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PRODUCTS PLANNİNG AND PROCESS SELECTİON Prepared by Şevkinaz Gümüşoğlu Prepared by Şevkinaz Gümüşoğlu using different references about POM using different references about POM
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P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Apr 01, 2015

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Page 1: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

PRODUCTS PLANNİNG AND PROCESS SELECTİON

Prepared by Şevkinaz GümüşoğluPrepared by Şevkinaz Gümüşoğlu using different references about POMusing different references about POM

Page 2: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

5-2

Planning new products and geting them to market quickly is the challenge facing manufacturers in industries .

In our changing world today customers demand that a company’s offerings be individualized to meet particular meets, situations and lifestyles.

They want product and services of superior quality available promptly. The firms requirements are innovation, flexibility, improvement, new practical competencies, design and redesign ways. They must orientate themselves to their customers in a new way.

Page 3: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Management must developed and meet the customer’s need by using the available resources and the technological capabilities of the organization.

New-product design is crucial to the survival of most firms. While a few firms experience little product change, most firms must continually revise their products. In fast-changing industries, new-product introduction is a way of life and highly sophisticated approaches have been developed to introduce new product.

Product design is seldom the responsibility of operations functions but operations is greatly affected by new-product introduction. Sometime, new products are constrained by existing operations and technology.

5-3

Page 4: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Therefore, it is extremely important to understand the new product design process and its interactions with operations. Product decisions affect each of the decision making areas of operations. Therefore they should be closely coordinated with operations to ensure the operation is integrated with production design.

There are three strategies for new-product introduction process:

5-4

Page 5: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Market-driven: According to this view, “You should make what you can sell” In this case, new products are determined by the market with little regard to existing technology and operations process. Customer needs are the primary basis for new-product introduction. Customer want products and services of superior quality available promptly. The requirements are for innovation, flexibility, quality based on active listening to customer so as to determine their concerns. Being prepared to deliver on such requirements will require companies to cultivate new practical competencies, to redesign the ways they do their work through business processes and to orient themselves to their customers in a new way. (kano system- voice of costumer)

Technology-driven: This approach would suggest that “ You should sell what you can make” Accordingly, new products should be derived from production technology. This view is dominated by vigorous use of technology and simplicity of operations changes.

Interfunctional view: New-product introduction is interfunctional in nature and requires cooperation among marketing, operations, engineering and other functions Using this approach the new-product design will fall some where between “making what you can sell” and “selling what you can make”.

5-5

Page 6: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

5-6

  The top manager of miraculously successful Sony is

saying; “ Our plan is to lead the public to new product rather than ask them what they want. The public does not know what is possible but we do.” No customer expressed a need for a Walkman sound system, but soon after Sony invented it, every one had to have music with them wherever they most. A similar example is air condition (Wills Carrier invened it and humanbeing had to use it wherever they want).

All enterprises today must use quick-connect electronic interfaces to coordinate product creation resource chains (CAD). Chrysler reduced its product development cycle from over 60 months to 36 month or less in the late 1980 s. Nowaday this cycle is about 12 month in the automotıve industry. For example this year Audio will offer 13 new models automobile to the market.

 

Page 7: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Copyright 2006 John W

iley & S

ons, Inc.

5-7

Chrysler old chairman Le Iacocca as declaring “We got to do cars differently. We got to do modular stuff.”

These approaches is required;New Product idea Product Design Rapid Prototyping Rapid Tooling Usuability Production Design Industrial Design Firms Prototyping companies Standard Communication interfaces, Design Files

of CAD software for Product Creation. Manufacturing companies supported CAM

softwareto produce designed files of CAD

Page 8: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

MAJOR FUNCTİONS OF PRODUCT PLANNİNG

Desingning for the customer; industrial design Reducing Time-to-Market;speed Improving Quality of Design;QFD Product Development:generating new product

ideas Desing Process;linking desing and

manufacturing, design for manufacturability, process selection

Special Considerations in Service Design5-8

Page 9: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

FORM AND FUNCTİONAL DESİGN

Copyright 2006 John W

iley & S

ons, Inc.

