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1、Chapter3 IntroductiontoLinearProgrammingtoaccompany OperationsResearch:Applications&Algorithms, 4thedition,byWayneL.Winston3.1-WhatIsaLinearProgrammingProblem?Eachsoldierbuilt:Sellfor$27anduses$10worthofrawmaterials.IncreaseGiapetto’svariablelabor/overheadcostsby$14.Requires2hours
2、offinishinglabor.Requires1hourofcarpentrylabor.Eachtrainbuilt:Sellfor$21andused$9worthofrawmaterials.IncreasesGiapetto’svariablelabor/overheadcostsby$10.Requires1houroffinishinglabor.Requires1hourofcarpentrylabor.ExamplefromlastweekGiapetto’s,Inc.,manufactureswoodensoldiersandtrai
3、ns.線性規(guī)劃模型(LinearProgrammingmodel)是在一組「線性」的限制式(asetoflinearconstraints)之下，尋找極大化(maximize)或極小化(minimize)一個特定的目標(biāo)函數(shù)(objectivefunction)線性規(guī)劃模型由下列三個部分組成:一組決策變數(shù)(Asetofdecisionvariables)一個特定的目標(biāo)函數(shù)(Anobjectivefunction)一組「線性」的限制式(Asetofconstraints)IntroductiontoLinearProgrammingAssumptionsfor
4、LinearProgramming參數(shù)具有「確定性」(certainty)目標(biāo)函數(shù)與限制式符合「固定規(guī)模報酬」之假設(shè)(constantreturnstoscale)「疊加性」之假設(shè)：決策變數(shù)間沒有互動性，即某函數(shù)之總價值只能藉由線性加總求得「連續(xù)性」(Continuity)之假設(shè)變數(shù)值必須再某一個可行範(fàn)圍內(nèi)1單位產(chǎn)品$4，3Hrs生產(chǎn)500單位產(chǎn)品$4*500=$2000，3*500=1,500Hrs生產(chǎn)ExampleofIndustriesProductionProblem生產(chǎn)兩種玩具模型:宇宙光SpaceRay.射擊手Zapper.資源限制(Resou
5、rces)1000磅特殊塑膠化合物(specialplastic)每週40小時生產(chǎn)時間(40hrsofproductiontimeperweek)市場需求(Marketingrequirement)每週總產(chǎn)量至多700打SpaceRays週產(chǎn)量不能過Zappers350打以上技術(shù)係數(shù)(Technologicalinputs)SpaceRays每打需要2pounds塑膠與3分鐘生產(chǎn)時間Zappers每打需要1pound塑膠與4分鐘生產(chǎn)時間ExampleofIndustriesProductionProblem生產(chǎn)需求:SpaceRay每打利潤(profit)
6、$8，Zappers每打利潤(profit)$5盡量多生產(chǎn)SpaceRay，剩餘資源再生產(chǎn)Zapper目前生產(chǎn)計畫:SpaceRays=450dozenZapper=100dozenProfit=$4100perweekExampleofIndustriesProductionProblem8(450)+5(100)決策變數(shù)(Decisionsvariables):X1=每週生產(chǎn)的SpaceRays打數(shù)X2=每週生產(chǎn)的Zappers打數(shù)目標(biāo)函數(shù)(ObjectiveFunction):極大化每週總利潤ExampleofIndustriesProduction
7、ProblemMax8X1+5X2(每週總利潤)subjectto2X1+1X2￡1000(塑膠原料,Plastic)3X1+4X2￡2400(生產(chǎn)時間,ProductionTime)X1+X2￡700(最大產(chǎn)量,Totalproduction)X1-X2￡350(組合)Xj>=0,j=1,2(非負(fù)值,Nonnegativity)ExampleofIndustriesProductionProblemGraphicalAnalysisofLinearProgramming滿足模型全部限制式的所有點集合稱為Thesetofallpointsthatsatis
8、fyalltheconstraintsofthemodelisca
