LECTURE 1 of Value engineering and operations

7/17/2019 LECTURE 1 of Value engineering and operations

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Challenge the future

DelftUniversity ofTechnology

Value Engineering and OperationsOptimization (AE4441)


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2

Overview of the course

Wednesdays and Thursdays: Lectures/studio classroom

sessions on optimization methods!ntroduction to "perations #esearch$ %y &rederic' ()

*illier and +erald ,) Lie%erman- ninth edition

&inished .ith .ritten eam in 0rst period 1.ee' 34- notyet scheduled5) 6"T open3%oo')

7eriod

7eriod 2

T.o assignments &ocus on value engineering approach

(olve a value engineering pro%lem .ith optimization methods

Lectures on value engineering

!ntroduction


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8

&inal grade:

9am holds for 4 ; of the 0nal grade

9ach of the assignments holds for 24 ; of the 0nal grade

< grade = >)> for each of the elements is re?uired to pass the

course

+rades are valid for one year only

Overview of the course, continued

!ntroduction


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@

How to buy the book

The %oo' can %e %ought via the A(A

Use needs to %e made of the ne. A(A .e%shop) Bou can0nd this .e%shop under the oo' section at the .e%site 1

...)vsv)tudelft)nl5) Bou can pay via iDeal) The %oo' .ill

%e delivered at the desired address)

!ntroduction
http://www.vsv.tudelft.nl/http://www.vsv.tudelft.nl/


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>

Overview of todays lecture

stpart Chapters -2-8)38)@

2ndpart


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Chapter 1: Introduction

The 0eld of "perations #esearch 1"#5 started in World War !!

This research on operations.as after.ards introduced in otherorganizations

"perations #esearch aims at determining optimal .ays to conduct

activities in an organization

!ntroduction


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Chapter 2: Overview of the OperationsResearch Modeling Approach

) De0ning the pro%lem and gathering data

2) Construct a mathematical model to represent the pro%lem

ndecision varia%les: the un'no.ns

"%Eective function: measure of performance Constraints: restrictions on decision varia%les

7arameters: constraint and o%Eective function constants

8) Develop a computer3%ased procedure for deriving solutions

to the pro%lem from the model

@) Test the model and re0ne if needed 1model validation5

>) 7repare for ongoing application of the model 1decisionsupport system5

) !mplement

Typical phases in an "# study:

6ote: these steps also hold for other0elds) !t holds for optimization approachesin general)

!ntroduction


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F

Chapter 2: Overview of the OperationsResearch Modeling Approach

) De0ning the pro%lem and gathering data

2) Construct a mathematical model to represent the pro%lem

ndecision varia%les: the un'no.ns

"%Eective function: measure of performance Constraints: restrictions on decision varia%les

7arameters: constraint and o%Eective function constants

8) Develop a computer3%ased procedure for deriving solutions

to the pro%lem from the model

@) Test the model and re0ne if needed 1model validation5

>) 7repare for ongoing application of the model 1decisionsupport system5

) !mplement

Typical phases in an "# study:

6ote: these steps also hold for other0elds) !t holds for optimization approachesin general)

!ntroduction


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G

ExampleResource optimization for operations

and maintenance of offshore wind farms5 7ro%lem: Large3scale roll3out of oHshore .ind energy

re?uires that its cost of electricity should %e reduced)

7otential for cost reduction in the 0eld of operations and

maintenance)

25The largest cost drivers are the vessels and technicians)

The follo.ing decision varia%les are identi0ed:

!ntroduction


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4

Iaimize

.here the availa%ility of the .ind3farm

days of preventive maintenance

costs 1salaries and e?uipment5

such that

minimum technician team size on a ("A

minimum technician team size on a CTA

- and are all integer values

)()()( DP CfCfAfY =

),,,,,( 654321 xxxxxxfA =

),,( 531 xxxfCP =

),,,,,(654321

xxxxxxfCD

=

%95A

qPMPM Re=

11 x

12 x

13 x

14

x 5x6x

654321 ,,,,, xxxxxx

#esulting mathematical model:

!ntroduction


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85 #esult o%tained %y computer3%ased procedure for

deriving solutions to the pro%lem from the model:

@5 Testing on eisting oHshore .indmill par's>5 Decision support tools for ongoing application 1daily

operations and ne. oHshore .indmill farms5

5 9nsure use of the tools

!ntroduction


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2

Linear ProgrammingIntroduction


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8

Linear ProgrammingIntroduction, continued

Iost common application of linear programming:

*o. to allocate limited resources among competing activities in

a %est possi%le .ay

Chapter 8

Constraints Decision varia%les

"%Eective

function


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An example problemDefine the problem

The WB6D"# +L


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An example problemDefine the problem

ecause of declining earnings- it has %een decided to revamp the companyKs

product line) Unpro0ta%le products are %eing discontinued) This releases

production capacity to launch t.o ne. products having large sales potential

7roduct : < glass door .ith aluminum framing

7roduct 2: < dou%le3hung .ood3framed .indo.