5-9

Form Design how product will

look? Functional Design

reliability maintainability usability

Page 10: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

RAPİD PROTOTYPİNG

Build a prototype form design functional design production design

Test prototype Revise design Retest

5-10

Copyright 2006 John W

iley & S

ons, Inc.

Page 11: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

USABİLİTY

Ease of use of a product or service ease of learning ease of use ease of remembering how to use frequency and severity of errors user satisfaction with experience(Simplicity& Compexity&Technology)

5-11

Copyright 2006 John W

iley & S

ons, Inc.

Page 12: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

HTTP://WWW.YOUTUBE.COM/WATCH?V=OFJQM2B1ERE SAPHTTP://WWW.YOUTUBE.COM/WATCH?V=WUGSYYOTLKQ YOUR CAR http://www.youtube.com/watch?v=9pIW62ZEEhEhttp://www.youtube.com/watch?v=DN__D5ixme0mobilephonehttp://www.youtube.com/watch?v=2IMoctL1C2gMercedes-mehmettungahttp://www.youtube.com/watch?v=F5vULbhGQu8Bicycleshttp://www.youtube.com/watch?v=r2PzpiD-Sh0Levitationhttp://www.youtube.com/watch?v=eVJtOO7mS3IFuture phone

5-12

Copyright 2006 John W

iley & S

ons, Inc.

Page 13: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

PRODUCTİON DESİGN Simplification

reducing number of parts, assemblies, or options in a product

Standardizationusing commonly available and

interchangeable parts Modularity

combining standardized building blocks, or modules, to create unique finished products

5-13

Copyright 2006 John W

iley & S

ons, Inc.

Page 14: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

5-14

Copyright 2006 John W

iley & S

ons, Inc.

Design SimplificationDesign Simplification

(b) Revised design(b) Revised design

One-piece base & One-piece base & elimination of elimination of fastenersfasteners

(c) Final design(c) Final design

Design for Design for push-and-snap push-and-snap assemblyassembly

(a) Original design(a) Original design

Assembly using Assembly using common fastenerscommon fasteners

Page 15: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

MEASURE DESİGN QUALİTY

Copyright 2006 John W

iley & S

ons, Inc.

5-15

% of revenue from new products or services

% of products capturing 50% or more of market

% of process initiatives yielding a 50% or more improvement in effectiveness

% of suppliers engaged in collaborative design

% of parts that can be recycled

% of parts used in multiple products

% of parts with no engineering change orders

Average number of components per product

Things gone wrong (TGW)

Page 16: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

QUALİTY FUNCTİON DEPLOYMENT (QFD)

Translates voice of customer into technical design requirements

Displays requirements in matrix diagramsfirst matrix called “house of quality”series of connected houses

5-16

Copyright 2006 John W

iley & S

ons, Inc.

Page 17: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

HTTP://WWW.GOOGLE.COM.TR/İMGRES?Q=QUALİTY+FUNCTİON+DEPLOYMENT&START=116&HL=TR&SA=X&BİW=1280&BİH=654&TBM=İSCH&PRMD=İMVNSB&TBNİD=6APCQNQCUJ9I_M:&İMGREFURL=HTTP://WWW.OSAKA-GU.AC.JP/PHP/NAKAGAWA/TRIZ/ETRIZ/EPAPERS/E2010PAPERS/EKATAGİRİTRIZSYMP2009/EKATAGİRİ-TRIZSYMP2009-100507.HTML&DOCİD=5JT_PHHTBHDNXM&İMGURL=HTTP://WWW.OSAKA-GU.AC.JP/PHP/NAKAGAWA/TRIZ/ETRIZ/EPAPERS/E2010PAPERS/EKATAGİRİTRIZSYMP2009/EFİGKATAGİRİ-5QFD.GIF&W=370&H=279&Eİ=SUVZUN6RC6NT4QSXY4GOCA&ZOOM=1&İACT=HC&VPX=883&VPY=220&DUR=1094&HOVH=195&HOVW=259&TX=101&TY=86&SİG=105109972529429050487&PAGE=6&TBNH=151&TBNW=200&NDSP=24&VED=1T:429,R:4,S:116,İ:95

5-17

Copyright 2006 John W

iley & S

ons, Inc.

