外文翻譯--線性規(guī)劃在企業(yè)決策中的應(yīng)用

1、<p>　　2013屆畢業(yè)生外文文獻翻譯</p><p>　　學(xué) 院 理學(xué)院 　　　</p><p>　　專 業(yè) 信息與計算科學(xué) </p><p>　　姓 名 李存正 　　　　</p><p>　　學(xué) 號 200901120224 </p&

2、gt;<p>　　指導(dǎo)教師 盧福良 　　　</p><p>　　線性規(guī)劃在企業(yè)決策中的應(yīng)用</p><p>　　第一章 線性規(guī)劃理論</p><p><b>　　1. 線性規(guī)劃簡介</b></p><p>　　線性規(guī)劃是運籌學(xué)中研究較早、發(fā)展較快、應(yīng)用廣泛、方法較成熟的一個重要分支,它是

3、輔助人們進行科學(xué)管理的一種數(shù)學(xué)方法.在經(jīng)濟管理、交通運輸、工農(nóng)業(yè)生產(chǎn)等經(jīng)濟活動中，提高經(jīng)濟效果是人們不可缺少的要求，而提高經(jīng)濟效果一般通過兩種途徑：一是技術(shù)方面的改進，例如改善生產(chǎn)工藝，使用新設(shè)備和新型原材料.二是生產(chǎn)組織與計劃的改進，即合理安排人力物力資源.線性規(guī)劃所研究的是：在一定條件下，合理安排人力物力等資源，使經(jīng)濟效果達到最好.一般地，求線性目標函數(shù)在線性約束條件下的最大值或最小值的問題，統(tǒng)稱為線性規(guī)劃問題[1]。滿足線性約束條

4、件的解叫做可行解，由所有可行解組成的集合叫做可行域[2]。決策變量、約束條件、目標函數(shù)是線性規(guī)劃的三要素。</p><p>　　2. 線性規(guī)劃的發(fā)展歷程</p><p>　　法國數(shù)學(xué)家 J.- B.- J.傅里葉和 C.瓦萊－普森分別于1832和1911年獨立地提出線性規(guī)劃的想法，但未引起注意。 </p><p>　　1939年蘇聯(lián)數(shù)學(xué)家Л.В.康托羅維奇在《生產(chǎn)組

5、織與計劃中的數(shù)學(xué)方法》一書中提出線性規(guī)劃問題，也未引起重視。 </p><p>　　1947年美國數(shù)學(xué)家G.B.丹齊克提出線性規(guī)劃的一般數(shù)學(xué)模型和求解線性規(guī)劃問題的通用方法──單純形法，為這門學(xué)科奠定了基礎(chǔ)。 </p><p>　　1947年美國數(shù)學(xué)家J.von諾伊曼提出對偶理論,開創(chuàng)了線性規(guī)劃的許多新的研究領(lǐng)域，擴大了它的應(yīng)用范圍和解題能力。 </p><p>　

6、　1951年美國經(jīng)濟學(xué)家T.C.庫普曼斯把線性規(guī)劃應(yīng)用到經(jīng)濟領(lǐng)域，為此與康托羅維奇一起獲1975年諾貝爾經(jīng)濟學(xué)獎。 </p><p>　　50年代后對線性規(guī)劃進行大量的理論研究，并涌現(xiàn)出一大批新的算法。例如，1954年C.萊姆基提出對偶單純形法，1954年S.加斯和T.薩迪等人解決了線性規(guī)劃的靈敏度分析和參數(shù)規(guī)劃問題，1956年A.塔克提出互補松弛定理，1960年G.B.丹齊克和P.沃爾夫提出分解算法等。 <

7、;/p><p>　　線性規(guī)劃的研究成果還直接推動了其他數(shù)學(xué)規(guī)劃問題包括整數(shù)規(guī)劃、隨機規(guī)劃和非線性規(guī)劃的算法研究。由于數(shù)字電子計算機的發(fā)展，出現(xiàn)了許多線性規(guī)劃軟件，如MPSX，OPHEIE，UMPIRE等，可以很方便地求解幾千個變量的線性規(guī)劃問題[3]。 </p><p>　　1979年蘇聯(lián)數(shù)學(xué)家L. G. Khachian提出解線性規(guī)劃問題的橢球算法，并證明它是多項式時間算法。</p&g

