Math 428: Introduction to Operations Research

1 Chapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingMath428:Intro ductiontoOp erationsResearchInstructor:ThomasShoresD epartmentofMathematicsWeek1,January15,20 08 AvH12 Instructor:ThomasShoresDepartmentofMathe maticsMath428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingOutline1 Chapter1:Intro duction2 Chapter2:OverviewofOR3 Chapter3:Intro ductiontoLinearProgrammingInstructor:Tho masShoresDepartmentofMathematicsMath428: Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingDe nitionsOp erationsResearch:Whatdo esitmean? Researchonop erations,soappliedtoproblemsconcerningho wtoconductandco ordinateop erationsinanorganization. Theapplicationofmathematicalmetho ds, ,optimization,tostudyorplanapro cess.

2 Managementscience ..p erhapsinthesenseofdaVinci: Nohumaninvestigationcanb ecalledrealscienceifitcannotb edemonstratedmathematically. outstatisticalorcomputersciencetechnique s,b othofwhicharefoundinthistext?Whatab outhumanmanagementissuessuchasextracting therealproblemfromlessquantativelyorient edcolleagues?Instructor:ThomasShoresDepa rtmentofMathematicsMath428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingDe nitionsOp erationsResearch:Whatdo esitmean? Researchonop erations,soappliedtoproblemsconcerningho wtoconductandco ordinateop erationsinanorganization. Theapplicationofmathematicalmetho ds, ,optimization,tostudyorplanapro cess. Managementscience ..p erhapsinthesenseofdaVinci: Nohumaninvestigationcanb ecalledrealscienceifitcannotb edemonstratedmathematically.

3 Outstatisticalorcomputersciencetechnique s,b othofwhicharefoundinthistext?Whatab outhumanmanagementissuessuchasextracting therealproblemfromlessquantativelyorient edcolleagues?Instructor:ThomasShoresDepa rtmentofMathematicsMath428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingDe nitionsOp erationsResearch:Whatdo esitmean? Researchonop erations,soappliedtoproblemsconcerningho wtoconductandco ordinateop erationsinanorganization. Theapplicationofmathematicalmetho ds, ,optimization,tostudyorplanapro cess. Managementscience ..p erhapsinthesenseofdaVinci: Nohumaninvestigationcanb ecalledrealscienceifitcannotb edemonstratedmathematically. outstatisticalorcomputersciencetechnique s,b othofwhicharefoundinthistext?Whatab outhumanmanagementissuessuchasextracting therealproblemfromlessquantativelyorient edcolleagues?

4 Instructor:ThomasShoresDepartmentofMathe maticsMath428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingDe nitionsOp erationsResearch:Whatdo esitmean? Researchonop erations,soappliedtoproblemsconcerningho wtoconductandco ordinateop erationsinanorganization. Theapplicationofmathematicalmetho ds, ,optimization,tostudyorplanapro cess. Managementscience ..p erhapsinthesenseofdaVinci: Nohumaninvestigationcanb ecalledrealscienceifitcannotb edemonstratedmathematically. outstatisticalorcomputersciencetechnique s,b othofwhicharefoundinthistext?Whatab outhumanmanagementissuessuchasextracting therealproblemfromlessquantativelyorient edcolleagues?Instructor:ThomasShoresDepa rtmentofMathematicsMath428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingDe nitionsOp erationsResearch:Whatdo esitmean?

5 Researchonop erations,soappliedtoproblemsconcerningho wtoconductandco ordinateop erationsinanorganization. Theapplicationofmathematicalmetho ds, ,optimization,tostudyorplanapro cess. Managementscience ..p erhapsinthesenseofdaVinci: Nohumaninvestigationcanb ecalledrealscienceifitcannotb edemonstratedmathematically. outstatisticalorcomputersciencetechnique s,b othofwhicharefoundinthistext?Whatab outhumanmanagementissuessuchasextracting therealproblemfromlessquantativelyorient edcolleagues?Instructor:ThomasShoresDepa rtmentofMathematicsMath428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingOriginsOrigins :Warneeds,esp eciallyWWI I,withpro cesseslikelogisticsplanning,resourceallo cation, (~1947)was rsttoformalizethesimplexmetho dforlinearprogrammingproblems,arguablyth emostfundamentalto (~1940)derivedmetho erman'sclassictext(1967-present)p :ThomasShoresDepartmentofMathematicsMath 428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingOriginsOrigins .

6 Warneeds,esp eciallyWWI I,withpro cesseslikelogisticsplanning,resourceallo cation, (~1947)was rsttoformalizethesimplexmetho dforlinearprogrammingproblems,arguablyth emostfundamentalto (~1940)derivedmetho erman'sclassictext(1967-present)p :ThomasShoresDepartmentofMathematicsMath 428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingOriginsOrigins :Warneeds,esp eciallyWWI I,withpro cesseslikelogisticsplanning,resourceallo cation, (~1947)was rsttoformalizethesimplexmetho dforlinearprogrammingproblems,arguablyth emostfundamentalto (~1940)derivedmetho erman'sclassictext(1967-present)p :ThomasShoresDepartmentofMathematicsMath 428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingOriginsOrigins :Warneeds,esp eciallyWWI I,withpro cesseslikelogisticsplanning,resourceallo cation, (~1947)was rsttoformalizethesimplexmetho dforlinearprogrammingproblems,arguablyth emostfundamentalto (~1940)derivedmetho erman'sclassictext(1967-present)p :ThomasShoresDepartmentofMathematicsMath 428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingOriginsOrigins :Warneeds,esp eciallyWWI I,withpro cesseslikelogisticsplanning,resourceallo cation, (~1947)was rsttoformalizethesimplexmetho dforlinearprogrammingproblems,arguablyth emostfundamentalto (~1940)derivedmetho erman'sclassictext(1967-present)p :ThomasShoresDepartmentofMathematicsMath 428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2.

