Master of business administration business economicsManagement science (Mba)

Master of business administration business economics management science semester 2

1. MBAFM/BI/BE-II Semester
Management Science
January-May: 2024
Dr. Shambhu Nath Singh
Associate Professor (Economics & Finance)
Department of Banking, Economics & Finance
Bundelkhand University, Jhansi

2. Syllabus: Management Science
•UnitI:ManagementScience-BasicConceptsandits
roleinDecisionMaking;LinearProgrammingProblem:
GraphicalandSimplexMethod;Duality
•UnitII:BigMMethod;IntegerProgrammingBranchand
Boundalgorithm;SensitivityAnalysis;Goal
ProgrammingProblemProgrammingProblem
•UnitIII:TransportationProblemandAssignment
Problem;QueuingTheory;
•UnitIV:NetworkAnalysisTechniques;PERT/CPM;
DecisionTheoryandDecisionTrees
•UnitV:InventoryManagement;GameTheory;
Simulation.

3. Evolution of Management Science
OperationResearchorManagementsciencecameinto
existenceduringsecondworldwar,whentheBritishand
theAmericanmilitarymanagementcalledagroupof
scientistswithdiverseeducationalbackgroundnamely
Physics,Biology,Statistics,Mathematics,Psychologyetc
toapplyascientificapproach,todealwithstrategicand
tacticalproblemsofvariousmilitaryoperations.tacticalproblemsofvariousmilitaryoperations.
Theobjectivewastoallocatescareresourcesinan
effectivemannertovariousmilitaryoperationsandto
theactivitieswithineachoperation.Thisnewapproach
tothesystematicandscientificstudyofoperationsofthe
systemwascalledOR.ThetermORwasfirstintroduced
byMcCloskyandThrefthenofBowdsey(asmalltownof
UK)in1940s.

4. Concept of Operation Research
In1950,ORwasrecognizedasasubjectof
academicstudyintheuniversities,sincethenthe
subjecthasbeengainingmoreandmore
importanceforthestudentsof Engineering,
Mathematics,PublicAdministration,Management,
BehavioralScienceetc.ItisalsoknownasDecision
Science,ManagementScienceandQuantitative
BehavioralScienceetc.ItisalsoknownasDecision
Science,ManagementScienceandQuantitative
Methods.
HenceORcanbeassociatedwith, “Anactof
winningthewarwithoutactuallyfightingit.”
AccordingtoH.M.Wagner,“ORisascientific
approachofproblemsolvingforexecutive
management.”

5. Steps in Designing Operation Research
ORisalogicalandsystematicapproachfor
decisionmaking.Therearesiximportantsteps
inORstudyandthesestepsarearrangedin
followinglogicalorder-
1.ObservetheProblemEnvironment1.ObservetheProblemEnvironment
2.AnalyzeandDefinetheProblem
3.DevelopaModel
4.SelectanAppropriateDataInput
5.ProvideaSolutionandTestReasonableness
6.ImplementtheSolution

6. 1-Observe the Problem Environment
StepIintheprocessofORstudyis
observingtheproblemenvironment.
Theactivitiesthatconstitutethisstep
arevisits,conferences,observations,arevisits,conferences,observations,
researchesandsoon.Withthehelpof
suchactivities,theORscientistsget
sufficientinformationandsupportto
proceedandisbetterpreparationto
formulatetheproblem.

7. 2-Analyze and Define the Problem
StepIIisanalyzinganddefiningthe
problem.Inthisstepnotonlythe
problemisdefinedbutalsouses,
objectivesandlimitationsoftheobjectivesandlimitationsofthe
studyareexpressedinthelightofthe
problem.Theendresultofthisstepis
aclearindicationofneedfora
solutionandunderstandingits
nature.

8. 3-Develop a Model
•StepIIIistoconstructamodel.Amodel
isrepresentationofsomerealsituation.
ORmodelsarebasicallymathematical
modelsrepresentationsystemprocess
orenvironmentintheformoftheorenvironmentintheformofthe
equations,relationshiporformulae.The
modelmayalsobemodifiedifthe
managementisnotsatisfiedwiththe
answerthatgives.