8、t;<p>　　1984年美國貝爾電話實驗室的印度數(shù)學(xué)家N.卡馬卡提出解線性規(guī)劃問題的新的多項式時間算法。用這種方法求解線性規(guī)劃問題在變量個數(shù)為5000時只要單純形法所用時間的1/50。現(xiàn)已形成線性規(guī)劃多項式算法理論。50年代后線性規(guī)劃的應(yīng)用范圍不斷擴大。建立線性規(guī)劃模型的方法。</p><p>　　3. 線性規(guī)劃的數(shù)學(xué)模型及其標準形式</p><p>　　3.1 線性規(guī)劃問

9、題的提出</p><p>　　在生產(chǎn)管理和經(jīng)營活動中經(jīng)常提出一類問題，即如何合理地利用有限的人力、物力、財力等資源，以便得到最好的經(jīng)濟效果。</p><p>　　線性規(guī)劃主要解決兩類問題：</p><p>　?。?）資源有限，要求生產(chǎn)的產(chǎn)品（或利潤）最多。</p><p>　?。?）任務(wù)（或產(chǎn)品）一定，要求消耗的資源（或成本）最少。</

10、p><p>　　3.2 線性規(guī)劃問題的特征</p><p>　?。?）每一個問題都用一組決策變量表示某一方案；這組決策變量的值就有代表一過具體方案。</p><p>　　（2）一般這些變量取值是非負的。</p><p>　　（3）存在一定的約束條件，這些約束條件可以用一組線性等式或線性不等式來表示。</p><p>　　（

11、4）都有一個要求達到的目標，它可用決策變量的線性函數(shù)（稱為目標函數(shù)）來表示。按問題的不同，要求目標函數(shù)實現(xiàn)最大化或最小化。</p><p>　　滿足以上四個條件的數(shù)學(xué)模型稱為線性規(guī)劃的數(shù)學(xué)模型。</p><p>　　3.3 從實際問題中建立數(shù)學(xué)模型的步驟；</p><p>　?。?）根據(jù)影響所要達到目的的因素找到?jīng)Q策變量；</p><p>　

12、　（2）由決策變量和所在達到目的之間的函數(shù)關(guān)系確定目標函數(shù)；</p><p>　　（3）由決策變量所受的限制條件確定決策變量所要滿足的約束條件。</p><p>　　3.4 所建立的線性規(guī)劃模型的特點；</p><p>　?。?）每個模型都有若干個決策變量，其中為決策變量個數(shù)。決策變量的一組值表示一種方案，同時決策變量一般是非負的。</p><p

13、>　　（2）目標函數(shù)是決策變量的線性函數(shù)，根據(jù)具體問題可以是最大化或最小化，二者統(tǒng)稱為最優(yōu)化[3]。</p><p>　?。?）約束條件也是決策變量的線性函數(shù)。</p><p>　　3.5 線性規(guī)劃模型的一般形式</p><p>　　目標函數(shù)： (1-1)</p><p>　　約束條件：

14、 (1-2)</p><p>　　在線性規(guī)劃的數(shù)學(xué)模型中，方程（3-1）稱為目標函數(shù)；（3-2）稱為約束條件。</p><p>　　3.6 線性規(guī)劃模型的標準形式</p><p><b>　　(1-3)</b></p><p><b>　　(1-4)</b></p>&

15、lt;p><b>　　其中.</b></p><p><b>　　簡寫形式為：</b></p><p><b>　　(1-5)</b></p><p><b>　　(1-6)</b></p><p><b>　　向量和矩陣表示：</b

16、></p><p><b>　　(1-7)</b></p><p><b>　　(1-8)</b></p><p>　　其中 ，</p><p>　　4. 線性規(guī)劃的解法</p><p>　　求解線性規(guī)劃問題的基本方法有圖解