7 OverviewofORChapter3:Intro ductiontoLinearProgrammingImpactHUGE:HP, 1998:Redesignsizesandlo cationsofbu ersinprinterpro ductionlinetomeetpro ~$280 MChina,1995:Optimallyselectandschedulema ssiveprojectsformeetingcountry' ~$425 MCitgoPetroleum,1987:Optimizere neryop erations,supply,distributionandmarketing ofpro ~$70 MInstructor:ThomasShoresDepartmentofMath ematicsMath428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingImpactHUGE:HP, 1998:Redesignsizesandlo cationsofbu ersinprinterpro ductionlinetomeetpro ~$280 MChina,1995:Optimallyselectandschedulema ssiveprojectsformeetingcountry' ~$425 MCitgoPetroleum,1987:Optimizere neryop erations,supply,distributionandmarketing ofpro ~$70 MInstructor:ThomasShoresDepartmentofMath ematicsMath428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingImpactHUGE:HP, 1998:Redesignsizesandlo cationsofbu ersinprinterpro ductionlinetomeetpro ~$280 MChina,1995:Optimallyselectandschedulema ssiveprojectsformeetingcountry' ~$425 MCitgoPetroleum,1987:Optimizere neryop erations,supply,distributionandmarketing ofpro ~$70 MInstructor:ThomasShoresDepartmentofMath ematicsMath428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingImpactHUGE:HP, 1998:Redesignsizesandlo cationsofbu ersinprinterpro ductionlinetomeetpro ~$280 MChina,1995:Optimallyselectandschedulema ssiveprojectsformeetingcountry' ~$425 MCitgoPetroleum,1987.

8 Optimizere neryop erations,supply,distributionandmarketing ofpro ~$70 MInstructor:ThomasShoresDepartmentofMath ematicsMath428:Intro ductiontoOp erationsResearchCoursewareTo olsOnthetextCD:StudentversionsofLINGO/LI NDO commericalmo anothercommericalmo suchasSolver thesearetheprincipalto olsOnthetextCD:StudentversionsofLINGO/LI NDO commericalmo anothercommericalmo suchasSolver thesearetheprincipalto olsOnthetextCD:StudentversionsofLINGO/LI NDO commericalmo anothercommericalmo suchasSolver thesearetheprincipalto olsOnthetextCD:StudentversionsofLINGO/LI NDO commericalmo anothercommericalmo suchasSolver thesearetheprincipalto olsOnthetextCD:StudentversionsofLINGO/LI NDO commericalmo anothercommericalmo suchasSolver thesearetheprincipalto :Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingAMo netheproblemofinterestandgatherrelevantd ata.

9 (Usersmaynotevenunderstandtheirproblem youhavetoclarifyit.) del.(Basically,cho osedecisionvariablesx1,x2,..,xn,constrai ntsondecisionvariablesandobjectivefuncti onsofthedecisionvariablestob eoptimized.) (s)fromthemo delanddop ost-optimalityanalysissuchassensitivityo fsolutions, what-if 's , del.(Doanswersmakesense,canyoutestagains tpriordata,arethereblunders,mathematical ornumericalinstabilities?)Iftestsfail, :ThomasShoresDepartmentofMathematicsMath 428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingAMo netheproblemofinterestandgatherrelevantd ata.(Usersmaynotevenunderstandtheirprobl em youhavetoclarifyit.) del.(Basically,cho osedecisionvariablesx1,x2,..,xn,constrai ntsondecisionvariablesandobjectivefuncti onsofthedecisionvariablestob eoptimized.) (s)fromthemo delanddop ost-optimalityanalysissuchassensitivityo fsolutions, what-if 's , del.

10 (Doanswersmakesense,canyoutestagainstpri ordata,arethereblunders,mathematicalornu mericalinstabilities?)Iftestsfail, :ThomasShoresDepartmentofMathematicsMath 428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingAMo netheproblemofinterestandgatherrelevantd ata.(Usersmaynotevenunderstandtheirprobl em youhavetoclarifyit.) del.(Basically,cho osedecisionvariablesx1,x2,..,xn,constrai ntsondecisionvariablesandobjectivefuncti onsofthedecisionvariablestob eoptimized.) (s)fromthemo delanddop ost-optimalityanalysissuchassensitivityo fsolutions, what-if 's , del.(Doanswersmakesense,canyoutestagains tpriordata,arethereblunders,mathematical ornumericalinstabilities?)Iftestsfail, :ThomasShoresDepartmentofMathematicsMath 428:Intro ductiontoOp erationsResearchChapter1:Intro ductionChapter2:OverviewofORChapter3:Int ro ductiontoLinearProgrammingAMo netheproblemofinterestandgatherrelevantd ata.