Lecture 3_introduction to Management

7/25/2019 Lecture 3_introduction to Management

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Lecture 3

Introduction to

ManagementScience

Chapter 1 in the textbook

DR. NOR KHAIRUSSHIMA 1


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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

DR. NOR KHAIRUSSHIMA #


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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

DR. NOR KHAIRUSSHIMA +


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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


/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


AND DECISION MAKING



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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

DR. NOR KHAIRUSSHIMA :


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1. Qan!i!a!ive Anal"sis Process

Model Develo$men!

Da!a Pre$ara!ion

Model Sol!ion

Re$or! ;enera!ion

DR. NOR KHAIRUSSHIMA


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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!

DR. NOR KHAIRUSSHIMA 1#


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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

DR. NOR KHAIRUSSHIMA 1+


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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*

DR. NOR KHAIRUSSHIMA 1:


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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


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/*

DR. NOR KHAIRUSSHIMA +2


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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

Ma, p&x&Gp>x>DR. NOR KHAIRUSSHIMA +7


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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

+9


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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> '

DR. NOR KHAIRUSSHIMA+:


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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*

DR. NOR KHAIRUSSHIMA 0>


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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$e ne,t mont$)*

DR. NOR KHAIRUSSHIMA 0#


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Lecture 3_introduction to Management

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