17、法和單純形法，但實際運用的主要是是單純形法，現(xiàn)在已有單純形法的標準軟件，可在電子計算機上求解約束條件和決策變量數(shù)達 10000個以上的線性規(guī)劃問題。為了提高解題速度，又有改進單純形法、對偶單純形法、原始對偶方法、分解算法和各種多項式時間算法。對于只有兩個變量的簡單的線性規(guī)劃問題，也可采用圖解法求解。這種方法僅適用于只有兩個變量的線性規(guī)劃問題[5]。它的特點是直觀而易于理解，但實用價值不大。不過通過圖解法求解可以理解線性規(guī)劃的一些基本概念

18、。下面著重介紹單純形法。</p><p>　　4.1 一般線性規(guī)劃問題的單純形解法</p><p>　　4.1.1 建立初始基本可行解</p><p>　　在線性規(guī)劃問題中，約束條件多為不等式，所以首先要將其化為標準型，同時建</p><p>　　立一個初始基本可行基。</p><p>　　4.1.2 最優(yōu)解檢驗<

19、;/p><p>　　找到一個可行判斷它是不是最優(yōu)解。判斷方法是檢驗?zāi)繕撕瘮?shù)中是否還有正的系</p><p>　　數(shù)，若有正的系數(shù)，則說明還有更好的解。只有當(dāng)目標函數(shù)中的全部系數(shù)為負值或0時，說明改解才是最優(yōu)解。</p><p><b>　　4.1.3 基變換</b></p><p>　　從一個基可行解到另一個基可行解的變換就

20、是進行一次基變換。</p><p>　　4.1.4 迭代（旋轉(zhuǎn)運算）</p><p>　　將約束條件的增廣矩陣中新基變量的系數(shù)通過矩陣的行變換或Gauss變換變?yōu)閱?lt;/p><p><b>　　位矩陣[6]。</b></p><p>　　4.2 非標準型線性規(guī)劃問題的解法</p><p><

21、b>　　4.2.1 大法</b></p><p>　　在一個線性規(guī)劃問題的約束條件中加入人工變量后，要求人工變量對目標函數(shù)的取值無影響，為此可取人工變量在目標函數(shù)中的系數(shù)為(為非常大的正數(shù))[7]，這樣目標函數(shù)要實現(xiàn)最大化，人工變量只能取零，因此必須把人工變量從基變量中換出，否則目標函數(shù)就不可能實現(xiàn)最大化。</p><p>　　4.2.2 兩階段法</p>

22、<p>　　第一階段：不考慮原問題是否存在基可行解，給原線性規(guī)劃問題加上人工變量，構(gòu)造僅含人工變量的目標函數(shù)和要求實現(xiàn)最小化。</p><p>　　第二階段：將第一階段得到的最優(yōu)單純形表，除去人工變量，將原目標函數(shù)的系數(shù)換掉該表的目標函數(shù)的系數(shù)行，作為第二階段計算的初始表。</p><p><b>　　4.3 對偶分析</b></p><

23、p>　　4.3.1 對偶問題的基本概念</p><p>　　在線性規(guī)劃問題中，如果把一個求最大值的線性規(guī)劃定義為“原”問題，那么與其同時存在一個求最小值的所謂對偶問題，并且原線性規(guī)劃的最優(yōu)解對應(yīng)著對偶線性規(guī)劃問題的最優(yōu)解。</p><p>　　4.3.2 對偶問題的性質(zhì)</p><p>　?。?）對稱性 對偶問題的對偶是原問題。</p><

24、;p>　?。?）弱對偶性 若是原問題的可行解，是對偶問題的可行解。則存在。</p><p>　?。?）無界性 若原問題（對偶問題）為無界解，則其對偶問題（原問題）無可行解。</p><p>　?。?）可行解是最優(yōu)解時的性質(zhì) 設(shè)是原問題的可行解，是對偶問題的可行</p><p>　　解，當(dāng)時，,是最優(yōu)解。</p><p>　　（5）對

25、偶定理 若原問題有最優(yōu)解，那么對偶問題也有最優(yōu)解且最優(yōu)值相同。</p><p>　　（6）互補松馳性 若,分別是對偶問題和原問題的可行解。那么和,當(dāng)且僅當(dāng),為最優(yōu)解。</p><p><b>　　4.4靈敏度分析</b></p><p>　　靈敏度分析主要有以下幾種情況[8]：</p><p>　?。?）資源數(shù)量變化的