9. 4-Select an Appropriate Data Input
Ifdatainputisnotappropriatethenno
modelwillworkappropriately.Hence,
selectanappropriatedatainputisavital
stepinORprocess.Importantactivitiesin
thisstepareanalyzinginternal-externalthisstepareanalyzinginternal-external
dataandfacts,collectingopinionsusing
computerdatabanks.Thepurposeofthis
stepistohaveasufficientdatainputto
operateandtestthemodel.

10. 5-Provide a Solution and Test Reasonableness
StepVinORprocessistogetasolutionwith
thehelpofamodelanddatainput.Sucha
solutionisnotimplementedimmediately.
First,thesolutionisusedtotestthemodel
andtofindlimitations,ifany.Ifthemodelisandtofindlimitations,ifany.Ifthemodelis
notbehavingproperly,updatingand
modificationofthemodelisconsideredat
thisstage.Theendresultofthisstepisa
solutionthatisdesirableandsupportsthe
currentorganizationalobjective.

11. 6-Implement the Solution
Implementationofthesolutionobtainedin
previousstepisthelaststepofORprocess.
Ifthegaparisesbetweenthesolution
providerandthepersonwhowishestouse,
itshouldbeeliminated.Todothis,ORitshouldbeeliminated.Todothis,OR
ScientistaswellasManagementshould
playapositiverole.Aproperly
implementedsolutionobtainedthroughOR
techniquesresultinimprovedworkingand
winsthemanagementsupport.

12. Operation Research Models
Amodelisdefinedasanidealrepresentationof
thereallifesituation.Variousitemslikeamap,
amultipleactivitycharts,PERTnetwork,break
evenequation,balancesheetetcareallthe
modelsbecauseeachofthemrepresentsafewmodelsbecauseeachofthemrepresentsafew
aspectsofthereallifesituation.Itmeans
modelrepresentsoneorfewaspectsofreality.
Theobjectiveofmodelistoprovideameans
foranalyzingthebehaviorofthesystemforthe
purposeofimprovingitsperformance.

13. Classification of Models
Themodelscanbeclassifiedasfollows:
1.Bydegreeofabstraction(Mathematicalmodels
andLanguagemodels)
2.Byfunction(Descriptivemodels,Predictive
modelsandNormativemodels)
3.Bystructure(IconicorPhysicalmodelsand3.Bystructure(IconicorPhysicalmodelsand
Analogueorschematicmodels)
4.Bynatureoftheenvironment (Deterministic
modelsandProbabilisticmodels)
5.Bytheextentofgenerality(Generalmodelsand
Specificmodels)
6.Bythetimehorizon(StaticmodelsandDynamic
models)

14. 1-By Degree of Abstraction
MathematicalmodelsorSymbolicmodels-This
modelusesasetofmathematicalsymbolsto
representthedecisionvariablesofasystem
underconsideration.Thesevariablesare
repeatedbymathematicalequationswhichrepeatedbymathematicalequationswhich
describethepropertiesofthesystem.For
example-linearprogrammingproblem
Languagemodels-Itisalsoabstracttype
model.Forcricketorhockeymathcommentary
aretheexampleofthismodel.

15. 2-By Function
DescriptiveModels-Itexplainsthevariousoperationsinnon
mathematicallanguageandtrytodefinethefunctional
relationshipandinteractionbetweenvariousoperations.
Theysimplydescribethesomeaspectsofthesystemonthe
basisofobservation,surveyorquestionnaireetcbutdonot
predictitsbehaviors.Forexample-theorganizationalcharts,
piediagramandlayoutplandescribesthefeaturesoftheir
respectivesystems.
PredictiveModels-ItexplainsorpredictsthebehaviorsofPredictiveModels-Itexplainsorpredictsthebehaviorsof
thesystem.Forexample-exponentialsmoothingforecast
modelpredictthefuturedemandandpredictingelection
resultsbeforeactuallythecountingiscompleted.
NormativeModelsorPrescriptiveModels-Itdevelopsthe
decisionrulesforoptimalsolutions.Theyareapplicableto
therepetitiveproblems,thesolutionprocessofwhichcanbe
programmedwithoutmanagerialinvolvement.LPisa
prescriptiveornormativemodelasitprescribewhatthe
managersmustfollow.