7roduct re?uires some of the production capacity in 7lants and 8- %ut none in

7lant 2) 7roduct 2 needs only 7lants 2 and 8

The mar'eting division has concluded that the company could sell as much of

either product as could %e produced %y these plants) *o.ever- %ecause %oth

products .ould %e competing for the same production capacity in 7lant 8- it is not

clear .hich mi of the t.o products .ould %e most pro0ta%le)

Chapter 8


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An example problemGather data

&irst values for the parameters needed

Chapter 8

Plant

Production time perbatch (Hours)

Product

1 2

Production timeavailable per week

(Hours)

1

2

3

1 0

0 2

3 2

4

12

18

Proft per batch 3000 !000

6um%er of hours of production time availa%le per .ee' in each plant for the ne. products

6um%er of hours of production time used in each plant for producing the ne. products

7ro0t for each of the ne. products


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Decision varia%les:

x: num%er of %atches of product produced per .ee'

x2: num%er of %atches of product 2 produced per .ee'

The o%Eective function

Z 8x M >x2 1total pro0t per .ee' in thousands of dollars5

The aim is to maimizeZ

Constraints

x @

2x22

8xM 2x2F

and

x4

x24

Chapter 8

An example problemIts linear programming model

6um%er of hours of production time availa%le per .ee' in plant

6um%er of hours of production time availa%le per .ee' in plant 2

6um%er of hours of production time availa%le per .ee' in plant 8


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F

Iaimize Z 8x M >x2

(u%Eect to

x @2x228xM 2x2F

x4

x24

Chapter 8

An example problemIts linear programming model


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An example problemDerive solutions

IaimizeZ 8x M >x2

x@

(u%Eectto

2x22

8xM 2x2F

Chapter 8


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An example problemFind optimal solution

Chapter 8

Z 8xM

>x2

&easi%leregion

Z 24

Z 84Z 8


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2

&or this situation a graphical approach suJces) The optimal solution is:

x 2x2

Z 8

- i)e) maimal pro0t .ithin the constraints is o%tained for a mi of 2

%atches of product per .ee'- and %atches of product 2 per .ee')

The resulting total pro0t is N8444 per .ee'

An example problemOptimal solution

7roduct : glass door .ith aluminum frami7roduct 2: Dou%le3hung .ood3framed .ind

Chapter 8


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Iaimize Z cxM c2x2M O) M cnxn

(u%Eect to

axM a2x2M O M anxnb

a2xM a22x2M O M a2nxnb2

amxM am2x2M O M amnxnbm

and

x4-x24- O-xn4

Chapter 8

Linear ProgrammingThe mathematical model, its general form

&unctionalconstraints

6onnegativity

constraints

6ote: other forms also possi%le

"%Eective function


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28Chapter 8

Linear ProgrammingThe mathematical model, its solutions

&easi%le solution:


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2@Chapter 8

Linear ProgrammingThe mathematical model, its solutions

The importance of C7& solutions:


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2>Chapter 8

Linear ProgrammingThe assumptions, proportionality

7roportionality:

The contri%ution of each activityjto the value of theo%Eective functionZis proportional to the level of activityxE1cExE5

andThe contri%ution of activityjto the left3hand3side of each

functional constraint is proportional to the level ofactivityxE1aiExE5

These situations

prevent a1straightfor.ard5 linearprogramming approachto solve for optimalsolutions for thedecision varia%les)

7roportionality violated


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2Chapter 8

Linear ProgrammingThe assumptions, additivity

x23xx2

Z 8x M >x2Mxx2

&unctions that do not satisfy this re?uirement- e)g):


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2Chapter 8

Linear ProgrammingThe assumptions, divisibility

Divisi%ility:

Decision varia%les in a linear programming model areallo.ed to have any values- including non3integer values-that satisfy the functional and non3negativity constraints


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2FChapter 8

Summary

7ro%lems dealing .ith assigning scarce resources to aseries of activities in an optimal .ay- can often %e solvedthrough linear programming

*ereto a mathematical model is esta%lishedThe o%Eective function rePects the measure of

performanceThe constraints rePect the limited resources

< search needs to %e carried to 0nd those levels ofactivities that maimize the o%Eective function and still

are .ithin the constraints

Chapter 8 considers a graphical approach) This is notfeasi%le .hen more than three levels of activity need to%e determined


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2GChapter 8

Summary, continued

The feasi%le region is the collection of all possi%lesolutions 1levels of activity5 that satisfy all constraints

Corner3point feasi%le 1C7&5 solutions are located at acorner of the feasi%le region

These C7& solutions are of interest %ecause the %estC7& solution must %e an optimal solution) !f the pro%lemhas multiple optimal solutions at least t.o must %e a C7&solution

The assumption of a linear o%Eective function su%Eect tolinear constraints is often allo.ed for real life pro%lems

LECTURE 1 of Value engineering and operations

Documents

value engineering pro

model validation5

mathematical model

ntroduction7172019 lecture

lem ndecision varia

ctive function constants8

nal grade grade

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