26、分析；</p><p>　　（2）目標函數(shù)中價值系數(shù)的變化分析；</p><p>　?。?）技術(shù)系數(shù)的變化；</p><p>　　（4）約束條件增減的變化分析。</p><p>　　第二章 企業(yè)決策理論</p><p><b>　　1. 企業(yè)決策概述</b></p><p&g

27、t;　　隨著企業(yè)計算機應(yīng)用和信息化程度的不斷深入，企業(yè)已經(jīng)積累了大量的業(yè)務(wù)和財務(wù)數(shù)據(jù)，并繼續(xù)隨著時間和業(yè)務(wù)的發(fā)展而呈幾何級膨脹趨勢。企業(yè)信息處理部門的工作重點已逐漸超越了簡單的數(shù)據(jù)收集，企業(yè)內(nèi)的各級人員都希望能夠快速、準確并方便有效地從這些大量雜亂無章的數(shù)據(jù)中獲取有意義的信息，決策者也希望能夠充分利用現(xiàn)有的數(shù)據(jù)指導(dǎo)企業(yè)決策和發(fā)掘企業(yè)的競爭優(yōu)勢[9]。決策效率和決策質(zhì)量的高低將直接影響企業(yè)的運營績效和市場競爭力。由于集團企業(yè)具有分布、異構(gòu)

28、、自治等特點，集團企業(yè)運營過程中的決策將是一個復(fù)雜的過程，對于不同的決策問題需要采用不同的決策方法。同時，在集團企業(yè)運營過程中，決策的形式也是多種多樣的，它在一定的階段表現(xiàn)為個體的行為，在一定的階段又表現(xiàn)為群體的活動，從而給集團企業(yè)管理中的決策分析提出了高要求。</p><p><b>　　2. 企業(yè)決策分類</b></p><p>　　2.1 按重要程度分類<

29、/p><p>　　在企業(yè)的決策中，我們按重要程度分類一般把決策分為三個層次，即戰(zhàn)略決策、戰(zhàn)術(shù)決策和業(yè)務(wù)決策[10]。</p><p>　　2.1.1 戰(zhàn)略決策</p><p>　　第一類戰(zhàn)略決策是與管理總的方針和開發(fā)企業(yè)所需要的資源有關(guān)的決策，它屬于長遠規(guī)劃，對企業(yè)的發(fā)展具有深遠影響，決策過程中要考慮很多不確定和冒風(fēng)險的因素。是集團企業(yè)決策信息模型中的最高層，負責(zé)管理、

30、控制、協(xié)調(diào)整個集團企業(yè)網(wǎng)絡(luò)的正常運行。其控制范圍包括涉及集團企業(yè)全體成員整體利益的事務(wù)和對整個企業(yè)集團運營活動的調(diào)控與制約。在這一層次，可以設(shè)定集團企業(yè)決策模型的范圍和內(nèi)容、集團企業(yè)的合作機制和行為準則的設(shè)定、運營過程的績效評價、利益分配機制和風(fēng)險控制機制等任務(wù)，為集團企業(yè)正常運營提供了戰(zhàn)略決策框架和行動指南。根據(jù)集團企業(yè)實際情況進行群體決策，擔(dān)負著全局優(yōu)化以及在新機遇下的集團企業(yè)組建過程中的決策工作。</p><p

31、>　　2.1.2 戰(zhàn)術(shù)決策</p><p>　　第二類決策稱為戰(zhàn)術(shù)決策，是在物資資源、設(shè)備等決策之后，規(guī)劃如何最有效的分配所獲得的資源（如生產(chǎn)能力、資金、材料、勞力等），以便獲得最大效益。定義集團企業(yè)各成員企業(yè)的各種基本決策活動過程。雖然由于集團企業(yè)的動態(tài)特性，各企業(yè)的實際情況和操作流程會有所不同，但我們總能找到一些存在于企業(yè)業(yè)務(wù)活動中相對穩(wěn)定且有相同或類似行為特征的實體。同時也能找出系統(tǒng)中不能再分的最小粒

