2 - Ashby Method - · PDF file2 - Ashby Method Outline • Processes ... *Using the CES...

2.8 - Materials processing and selection

2 - Ashby Method

Outline

• Processes classification and their attributes

• Steps of selection

• Material-process-shape relations

• Processes selection: Screening and ranking

• Cost modelling: Resource-based approach

• Case study

Resources:

• M. F. Ashby, “Materials Selection in Mechanical Design” Butterworth Heinemann, 1999

Chapter 11

• The Cambridge Material Selector (CES) software -- Granta Design, Cambridge

(www.grantadesign.com)

Processes selection

• Process selection depends on material and shape

• Process attributes are used as criteria for selection

Processes classification

Primary processesCreate

shapes

Secondary processesModify

shapes

Processes classification: Primary processes

CASTING

In casting, a liquid is poured into a mould where it solidifies by cooling (metals) or by reaction(thermosets).

Casting is distinguished from moulding, by the low viscosity ofthe liquid: it fills the mould by flow under its own weight (gravity casting) or under a modest pressure (centrifugal casting and pressure die casting).


MOULDING

Moulding is casting, adapted to materials which are very viscous when molten, particularlythermoplastics and glasses.

The hot, viscous fluid is pressed or injected into a die under considerable pressure, where it cools and solidifies.


DEFORMATION PROCESSING

Deformation processing can be hot, warm or cold. The high temperature lowers the yield strength and allows simultaneous recrystallization, both of which lower the forming pressures.

Extrusion, hot forging and hot rolling have much in common with moulding, though the material is a true solid not a viscous liquid.


POWDER METHODS

Powder methods create the shape by pressing and then sintering fine particles of the material.

The powder can be cold-pressed and then sintered (heated at up to 0.8Tm to give bonding); it can be pressed in a heated die (‘die pressing’); or, contained in a thin preform, it can be heated undera hydrostatic pressure (‘hot isostatic pressing’).

Metals and ceramics which are too high-melting to cast and too strong to deform can be made (by chemical methods) into powders and then shaped in this way.


SPECIAL METHODS

Special methods include techniques which allow a shape to be built up atom-by-atom, as inelectro-forming and chemical and physical vapour deposition.

They include, too, various sprayforming techniques in which the material, melted by direct heating, is sprayed onto a former -- processes which lend themselves to the low-number production of small parts, made from difficult materials.

Processes classification: Secondary processes

MACHINING

Almost all engineering components, whether made of metal, polymer or ceramic,are subjected to some kind of machining or grinding (a sort of micro-machining) during manufacture.To make this possible they should be designed to keep the symmetry high: symmetric shapes need fewer operations.

Metals differ greatly in their machinability: ease of formation, ability to give a smooth surface, and to give economical tool life.

Processes classification: Other processes

JOINING

Joining is made possible by a number of techniques.

Bolting and riveting, welding, brazing and soldering are commonly used for metals.

Polymers are joined by snap-fasteners, and by thermal bonding.

Ceramics can be diffusion-bonded to themselves, to glasses and to metals.

Improved adhesives give new ways of bonding all classesof materials.

Processes classification: Other processes

FINISHING

Finishing describes treatments applied to the surface of the component or assembly.

They include polishing, plating, anodizing and painting, they aim to improve surface smoothness, protect against corrosion, oxidation and wear, and to enhance appearance.

Plating and painting are both made easier by a simple part shape with largely convex surfaces.

HEAT TREATMENT

Heat treatment is a necessary part of the processing of many materials.

Age-hardening alloys of aluminium, titanium and nickel derive their strength from a precipitate produced by a controlled heat treatment.

The hardness and toughness of steels is controlled in a similar way: by quenching from the ‘austenitizing’ temperature (about 800°C) and tempering.

Data organisation: Processes

Family

Joining

Shaping

Surfacing

Class

Casting

Deformation

Moulding

Composite

Powder

Machining

Rapid prototyping

Member

Compression

Rotation

Injection

RTM

Blow

Attributes

A process record

Material

Shape

Size Range

Min. section

Tolerance

Roughness

Economic batch

Supporting information

-- specific

-- general

Material

Shape

Size Range

Min. section

Tolerance

Roughness

Economic batch


-- specific

-- general

Structured

information

Unstructured

information

Difficult !

Kingdom

Processes

Structured data for Injection Moulding

INJECTION MOULDING of thermoplastics is the equivalent of pressure die casting of metals. Molten polymer is injected under high pressure into a cold steel mould. The polymer solidifies under pressure

and the moulding is then ejected.

Injection moulding (Thermoplastics)

Process CharacteristicsDiscrete TruePrototyping False

ShapeCircular Prism True

Non-circular Prism True

Solid 3-D TrueHollow 3-D True

Physical AttributesMass range 0.01- 25 kg

Roughness 0.2 - 1.6 µm

Section thickness 0.4 - 6.3 mmTolerance 0.1 - 1 mm

Economic AttributesEconomic batch size 1e+004 - 1e+006

Relative tooling cost high

Relative equipment cost high

+ links to materials

Unstructured data for Injection Moulding

Design guidelines. Injection moulding is the best way to mass-produce small, precise, plastic parts with complex shapes. The surface finish is good; texture and pattern can be moulded in, and fine detail reproduces well. The

only finishing operation is the removal of the sprue.