16. 3-By Structure
IconicorPhysicalModels-Inthispropertiesofrealsystem
arerepresentedbythepropertiesofthemselves,frequently
withachangeofscale.Thisisaphysicalorpictorial
representationofvariousaspectsofasystem.Forexample-
Toys,modelofabuilding,scaledupmodelofacellin
biologyetc.
AnalogueorSchematicModels-AnaloguemodelscanAnalogueorSchematicModels-Analoguemodelscan
representdynamicsituationsandareusedmoreoftenthan
iconicmodelssincetheyareanalogoustothecharacteristics
ofthesystemunderstudy.Theyuseonesetofthe
propertiestorepresentsomeothersetofpropertieswhich
thesystemunderstudypossesses.Forexample-Anetwork
ofwaterpipestorepresenttheflowofcurrentinan
electricalnetworkorgraphs,organizationalchartsandso-
on.

17. 4-By Nature of the Environment
DeterministicModels-Itismodelwhichdoesnot
takeuncertaintyintoaccount.Indeterministic
modelsvariablesarecompletelydefinedandthe
outcomesarecertain.Forexample-alinear
programmingproblem,anassignmentproblem,
EOQ,andtransportationmodelarethe
deterministicmodels.deterministicmodels.
ProbabilisticModelsorstochasticModels-Itisa
modelwhichtakesriskanduncertaintyasan
importantaspectoftheproblem.Theinputand
outputvariablestaketheformofprobability
distribution.Forexample-Stochasticprobability
modelsandtheexponentialsmoothingmodelfor
forecastingdemandaretheprobabilisticmodels.

18. 5-By the Extent of Generality
Generalmodels-Linearprogrammingmodelis
knownasageneralmodelsinceitcanbeused
foranumberoffunctions(i.e.productmix,
productionscheduling,marketingetc)ofan
organization.organization.
Specificmodels-Salesresponseequationasa
functionofadvertisingisapplicableinthe
marketingfunctionaloneisatypeofspecific
model.

19. 6-By the Time Horizon
StaticModels-Thisisamodelwhichdoesnottake
timeintoaccount.Itassumesthatthevaluesof
thevariablesdonotchangewithtimeduringa
certainperiodoftimehorizon.Theyareeasierto
formulate,manipulateandsolve.Forexample-LPP,
Transportation,AssignmentandEOQ.Transportation,AssignmentandEOQ.
DynamicModels-Thismodelconsiderstimeasone
oftheimportantvariable.Theyareusedfor
optimizationofmultistageproblemswhichrequire
aseriesofdecisionswiththeoutcomeofeach
dependingupontheresultsfthepreviousdecision
intheseries.Forexample-dynamicprogramming
andreplacementproblem.

20. Scope of Operation Research
Intherecentyearsofdevelopment,ORhasenteredsuccessfullyin
differentareasofresearch.Itisusefulinthefollowingimportant
fieldslike-
1-Inagriculture
Withthesuddenincreaseofpopulationandresultingshortageof
food,everycountryisfacingtheproblemofOptimumallocationof
landtoavarietyofcropsaspertheclimaticconditions.Optimum
distributionofwaterfromnumerousresourceslikecanalforirrigation
purposes.Hencethereisarequirementofdeterminingbestpoliciespurposes.Hencethereisarequirementofdeterminingbestpolicies
underthegivenrestrictions.Thereforeagoodquantityofworkcanbe
doneinthisdirection.
2-
Infinance
Intherecenttimesofeconomiccrisis,ithasbecomeveryessentialfor
everygovernmenttodoacarefulplanningfortheeconomicprogress
ofthecountry.ORtechniquescanbeappliedin-
1.Todeterminetheprofitplanforthecompany
2.Tomaximizethepercapitaincomewithleastamountofresources
3.Todecideonthebestreplacementpolicies,etc