Page 18: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

"A GROUP OF COURAGEOUS PEOPLE WORKİNG İN HARMONY PURSUİNG THE FİNEST DETAİL TO UNLOCK THE ORGANİZATİON AND ROLL OUT PRODUCTS THAT THE MULTİTUDES İN THE MARKETPLACE WİLL VALUE." GLENN MAZUR

5-18

Copyright 2006 John W

iley & S

ons, Inc.

Page 19: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

VOİCE OF THE CUSTOMERTHROUGH EACH STAGE OF THE PRODUCT DEVELOPMENT AND PRODUCTİON PROCESS, THAT İS, THROUGH THE PRODUCT REALİZATİON CYCLE.THESE REQUİREMENTS ARE THE COLLECTİON OF CUSTOMER NEEDS, İNCLUDİNG ALL SATİSFİERS, EXCİTERS/DELİGHTERS, AND DİSSATİSFİERS.

5-19

Copyright 2006 John W

iley & S

ons, Inc.

Page 20: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

What Does QFD Do?

Better Designs in Half the Time!

QFD Is a Productivity EnhancerQFD Is a Productivity Enhancer

CUSTOMERCONCEPT

Plan Design Redesign Manufacture

Plan Design RedesignManufacture Benefits

“Traditional Timeline”

Page 21: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

QF

D

Flo

wd

ow

n Customer Wants

Technical Requirements

Part Characteristics

Manufacturing Process

Production Requirements

ManufacturingEnvironment

ManufacturingEnvironment

Customer Wants

Product Functionality

System Characteristics

Design Alternatives

SoftwareEnvironment

SoftwareEnvironment

Customer Wants

Service Requirements

Service Processes

Process Controls

ServiceEnvironment

ServiceEnvironment

Flowdown Relates The

Houses To Each Other

Flowdown Relates The

Houses To Each Other

Levels

Of

Gra

nu

lari

tyLe

vels

Of

Gra

nu

lari

ty

Page 22: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

1. Identify Customer Attributes These are product or service requirements IN THE CUSTOMER’S

TERMS. Market Research;

Surveys; Focus Groups.

“What does the customer expect from the product?” “Why does the customer buy the product?”

Salespeople and Technicians can be important sources of information – both in terms of these two questions and in terms of

product failure and repair. OFTEN THESE ARE EXPANDED INTO Secondary and Tertiary

Needs / Requirements.

Page 23: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

The Four Houses of Quality

The Cascading Voice of the CustomerNOTES:

“Design Attributes” are also called “Functional Requirements”

“Component Attributes” are also called “Part Characteristics”

“Process Operations” are also called “Manufacturing Processes” and the “Quality Control Plan” refers to

“Key Process Variables.

WH

ATS

HOWS

X

YCritical to Quality

Characteristics(CTQs)

Key ManufacturingProcesses

Key Process Variables

Page 24: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

A SERİES OF CONNECTED QFD HOUSES

5-24

Copyright 2006 John W

iley & S

ons, Inc.C

ust

om

er

req

uir

emen

ts

House House of of

qualityquality

Product characteristics

A-1

Pro

du

ct

char

acte

rist

ics

Parts Parts deploymentdeployment

Part characteristics

A-2

Par

t ch

arac

teri

stic

s

Process Process planningplanning

Process characteristics

A-3

Pro

cess

ch

arac

teri

stic

s

Operating Operating requirementsrequirements

Operations

A-4

Page 25: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

25

Page 26: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

HİSTORY OF QFD Dr. Mizuno, Prof. Emeritus Mitsubishi Heavy Industries

Kobe Shipyards, 1972 Toyota Minivans (1977 Base)

1979 - 20% Reduction In Start-Up Costs 1982 - 38% 1984 - 61%

Dr. Clausing, Xerox, 1984 Any Manufacturing Or Service Industry

Page 27: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

HOUSE OF QUALİTY

5-27

Copyright 2006 John W

iley & S

ons, Inc.