The economics. Capital cost are medium to high; tooling costs are high, making injection moulding economic only for large batch-sizes (typically 5000 to 1 million). Production rate can be high particularly for small mouldings. Multi-

cavity moulds are often used. The process is used almost exclusively for large volume production. Prototype mouldings can be made using cheaper single cavity moulds of cheaper materials. Quality can be high but may be traded off against production rate. Process may also be used with thermosets and rubbers.

Typical uses. The applications, of great variety, include: housings, containers, covers, knobs, tool handles,

plumbing fittings, lenses, etc.

The environment. Thermoplastic sprues can be recycled. Extraction may be required for volatile fumes. Significant dust exposures may occur in the formulation of the resins. Thermostatic controller malfunctions can be

extremely hazardous.

The process. Most small, complex plastic parts you pick

up – children’s toys, CD cases, telephones – are injection moulded. Injection moulding of thermoplastics is the equivalent of pressure die casting of metals. Molten

polymer is injected under high pressure into a cold steel mould. The polymer solidifies under pressure and the

moulding is then ejected.

Various types of injection moulding machines exist, but the most common in use today is the reciprocating screw machine, shown schematically here. Polymer granules

are fed into a spiral press like a heated meat-mincer where they mix and soften to a putty-like goo that can be forced

through one or more feed-channels (“sprues”) into the die.

Heater Screw

Granular PolymerMould

Nozzle

Cylinder

N o.8-CMYK-5/01

*Using the CES EduPack Level 2 DB

Steps of selection: Materials

Screening, using constraintseliminate materials which can’t to the job

Ranking, using objectivesfind materials which do the job best

All materials

Subset of materials

Structured

data

Further Information :search “family history” of candidates

Shortlist of candidates

Unstructureddata

Steps of selection: Processes

Screening, using constraintseliminate processes which can’t to the job

Ranking, using cost indicesfind processes which do the job economically

All processes

Subset of processes

Structured

data

Further Information :search “family history” of candidates

Shortlist of candidates

Unstructureddata

Ranking using cost indices is an efficient criterion for first selection of processes.

Screening using constraints derived from requirements: material class, shape class, process attributes.

Steps of selection: Processes

Step 2 Screening: eliminate processes that cannot do the job

Step 3 Ranking: find the processes that do the job most cheaply

Step 4 Supporting information: explore pedigrees of top-ranked candidates

Step 1 Translation: express design requirements as constraints & objectives

� Process selection has the same 4 basic steps

Because there are thousands of variants of processes,

supporting information plays a particularly important role

Process selection has the same 4 basic steps

Step 1: Translate design requirements

From which we obtain …

• Screening criteria expressed as numerical limits on process attribute-values

Or expressed as requirements for material, shape, ….

• Ranking criteria based on indices that characterise

the economic performance

Design concept

Analyse: Function What must the process do? (Shape? Joint? Finish?)

Objective(s) What is to be maximised or minimised? (Cost? Time? Quality?)

Constraints What material, shape, size, tolerance, etc. must it treat or provide?

Free variables Which variables are free? (Choice of process? Process chain options?)

Step 1: Translate design requirements

Example: casing for a road-pressure sensor

Function Casing for road-pressure sensor

Constraints Material: Al alloy

Shape: non-circular prismaticMinimum section: 2 0.025 mm

Objectives Minimise cost

Free variable Choice of process

The sensor lies across the road, covered by a rubber mat. Vehicle pressure deflects

top face, changing capacitance between topface and copper conducting strip.

±

Shaping (primary process)

Step 2: Screening by material, process and shape relations

MATERIALS

SHAPES

PROCESSES

• Ceramics• Glasses• Polymers

• Metals• Elastomers• Composites• Natural materials

• Axisymmetric• Prismatic• Flat sheet

• Dished sheet• 3-D solid• 3-D hollow

• Deformation• Moulding• Powder methods

• Casting• Machining• Composite forming• Molecular methods



Some processes can make only simple shapes, others, complex shapes.

� Wire drawing, extrusion, rolling, shape rolling:

prismatic shapes

All shapes

Prismatic Sheet 3-D

Circular Non-circular Flat Dished Solid Hollow

� Casting, molding, powder methods:

3-D shapes

� Stamping, folding, spinning, deep drawing:

sheet shapes



Step 2: Screening by processes attributes

Step 3: Ranking by economic criteria

The influence of many of the inputs to the cost of a process are captured by a single attribute: the economic batch size.

The easy way to introduce economy into the selection is to rank candidate processes by economic batch sizeand retain those which are economic in the range required.

Step 3: Ranking by economic criteria

The economic batch size is commonly cited for processes.

A process with an economic batch

size with the range B1 - B2 is one which is found by experience to be competitive in cost whenthe output lies in that range.