21. Scope of Operation Research
3-Inindustry
Iftheindustrymanagermakeshispoliciessimplyonthebasisofhis
pastexperienceandadayapproacheswhenhegetsretirement,then
aseriouslossisencounteraheadoftheindustry.Thisheavylosscan
berightawaycompensatedthroughappointingayoungspecialistof
ORtechniquesinbusinessmanagement.ThusORishelpfulforthe
industrydirectorindecidingoptimumdistributionofseverallimited
resourceslikemen,machines,material,etctoreachattheoptimum
decision.
4-Inmarketing4-Inmarketing
WiththeassistanceofORtechniquesamarketingadministratorcan
decideupon-
1.Wheretoallocatetheproductsforsalesothatthetotalcostof
transportationissettobeminimum
2.Theminimumperunitsaleprice
3.Thesizeofthestocktocomeacrosswiththefuturedemand
4.Howtochoosethebestadvertisingmediawithrespecttocost,time
etc?
5.How,whenandwhattobuyattheminimumlikelycost?

22. Scope of Operation Research
5-Inpersonnelmanagement
ApersonnelmanagercanutilizeORtechniques-
1.Toappointthehighlysuitablepersononminimumsalary
2.Toknowthebestageofretirementfortheemployees
3.Tofindoutthenumberofpersonsappointedinfulltimebasiswhenthe
workloadisseasonal
6-Inproductionmanagement
AproductionmanagercanutilizeORtechniques-AproductionmanagercanutilizeORtechniques-
1.Tocalculatethenumberandsizeoftheitemstobeproduced
2.Inschedulingandsequencingtheproductionmachines
3.Incomputingtheoptimumproductmix
4.Tochoose,locateanddesignthesitesfortheproductionplans
7-InL.I.C
ORapproachisalsoapplicabletofacilitatetheL.I.Cofficestodecide-
1.Whatshouldbethepremiumratesforarangeofpolicies?
2.Howwelltheprofitscouldbeallocatedinthecasesofwithprofitpolicies?

23. Role of Operations Research in Decision-Making
TheOperationResearchmaybeconsideredasatool
whichisemployedtoraisetheefficiencyof
managementdecisions.ThebenefitsofORstudy
approachinbusinessandmanagementdecisionmaking
maybecategorizeasfollows-
1-Bettercontrol-Themanagementoflargeconcernsfinds
itmuchexpensivetogivecontinuousexecutive
supervisionsoverroutinedecisions.AnORapproachsupervisionsoverroutinedecisions.AnORapproach
directstheexecutivestodedicatetheirconcentrationto
morepressingmatters.Forinstance-ORapproach
handlesproductionschedulingandinventorycontrol.
2-Bettercoordination-Sometimes,ORhasbeenvery
helpfulinpreservingthelawandordersituationoutof
disorder.Forinstance,anORbasedplanningmodel
turnsouttobeavehicleforcoordinatingmarketing
decisionswiththerestrictionsforcedonmanufacturing
capabilities.

24. Role of Operations Research in Decision-Making
3-Bettersystem-ORstudyisalsoinitiatedto
examineaparticularproblemofdecisionmaking
likesettingupanewwarehouse.LaterOR
approachcanbemoredevelopedintoasystemto
beemployedfrequently.Asaresultthecostof
undertakingthefirstapplicationmaygetbetter
profits.
undertakingthefirstapplicationmaygetbetter
profits.
4-Betterdecisions-ORmodelsregularlygiveactions
thatdoenhanceansensitivedecisionmaking.
Sometimesasituationmaybesocomplexthatthe
humanmindcanneverexpecttoassimilateallthe
significantfactorswithouttheaidofORand
computeranalysis.