32、度的原子過程，利用技術(shù)，我們將企業(yè)中的各類實體和原子過程封裝成對象，根據(jù)產(chǎn)品結(jié)構(gòu)信息和集團企業(yè)實際運行狀態(tài)信息，將客戶的訂單分解到集團企業(yè)的各成員企業(yè)，并派生出由不同的原子過程組成的工作流，對資源進行分配，并完成對工作流監(jiān)督、控制的任務(wù)。</p><p>　　2.1.3 業(yè)務(wù)決策</p><p>　　第三類叫業(yè)務(wù)決策，完成集團企業(yè)具體任務(wù)的執(zhí)行工作，包括物流在各企業(yè)間的合理流動以及從原材料

33、到成品的物理加工過程，如原材料的運輸、零件加工、部件裝配、檢測、倉儲等過程。在本層中，完成制造、銷售、供應(yīng)、運輸?shù)热蝿?wù)的同時，還要對第一線的信息進行采集、整理、反饋以供上層決策時使用。是在資源合理分配后，進行日常業(yè)務(wù)和計劃的決策，線性規(guī)劃模型最適合進行戰(zhàn)術(shù)決策，解決諸如勞動力和生產(chǎn)能力等資源的合理分配，運輸和指派方案的最優(yōu)選擇、廣告和推銷費用的預(yù)算等問題，同時它也在投資方案選擇、配料、選址、生產(chǎn)計劃、環(huán)境（如空氣、水）污染控制、下料等優(yōu)

34、化方面有廣泛的應(yīng)用。</p><p>　　2.2 按企業(yè)決策的環(huán)境分類</p><p>　　在企業(yè)的決策中，我們按企業(yè)決策的環(huán)境可分為確定性決策、風(fēng)險決策和不確定性決策。</p><p>　　2.2.1 確定性決策</p><p>　　確定性決策是指未來環(huán)境完全可預(yù)測，而且在此確定的未來環(huán)境下待選擇的決策方案的后果也是可以確定的。簡單講，就是

35、一種方案只有一種確定的結(jié)果。</p><p>　　2.2.2 風(fēng)險決策</p><p>　　風(fēng)險決策是指未來環(huán)境有幾種可能的狀態(tài)和相應(yīng)的后果，人們無法得到關(guān)于未來環(huán)境的充分可靠的信息，但可以預(yù)測每一種狀態(tài)和后果出現(xiàn)的概率。對利潤、效益等問題的決策一般都是風(fēng)險型決策</p><p>　　2.2.3 不確定性決策</p><p>　　不確定性決策

36、是指未來環(huán)境出現(xiàn)某種狀態(tài)的概率難以估計，甚至連可能出現(xiàn)的狀態(tài)</p><p>　　和相應(yīng)的后果都是未知的。這類決策，主要依靠決策者的經(jīng)驗和主觀判斷。</p><p>　　2.3 按企業(yè)決策的主體分類</p><p>　　在企業(yè)的決策中，我們按企業(yè)決策的主體可分為個人決策和群體決策。</p><p>　　2.3.1 個人決策</p>

37、<p>　　個人決策是指決策的主體是一個人，即最終方案的選擇僅僅由一個人拍板決定。 </p><p>　　2.3.2 群體決策</p><p>　　群體決策是指決策的主體是兩人或兩人以上。企業(yè)中許多重要的決策都是由決策群體制定的，屬于群體決策。</p><p>　　2.4 按企業(yè)決策的目標分類</p><p>　　在企業(yè)的決策中

38、，我們按決策目標可分為單目標決策和多目標決策。</p><p>　　2.4.1 單目標決策</p><p>　　單目標決策是指決策行動只要求實現(xiàn)一種目標，此種決策相對比較簡單。</p><p>　　2.4.2 多目標決策</p><p>　　多目標決策是指一項同時需要實現(xiàn)多個目標的決策。在做出一項復(fù)雜決策時，需 </p><

