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Lecture 3
Introduction to
ManagementScience
Chapter 1 in the textbook
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OBJECTIVES
Problem Solving and Decision Making
Qan!i!a!ive Anal"sis and Decision Making
Qan!i!a!ive Anal"sis
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PROBLEM SOLVING AND
DECISION MAKING
1. Managemen! science
#. Problem solving
$rocess iden!i%"ing a di%%erence be!&een ac!al and !'e
desired s!a!e o% a%%air (akes ac!ion !o resolve !'e di%%erence
An a$$roac' !o decision making based on !'e
scien!i%ic me!'od
Makes e)!ensive se o% *an!i!a!ive anal"sis
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+. S!e$s o% $roblem solvingIden!i%" and de%ine !'e $roblem
De!ermine !'e cri!eria %or evala!ing al!erna!ives
,'oose an al!erna!ive -make a decision
/vala!e !'e resl!s
De!ermine !'e se! o% al!erna!ive sol!ions
/vala!e !'e al!erna!ives
Im$lemen! !'e selec!ed al!erna!ive
Decision
making
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1. DecisionMaking Process
QUANTITATIVE ANALYSIS
AND DECISION MAKING
Singlecri!eriondecision $roblems
Ml!icri!eriondecision $roblems
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/vala!e !'eal!erna!ives
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1. Anal"sis P'ase o% DecisionMaking Process
Qali!a!ive Anal"sis
based largel" on !'e manager3s 4dgmen! and
e)$erience
incldes !'e manager3s in!i!ive 5%eel6 %or !'e $roblem
is more o% an ar! !'an a science
QUANTITATIVE ANALYSIS
AND DECISION MAKING
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QUANTITATIVE ANALYSIS
AND DECISION MAKING
Qan!i!a!ive Anal"sis anal"s! &ill concen!ra!e on !'e *an!i!a!ive %ac!s or da!a
associa!ed &i!' !'e $roblem
anal"s! &ill develo$ ma!'ema!ical e)$ressions !'a!
describe !'e ob4ec!ives8 cons!rain!s8 and o!'er
rela!ions'i$s !'a! e)is! in !'e $roblem
anal"s! &ill se one or more *an!i!a!ive me!'ods !o
make a recommenda!ion
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#. Po!en!ial Reasons %or a Qan!i!a!ive Anal"sis
A$$roac' !o Decision Making
QUANTITATIVE ANALYSISAND DECISION MAKING
('e $roblem is com$le).
('e $roblem is ver" im$or!an!
('e $roblem is ne&
('e $roblem is re$e!i!ive
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QUANTITATIVE ANALYSIS
1. Qan!i!a!ive Anal"sis Process
Model Develo$men!
Da!a Pre$ara!ion
Model Sol!ion
Re$or! ;enera!ion
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ADVANTAGES OF MODELS
1. ;enerall"8 e)$erimen!ing &i!' models -com$ared
!o e)$erimen!ing &i!' !'e real si!a!ion=
re*ires less !ime
is less e)$ensive
involves less risk
#. ('e more closel" !'e model re$resen!s !'e real
si!a!ion8 !'e accra!e !'e conclsions and$redic!ions &ill be.
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1.Ob4ec!ive ?nc!ion a ma!'ema!ical e)$ression !'a! describes !'e $roblem3s
ob4ec!ive8 sc' as ma)imi@ing $ro%i! or minimi@ing cos!
/)am$le=P 1>)
#.,ons!rain!s
a se! o% res!ric!ions or limi!a!ions8 sc' as $rodc!ion ca$aci!ies
/)am$le =
2) B 0>
) C >
MATHEMATICAL MODELS
?or o$!imi@ing !'e $ro%i!
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MATHEMATICAL MODELS
+. Uncon!rollable In$!s environmen!al %ac!ors !'a! are no! nder !'e con!rol o%
!'e decision maker
A%%ec! !'e ob4ec!ive %nc!ion and cons!rain!s
0. Decision ariables
con!rollable in$!sE decision al!erna!ives s$eci%ied b" !'edecision maker8 sc' as !'e nmber o% ni!s o% Prodc! F
!o $rodce
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2. De!erminis!ic Model i% all ncon!rollable in$!s !o !'e model are kno&n and
canno! var"
7. S!oc'as!ic -or Probabilis!ic Model
i% an" ncon!rollable are ncer!ain and sb4ec! !o varia!ion
S!oc'as!ic models are o%!en more di%%icl! !o anal"@e.
MATHEMATICAL MODELS
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9. ,os!Gbene%i! considera!ions ms! be made in
selec!ing an a$$ro$ria!e ma!'ema!ical model.