Trade-off matrix

Design characteristics

Customer requirements

Target values

Relationship matrix

Competitive assessment

Imp

ort

ance

11 22

33

44

55

66

Page 28: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

5-28

Copyright 2006 John W

iley & S

ons, Inc.

SS = SilverstoneMG = MirorrglideT = Titanium

COMPLETEDHOUSE OF QUALİTY(TEA POT EXEMPLA)

Page 29: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

BENEFİTS OF QFD

Promotes better understanding of customer demands

Promotes better understanding of design interactions

Involves manufacturing in design process Breaks down barriers between functions and

departments Provides documentation of design process

5-29

Copyright 2006 John W

iley & S

ons, Inc.

Page 30: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Product Selection

Product is the structuring of competent parts or activities so that as a unit they can provide a specified value. Product specification is typically an engineering function. In service industries requirement. Design, production an marketing costs are reduced by standardizing and simplifying the product. After prototype units one designed and produced, the products are further analyzed and tested to see how well the quality, performance and costs conform to the design objectives. Simplification may take place to reduce unnecessary variety in the product line by discussing the number and variety of product produced.

Product selection are influenced by;1.The firm’s resource and technology base2.The market environment3.The firm’s motivation to use capabilities to meet the need of the market place.

  5-30

Copyright 2006 John W

iley & S

ons, Inc.

Page 31: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Product-Mix Decision

 Within the product-line grouping, decision must be made to select which mix of products to in view of costs, capacity and other limitation. Linear programming is a useful technique for assisting in product-mix decisions.It applies to situations where there firm has a demand for whatever quantity of two or more products it can produce. Another typical application is for the selection of the least costly mix of raw materials .

Linear ProgrammingLP is a mathematical technique for maximizing or minimizing a linear objective function, subject to linear constraints. It has wide variety of applications. It assumes that cost and revenue values are known (certainty) profits from various activities are additive, resource quantity for various activities are additive (additivity) it doesn’t allow negative production values (non-negativity)

It has widespread application such as mix product decision, capacity planning capital budgeting, line balancing, agregate planning and scheduling.

5-31

Page 32: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Objective (Goal)Objective (Goal) To maximize total profit

Decision VariablesDecision Variables What do we have to decide on? What are the variables that we can control ?

We have to decide on amounts of products to be produced.

5-32

Copyright 2006 John W

iley & S

ons, Inc.produced be to1- Profnumberthe:x1 oduct

produced be to2-roductofnumberthe:x2 P

Page 33: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

1-Graphical solution method: For the simple linear problems, the easiest procedure is the graphical method.Example1. A chemical firm produces automobile cleaner X and polisher Y and realizes $10 profit on each box of X and $30 on Y. Both products require processing through the same machines A and B, but X requires 4 hours in A 8 in B, where as Y requires 6 hours in A and 4 in B. During the forthcoming week machines A and B have 12 and 16 hours of available capacity, respectively Assuming that demands exists for both products, how many boxes of each should be produces to realize the optimal profit P?

First step: Formulate the problem in ten of linear objective function and linear const. X: No.of cleaner X to be produced.Y: No. of polisher Y to be produced.Objective function is:Maximize P = $10 x + $30yThe constraints are:

4x + 6y 128x + 4y 16Also x and y 0

 in two dimensions.