39、;p>　　要妥善處理好多個目標的沖突問題。</p><p>　　應(yīng)用線性規(guī)劃方法解決企業(yè)決策問題時，求解方法已經(jīng)不存在問題，各種大型求解線性規(guī)劃問題的計算機程序到處可以找到，使用也比較方便，應(yīng)用中的主要問題是根據(jù)實際情況建立合理的線性規(guī)劃模型，這是從事系統(tǒng)分析工作者的主要工作[11]。下面將介紹線性規(guī)劃模型的特點和建模的基本步驟，并列舉若干實例來說明線性規(guī)劃在企業(yè)決策中的應(yīng)用。</p><

40、;p>　　Linear programming in the corporate decision-making</p><p>　　Chapter I The theory of linear programming</p><p>　　Linear programming Introduction</p><p>　　Linear programming

41、 operations research study earlier, an important branch of the rapid development of a wide range of applications, the method is more mature, it is a mathematical method of scientific management to help people in economic

42、 management, transportation, industrial and agricultural production and other economic activities, improve the economic effect is the one indispensable requirements, and improve the economic effect is generally in two wa

43、ys: First, technical improvements, such as</p><p>　　The course of development of linear programming</p><p>　　French mathematician J. - B. - J. Fourier and C. Valle - Epson independently proposed

44、 the idea of linear programming in 1832 and 1911, but did not attract attention.</p><p>　　1939 the Soviet mathematician Л.В. Cantor Petrovich mathematical methods in the production organization and planning

45、"a book made linear programming problem, did not pay attention. </p><p>　　1947 American mathematician GB Danzig general mathematical model of linear programming and general method for solving linear pro

46、gramming problems-simplex method, laid the foundation for this discipline.</p><p>　　1947 the American mathematician J.von Neumann linear programming duality theory, creating a new field of study, has expande

47、d its scope of application and problem-solving ability.</p><p>　　1951 U.S. economist TC Koopmans linear programming applied to the field of economy, this Cantor Petrovich won the 1975 Nobel Prize in Economic

48、s.</p><p>　　A large number of theoretical studies on linear programming in the 1950s, and the emergence of a large number of new algorithms. For example, in 1954, C. Lai Muji proposed dual simplex method, 19

49、54 S. Vegas and T. Sadi solve linear programming sensitivity analysis and parametric programming, 1956 A. Tucker complementary slackness theorem 1960 GB Danzig and P. Wolfe decomposition algorithm.</p><p>　　

50、Linear programming research has directly contributed to other mathematical programming problems including integer programming, stochastic programming and nonlinear programming algorithm. Due to the development of the dig

51、ital computer, there are a number of linear programming software, such as MPSX, OPHEIE, UMPIRE, you can easily solve the thousands of variable linear programming problems [3].</p><p>　　In 1979 Soviet mathema

52、tician LG Khachian, ellipsoid method proposed for solving linear programming problems, and prove that it is a polynomial time algorithm.</p><p>　　1984 Bell Telephone Laboratories Indian mathematician N. Ka M

53、aka new polynomial time algorithm proposed for solving linear programming problems. Solving linear programming problems with this approach in the number of variables to 1/50 of the time as long as the simplex method used

54、 in 5000. Has now formed the theory of polynomial algorithm for linear programming. Expanding range of applications of linear programming in the 1950s. To establish the method of linear programming model.</p><

55、p>　　Linear programming mathematical model and its standard form</p><p>　　3.1 Linear programming problems raised</p><p>　　Frequently asked a class of problems in production management and busi

56、ness activities, the rational use of the limited human, material, financial and other resources in order to get the best economic effect.</p><p>　　Linear programming to solve two problems:</p><p&g

57、t;　　Limited resources, request product (or profit) the most.</p><p>　　Task (or product) must require the resources consumed (or cost) at least.</p><p>　　3.2 Characteristics of the linear program

58、ming problem</p><p>　　(1)Every problem with a set of decision variables of a program; this set of values ??of the decision variables there on behalf of an over-specific programs.</p><p>　　(2)Usu

59、ally these variables the value is non-negative.</p><p>　　(3)There are some constraints, these constraints can use a set of linear equations or linear inequalities.</p><p>　　(4)Has a requirem