:. ?re*en!l" a less com$lica!ed -and $er'a$s less$recise model is more a$$ro$ria!e !'an a more
com$le) and accra!e one de !o cos! and ease o%
sol!ion considera!ions.
MATHEMATICAL MODELS
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TRANSFORMING MODEL INPUTSINTO OUTPUT
Uncontrollable Inputs(Environmental Factors)
Uncontrollable Inputs(Environmental Factors)
ControllableInputs
(Decision Variables)
ControllableInputs
(Decision Variables)
utput(!ro"ected #esults)
utput(!ro"ected #esults)
Mat$ematicalModel
Mat$ematicalModel
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EXAMPLE: PROJECT SCHEDULING
Consider t$e construction o% a &''unitbungalos* +$e pro"ect consists o% $undreds o%activities involving e,cavating- %raming- iring-
plastering- painting- landscaping- and etc* Some o%
t$e activities must be done se.uentiall/
and ot$ers can be done at t$e same time* 0lso-
some o% t$e activities can be completed %astert$an normal b/ purc$asing additional resources(or1ers- e.uipment- etc*)*
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EXAMPLE: PROJECTSCHEDULING
2uestion4$at is t$e best sc$edule %or t$e activities and %or$ic$ activities s$ould additional resources bepurc$ased5 6o could management science be
used to solve t$is problem5
0nser
Management science can provide a structured-
.uantitative approac$ %or determining t$eminimum pro"ect completion time based on t$eactivities7 normal times and t$en based on t$eactivities7 e,pedited (reduced) times*
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EXAMPLE: PROJECTSCHEDULING
2uestion
4$at ould be t$e uncontrollableinputs5
0nser
8ormal and e,pedited activit/ completiontimes
0ctivit/ e,pediting costs
Funds available %or e,pediting
!recedence relations$ips o% t$e activities
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pounds
o% steel to ma1e a unit o%product>*
Let x& and x> denote t$is mont$7s production
level o% product & and product >- respectivel/*Denote b/p
&andp
>t$e unit pro;ts %orproducts&
and >- respectivel/*
Iron 4or1s $as a contract calling %or at least munits o% product &t$is mont$* +$e ;rm7s %acilitiesare suc$ t$at at most uunits o% product >ma/ beproduced mont$l/*
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EXAMPLE: IRON WORKS,
INC. Mat$ematical Model
+$e total mont$l/ pro;t
@ (pro;t per unit o% product &) ,
(mont$l/ production o% product &) G
(pro;t per unit o% product >) ,
(mont$l/ production o% product >)
@ p&x&Gp>x>
4e ant to ma,imi9e total mont$l/ pro;t
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EXAMPLE: IRON WORKS, INC.
Mat$ematical Model (continued) +$e total amount o% steel used during mont$l/
production e.uals
(steel re.uired per unit o% product &) ,
(mont$l/ production o% product &) G(steel re.uired per unit o% product >) ,
(mont$l/ production o% product >)
@ a&x&G a>x>
+$is .uantit/ must be less t$an or e.ual to t$eallocated bpounds o% steel
a&x&G a>x> H bDR. NOR KHAIRUSSHIMA
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EXAMPLE: IRON WORKS, INC.
Mat$ematical Model (continued):+$e mont$l/ production level o% product & mustbe greater t$an or e.ual to m
x& m
:+$e mont$l/ production level o% product > mustbe less t$an or e.ual to u
x>H u
: 6oever- t$e production level %or product >cannot be negative
x> '
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EXAMPLE: IRON WORKS,
INC.
Mat$ematical Model Summar/
Ma, p&x&Gp>x>
s*t* a&,&G a>x> H b
x& m
x> H u
x> '
b"ectiveFunction
JSub"ecttoK
Constraints
DR. NOR KHAIRUSSHIMA +'''- a&@ >- a>@ 3- m@ B'- u@A>'-p&@ &''-p>@ >''* #erite t$e model
it$ t$ese speci;c values %or t$euncontrollable inputs*
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Ex!"#$: I%&' W&%(), I'*.
0nser
Substituting- t$e model is
Ma, &''x&G >''x>
s*t* >x&G 3x> H >'''
x& B'
x> H A>'
x> '
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Ex!"#$: I%&' W&%(), I'*.
2uestion
+$e optimal solution to t$e current model isx& @ B'
andx>@ B>B >3* I% t$e product ere engines- e,plain
$/ t$is is not a true optimal solution %or t$e realli%eproblem* 0nser
ne cannot produce and sell >3 o% an engine*+$us t$e problem is %urt$er restricted b/ t$e %act
t$at bot$ ,& and ,> must be integers* (+$e/ couldremain %ractions i% it is assumed t$ese %ractions areor1 in progress to be completed t$e ne,t mont$)*
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THE END