We begin by constructing a graph that represents the LP

 

5-33

.

Page 34: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Second step: Variables are X and Y. The constraint.Are plotted as equalities. We use a ruler to make a heavy horizontal line for the X axis and a heavy vertical line for the Y axis.To graph:A: if x=0 y=2

if y=0 x=3B: ifx=0 y=4

ify=0 x=2 

Note that the graph established a feasible region bounded by the explicit capacity const of A and B and the implicit constraints that production of x>0 and production y>0      

5-34

Page 35: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Third step: The slope of the objective function.P =10x+30y

 The standard slop intercept form of a linear equation is

Y= mX + bwhere m is the slope of the line 8that is, change in Y pen unit change in x) and b is there Y intercept.

Expressing our objectives in this form , we have.30 y = -10x +PY= (-1/3) x + P/30

 The slope = -1/3; that is, the line decreases one unit in Y for every three positive units of X. This is plotted at any convenient spot within the feasible solution region. We could plot a similar line for any other value of Z. These profit lines are parallel.

Fourth step: The slope of the objective function is moved away from the origin until restrained by the furthermost intersection of A and the implicit constraint x>0. The optimal solution will always be at a corner in the feasible region. This corner will be the last point in the feasible solution region

5-35

Page 36: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Fifth step: The arrow point to the solution, within is determined by the x and y coordinates at time co. In this example x=0 y=2 P = $10 (0) + $30(2) = $60

4(0)+6(2) 12 12=128(0)+4(2) l6 816

 In this example the firm should produce no cleaner and two boxes of polisher for a profit $60. We can see from the graph, the constraint imposed by machine B (8x+4y <16) has no effect, for it is the 12 hours of machine A (4x+6y<12) that are constraining production of the more profitable polisher. The graph also reveals that profit would continue to increase if more hours could be made available on machine A up to the point of doubling output (to x=0 end y=4) At this point, the time available from machine B would become constraining

  5-36

Page 37: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Ch 11 Supp - 4© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

LİNEAR PROGRAMMİNG:EXAMPLE 2 MODEL FORMULATİON

Resource requirementsLabor Clay Revenue

Product(hr/unit)(lb/unit)($/unit)Bowl 1 4 40Mug 2 3 50

There are 40 hours of labor and 120 pounds of clay available each dayDecision variables

x1 = number of bowls to produce

x2 = number of mugs to produce

Page 38: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Ch 11 Supp - 5© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

OBJECTİVE FUNCTİON & CONSTRAİNTS

Maximize Z = $40 x1 + 50 x2

Subject to x1 + 2 x2 40 hr (labor constraint)

4 x1 + 3 x2 120 lb (clay constraint)

x1 , x2 0

Solution is x1 = 24 bowls

x2 = 8 mugs

Revenue = $1,360

Page 39: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Ch 11 Supp - 6© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

GRAPHİCAL SOLUTİON METHOD

1. Plot model constraint on a set of coordinates in a plane

2. Identify the feasible solution space on the graph where all constraints are satisfied simultaneously

3. Plot objective function to find the point on boundary of this space that maximizes (or minimizes) value of objective function

Page 40: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Ch 11 Supp - 7© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

GRAPH OF POTTERY PROBLEM

20 30 40 50 6010

20

30

40

50

60

10

x1

x2

4 x1 + 3 x2 120 lb

x1 + 2 x2 40 hr

Area common toboth constraints

Page 41: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Ch 11 Supp - 8© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

PLOT OBJECTİVE FUNCTİON

$800 = 40x1 + 50 x2

Optimal point

20 30 4010 x1

20

30

40

10

x2

B.