60、ent to achieve, it can be used a linear function of the decision variables (called the objective function). Different problem, the objective function is maximized or minimized.</p><p>　　Meet the above four c

61、onditions mathematical model called the mathematical model of linear programming.</p><p>　　3.3 From the actual problem, create a mathematical model of the steps;</p><p>　　Based on impact to achi

62、eve the objective factors to find the decision variables;</p><p>　　Where the decision variables and achieve the purpose of the functional relationship between objective function;</p><p>　　Restri

63、ctions suffered by the decision variables to determine the constraints to be met by the decision variables.</p><p>　　3.4 Created by the characteristics of the linear programming model;</p><p>　　

64、Each model has a number of decision variables, which is number. Which means that a program of a set of values ??of the decision variables, the decision variables are generally non-negative.</p><p>　　The obje

65、ctive function is a linear function of the decision variables, according to the specific issues can be maximized or minimized, both collectively referred to as optimization [3].</p><p>　　Constraints is a lin

66、ear function of the decision variables.</p><p>　　3.5 The general form of the linear programming model</p><p>　　Objective function: (1-1)</p><p>　　Constraints：

67、 (1-2)</p><p>　　Linear programming mathematical model, the equation (3-1) is referred to as the objective function; (3-2) referred to as the constraint condition.</p><p>　　3.6 The s

68、tandard form of the linear programming model</p><p><b>　　(1-3)</b></p><p><b>　　(1-4)</b></p><p><b>　　Among.</b></p><p>　　The abbrevi

69、ated form:</p><p><b>　　(1-5)</b></p><p><b>　　(1-6)</b></p><p>　　Vectors and matrices:</p><p><b>　　(1-7)</b></p><p><

70、b>　　(1-8)</b></p><p>　　Among ，</p><p>　　The solution of the linear programming</p><p>　　Graphical method and simplex method for solving linear progra

71、mming problems, but the practical application of the simplex method, now has the simplex method standard software in the computer to solve the constraints and the number of decision variables of 10000a linear programming

72、 problem. In order to improve the speed of problem-solving, but also to improve the simplex method, dual simplex method, the original dual decomposition algorithm and polynomial time algorithm. Graphical method to solve&

73、lt;/p><p>　　4.1 General linear programming problem Simplex Method</p><p>　　4.1.1 To establish an initial basic feasible solution</p><p>　　Linear programming problem, many constraints a

74、s inequality, so first you want to translate it into a standard, built at the same time</p><p>　　Established an initial basic feasible basis.</p><p>　　4.1.2 Optimal solution test</p><

75、p>　　Find a feasible to determine if it is not the optimal solution. Method to judge whether the test objective function is the Department of</p><p>　　, If the number of positive coefficients, then there i

76、s a better solution. Only when all the coefficients in the objective function is negative or 0, change the solution is the optimal solution.</p><p>　　4.1.3 Base change</p><p>　　Transform from a

77、basic feasible solution to another basic feasible solution is a base change.</p><p>　　4.1.4 Iteration (rotation operation)</p><p>　　Constraints augmented matrix in the new base variable coeffici

78、ents through the rows of the matrix transform or Gauss transform into a single-</p><p>　　Bit matrix [6].</p><p>　　4.2 Non-standard linear programming problem solution</p><p>　　4.2.T

79、he way of M</p><p>　　Artificial variable in the constraints of a linear programming problem, requiring artificial variables on the objective function value, this desirable artificial variables in the objecti

80、ve function coefficients (very large positive number) [7],so that the objective function to be maximized, artificial variables can only take zero, so the artificial variables must be swapped out from the base variable, o

81、therwise the objective function can not be achieved to maximize.</p><p>　　4.2.2 Two-stage method</p><p>　　Phase I: without regard to the original problem exists basic feasible solution to the or

82、iginal linear programming problem with artificial variables, the construct containing only the objective function of the artificial variables and requirements are minimized.</p><p>　　Second stage: the first

83、stage to obtain the optimal simplex tableau removed artificial variables replace the original objective function coefficients of the objective function of the table the coefficient line, calculated as the second stage of