25. LINEAR PROGRAMMING
PROBLEM (LPP)
Now-a-daysMen,Money,Materialsetc
arenotavailableinsufficientquantity.
Thatiswhy,Economistsarebusyin
developingnewtechniquesandtheir
applications.
Togetthemaximum profitfrom
applications.
Togetthemaximum profitfrom
limitedanddefiniteresourcesLPPis
used.LPPisamathematicaltechnique
forsolvingmaximizationand
minimizationproblemsubjecttocertain
constraints,involvingthevariables
havinglinearrelationshipwitheach
other.

26. Mathematical Form
LPPwasdevelopedbyRussian
MathematicianL.V.Kantrovichin
1939.
Letusconsidertwodecision
variablesx
1
andx
2
then-
variablesx
1
andx
2
then-
MaxorMinZ=c
1
x
1
+c
2
x
2
Subjectto
a
11
x
1
+ a
12
x
2
≤ or = or ≥ b
1
a
21
x
1
+ a
22
x
2
≤ or = or ≥ b
2
and x
1
, x
2
≥ 0

27. Question/Problem
AcompanyisproducingtwoproductsA
andB.ProductAismanufacturedby2units
ofchemicalsand1unitofcompound,andBis
manufacturedby1unitofchemicaland2
unitsofcompounds.Only8,00unitsofunitsofcompounds.Only8,00unitsof
chemicalsand1,000unitsofcompoundsare
availabletothecompany.Theprofitperunit
ofAandBare30and20rupeesrespectively.
GiveamathematicalformulationofthisLPP
intermsofmaximizingtheprofitandsolveit
byGraphicalaswellasSimplexMethod.

43. Duality Theorem
DualityTheoremStatesthatforeveryLPP,thereisauniqueanotherLPP,
associatedwithit,involvingsamedataandcloselyrelatedtooptimal
solution.
Theoriginalproblemistermedas‘primal’andtheotherproblemistermed
as‘dual’,orwecansaythatgivenproblemisprimalanditsoutcomeisdual.
ForeveryMax/Min.probleminLPP,thereisuniquesimilarproblemof
Min/MaxinvolvingdataoforiginalLPP,orMin/MaxZofprimalisMax/Min
Zofitsdual.
Maximumfeasiblevalueofprimalobjectivefunction=Minimumfeasible
valueofdualobjectivefunction.valueofdualobjectivefunction.
TworeasonsfortheimportanceofDuality:-
1.Iftheprimalcontains,alargenumbersofconstraintsandsmallnumbersof
variables,thenthecalculationcanbereducedbyconvertingitindualand
thensolvingit.
2.Fromthecostoreconomicpointofview,theinterpretationofdual
variables,whichareusefulinmakingfuturedecisionsandtheactivities
beingprogrammed?
Thedualofdualoutcomeofanyproblemisprimalofthatproblemonly.
CoefficientofobjectivefunctionofprimalistheRHSvalueofconstraintsof
itsdual,andRHSvalueofconstraintsinprimalisthecoefficientofobjective
functionofitsdual.

44. Question: Find the dual of following LPP or the given primal-
Max Z = 90x + 40y
Subject to,x + 2y ≥ 60; & 3x + 4y ≥ 60
and x, y ≥ 0
Primal or Original Problem
Maximize
Z = 90x + 40y
Subjectto,
Dual Problem
Minimize
Z = 60a + 60b
Subjectto,Subjectto,
x + 2y ≥ 60
3x + 4y ≥ 60
and x, y ≥ 0
Subjectto,
a + 3b ≤ 90
2a + 4b ≤ 40
and a, b ≥ 0

45. With the Best Compliments
Thanking to all…..
By
Dr. Shambhu Nath Singh
Associate ProfessorAssociate Professor
(Former District Economic & Statistical Officer)
M. Sc. (Physics), MBA (Finance), MA (Economics)
JRF in Management, NET in Economics
Coordinator Ph. D. Coursework
Bundelkhand University, JHANSI
Mobile-09450075770; 08299233527 (WhatsApp)
[email protected]

46. Unit 1 is over. Unit 1 is over.
Thank You so much....
Dr. Shambhu Nath Singh