Page 42: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Ch 11 Supp - 9© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

COMPUTİNG OPTİMAL VALUES

A

.

x1 + 2 x2 =40

4 x1 + 3 x2 =120

4 x1 + 8 x2 =160

-4 x1 - 3 x2 =120

5 x2 = 40

x2 = 8

x1 + 2 (8) =40

x1 =24

Z = $50(24) + $50(8)

Z = $1,360

8B

C

x1 + 2 x2 =40

4 x1 + 3 x2 =120

20 30 4010 x1

20

30

40

10

x2

Page 43: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Ch 11 Supp - 10© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

EXTREME CORNER POİNTS

A

.BC

x1 = 0 bowls

x2 =20 mugs

Z = $1,000

x1 = 224 bowls

x2 =8 mugs

Z = $1,360x1 = 30 bowls

x2 =0 mugs

Z = $1,200

20 30 4010 x1

20

30

40

10

x2

Page 44: P RODUCTS P LANNING AND P ROCESS S ELECTION Beni Asllani University of Tennessee at Chattanooga Prepared by Şevkinaz Gümüşoğlu using different references.

Ch 11 Supp - 11© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

OBJECTİVE FUNCTİON DETERMİNES OPTİMAL SOLUTİON

A

B

C

Optimal point:

x1 = 30 bowls

x2 =0 mugs

Z = $2,100

20 30 4010 x1

20

30

40

10

x2

4 x1 + 3 x2 120 lb

x1 + 2 x2 40 hr

Z = 70 x1 + 20 x2

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GRAPHICAL SOLUTION METHOD EXAMPLE 3: A company is already producing some products.

However there are some idle capacities of the facilities. There are three plants. The idle capacities in terms of labor hours per week are as follows

The management wants to utilize the unused capacities by producing two new products.

Product-1: An 8 foot glass door with aliminum framing

Product-2: A 4x6 double hung window with wood-framing

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Copyright 2006 John W

iley & S

ons, Inc.

Plant Idle Capacity(hours/week) Plant -1 4Plant -2 12Plant -3 18

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The products are produced in batches Plant-1 produces aliminum frames Plant-2 produces wood frames Plant-3 produces glass and assembles the

products The unit profits per products are 3000

and 5000 respectively. The labor hours required to produce

different parts of the products at different plants are as follows :

5-46

Copyright 2006 John W

iley & S

ons, Inc.

PlantPlant

Production Time per Batch Production Time per Batch (hours)(hours)

Product -1Product -1 Product-2Product-2

Plant -1Plant -1 11 00

Plant-2Plant-2 00 22

Plant-3Plant-3 33 22

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5-47

Copyright 2006 John W

iley & S

ons, Inc.

ConstraintsConstraints

Resources are limited

4x1

122x2

18x23x 21

4 hours available at Plant -1

12 hours available at Plant -2

18 hours available at Plant-3

Objective Function Objective Function

21 x5 x3Z Total profit to be maximized

0x,0x 21

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x1

x2GRAPHİCAL SOLUTİON

0xand0for x spaceSolution 21

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x1

x2

4

41 x

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x1

x2

4

6

122 2 x

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x1

x2

4

6

1823 21 xx

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x1

x2

4

6

1053 21 xxZ

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x1

x2

4

6

1053 21 xxZ

2053 21 xxZ

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x1

x2

4

6

3053 21 xxZ

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x1

x2

4

6

3653 21 xxZ

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EXAMPLE :4 The Primo Insurance Company is introducing two new

product lines: special risk insurance and mortgages. The expected profit is $5 per unit on special risk insurance and $2 per unit on mortgages. Management wishes to establish sales quotas for the new product lines to maximize total expected profit. The work requirements are as follows:

(a) Formulate a linear programming model for this problem.

(b) Use the graphical method to solve this model.5-56

Copyright 2006 John W

iley & S

ons, Inc.

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X1= no. of special risk insurance X2= no. of mortgage. ZMax = 5X1+2X2

s.t. 3X1+2X2<=2400X2<=8002X1<=1200X1,X2>=0

5-57

Copyright 2006 John W

iley & S

ons, Inc.

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5-58

Copyright 2006 John W

iley & S

ons, Inc.