84、 the initial table.</p><p>　　4.3 Duality analysis</p><p>　　4.3.1 The basic concept of the dual problem</p><p>　　Linear programming problem, seeking a maximum linear programming defi

85、ned as "original", then exist with a minimum so-called dual problem corresponds to the dual linear programming problem and the optimal solution of the original linear programming optimal solution.</p>&l

86、t;p>　　4.3.2 The nature of the dual problem</p><p>　　Dual symmetry of the dual problem of the original problem.</p><p>　　The weak duality if a feasible solution of the original problem is a fe

87、asible solution to the dual problem.Then there exists。</p><p>　　Unbounded if the original problem (the dual problem) is unbounded solution, no feasible solution of the dual problem (the original problem).<

88、;/p><p>　　Feasible solution is the nature of the optimal solution set is a feasible solution of the original problem, the feasibility of the dual problem solution,when，,is the optimal solution.</p><p

89、>　　The duality theorem if the original problem, the optimal solution, then the dual problem of the optimal solution and the optimal value of the same.</p><p>　　Complementary relaxation if ,feasible soluti

90、on to the dual problem and the original problem,then and,If and only if,is Optimal solution。</p><p>　　4.4 Sensitivity Analysis</p><p>　　Sensitivity analysis are the following:</p><p&g

91、t;　　Analysis of the change of the amount of resources;</p><p>　　Objective function value of the coefficient of variation;</p><p>　　Changes in the technical coefficients </p><p>　　Co

92、nstraints increase or decrease change.</p><p>　　Chapter II The theory of corporate decision-making</p><p>　　Overview of the corporate decision-making</p><p>　　With the deepening of

93、 enterprise computer applications and the level of information, the company has accumulated a large number of business and financial data, and continue exponentially with time and business development trend of expansion.

94、 The focus of the enterprise information processing sector has gradually beyond simple data collection, staff at all levels within the enterprise want to be able to quickly, accurately and easily and effectively obtain m

95、eaningful information from a large numb</p><p>　　Corporate decision-making classification</p><p>　　2.1 Classified by important</p><p>　　In corporate decision-making, according to an

96、 important degree of classification general decision-making is divided into three levels, namely strategic decision, tactical decision-making and business decisions.</p><p>　　2.1.1 Strategic decision-making&

97、lt;/p><p>　　First class strategic decision-making with the overall approach of the management and development companies need resources decision-making, it belongs to the long-term planning, the development of e

98、nterprises has a profound impact on the decision-making process to consider many factors of uncertainty and risk-taking. The top of the Group's corporate decision-making information model, responsible for the managem

99、ent, control, and coordination of the normal operation of the entire corporate network</p><p>　　2.1.2 Tactical decisions</p><p>　　The second type of decision-making is called a tactical decision

100、, after the material resources, equipment and other decision-making, planning how the most effective allocation of resources (such as production capacity, capital, materials, labor, etc.) in order to obtain the maximum b

101、enefit. Defined group member enterprises basic decision-making activities. Although due to the dynamic characteristics of the Group companies, the company's actual situation and operating procedures will be different

102、</p><p>　　2.1.3 Business decisions</p><p>　　The third category called business decisions to complete the work of the implementation of the specific tasks of the Group companies, including logist

103、ics in the rational flow between enterprises as well as the physical process from raw materials to finished products, such as the transportation of raw materials, spare parts processing, component assembly, testing, stor

104、age, etc.process. In this layer, the completion of the manufacture, sale, supply, transportation and other tasks at the same time,</p><p>　　2.2 Press the corporate decision-making environment classification.

105、</p><p>　　In corporate decision-making, according to the corporate decision-making environment can be divided into decision making under uncertainty, risk, decision-making and decision making under uncertain

106、ty.</p><p>　　2.2.1 Decision making under uncertainty</p><p>　　Decision making under uncertainty is the future of the environment is completely predictable, and the consequences of the decision-m

107、aking program to be selected in the uncertain future in this environment is determined. Simply speaking, is a program only one identified.</p><p>　　2.2.2 Risk Decision</p><p>　　The risk decision

108、 refers to several possible states and the corresponding consequences in the future environment, people can not get adequate and reliable information about the future of the environment, but can predict the probability o