(chǎn)品的產(chǎn)量分別為x1件和x2件。顯然，x1，x20線性規(guī)劃模型為：解上述線性規(guī)劃問題的語句為：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 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 unglam