Example: Process for a spark-plug insulator

• Material class Alumina

• Shape class 3-D, hollow

• Mass 0.05 kg

• Min. section 3 mm

• Tolerance < 0.5 mm

• Roughness < 100 µµµµm

• Batch size >1,000,000

Constraints

Specification

Function Insulator

Free

variables Choice of process

Insulator

Bodyshell

Central

electrode

Objective Minimise cost


Tree stage: Select CERAMIC (or Alumina)

Rank: bar chart for ECONOMIC BATCH SIZE.

Limit stage: Physical attributes Minimum Maximum

Mass range 0.6 kg

Section thickness mm

Tolerance mm

Roughness µm

Shape

Circular prismatic

Non-circular prismatic

Flat sheet

Dished sheet

Solid 3-D

Hollow 3-D

0.05 0.06

3

bbbb

0.5

100


Desired Batch Size

Ec

on

om

ic b

atc

h s

ize

(u

nits

)

1

10

100

1000

10000

100000

1e+006

1e+007

1e+008

Blow Moulding

Powder methods

Inject ion Moulding

Sheet forming

Die Casting

Compre ssion M oulding

Expanded foam molding

Rotational

Moulding

Rolling and forging

Resin transfer

molding (RT M)

Electro-discharge machining

Thermoforming Rapid prototyping

Lay-Up

methods

Sand cast ing

Polymer Casting

Economic batch size

To evaluate the competitiveness in cost of a process, depending on the batch size, it is necessary to develop a suitable cost model.

Cost estimation and modelling

Cost estimation and modelling

� Cost estimate for competitive bidding -- absolute cost is wanted, to 3%±

� Cost estimate for ranking -- a relative cost is sufficient – need generality

Cost estimation for purposes of competitive bidding requires precision: profit margins are often less than 10%; an error of a few % can spell disaster.

Cost estimation for ranking of choice – our purpose here – requires only relative values, allowing the conclusion that one process is more or less

expensive than another. That means the model can be approximate, but it

must be broad, to allow comparison between different process families.

Cost modelling: Resource-based approach

Manufacturing

process

Materials

Energy

Capital

Time

Space

Product

All of these have an associated cost

Generic inputs to any manufacturing process

The cost model requires inputs that are common to all families of process.

Each input has an associated cost. The cost of one unit of output is the sum of the contributions from each of these.

• Capital includes the cost of production equipment and tooling.• Time includes labor and administration and other overheads.• Information includes R&D costs or royalty and other payments to the

originator of the process, if they exist.

Information


Resource-based approach

The manufacture of a component consumes resources.

The process cost is the sum of the costs of the resources it consumes.

n = batch size

n = batch rate.


Resource-based approach

The manufacture of a component consumes resources.

The process cost is the sum of the costs of the resources it consumes.

n = batch size

n = batch rate.


1 0

10 0

100 0

1000 0

1.E+00 1.E+01 1.E+02 1 .E+0 3 1 .E+0 4 1 .E+0 5

Batch size (units)

Co

st

per

un

it (

$/u

nit

)Material and process A

Material and process C

Material and process B

Tooling costs

dominate

Material and labor costs dominate

n

C

n

CCC

L.grosstm

&

&

++= *

Meaning of “economic batch size”


Input information sources

� Web sources

• American Metal Market On-line, www.amm.com• Iron & Steel Statistics Bureau, www.issb.co.uk• Kitco Inc Gold & Precious Metal Prices, www.kitco.com/gold.live.html - ourtable

• London Metal Exchange, www.lme.co.uk

• Metal Bulletin, www.metalbulletin.plc.uk• Mineral-Resource, minerals.usgs.gov/minerals

• The Precious Metal and Gem Connection, www.thebulliondesk.com/default.asp

� Ask suppliers

� Material and process costs vary with time

and depend on the quantity you order

� CES has approximate cost for 2900 materials and 80 processes

Thomas Register of European Manufacturers, TREM

Thomas Register of North American Manufacturers

www.tremnet.com

Cost modelling in CES

Materials Tooling

Batch size

( )

+∑

+

∑+

−= oh

wo

ctm Ct.L

C

n

1

n

C

f1

CmC &

&

Rate of production

Capital, Labor, Information, Energy...

Material costs Cm per kg, and a mass m is used per unit;

f is the scrap fraction (the fraction thrown away) f1

Cm m

−

Tooling Ct is “dedicated” -- it is written off against the number of parts to be made, n n

Ct

Capital cost Cc of equipment is “non-dedicated”

It is written off against time, giving an hourly rate.

The write-off time is two . The rate of production is units/hour.

The load factor (fraction of time the equipment is used) is L.n&

wo

c

t.L

C

n

1

&

The gross overhead rate contributes a cost per unit of time

that, like capital, depends on production rate oh

C&

n& n

Coh

&

&


Cost of equipment Cc

Cost of tooling Ct

Production rate

Characteristics of the process

The database has approximate value-ranges for thesen&

++

+

−= oh

wo

ctm Ct.L

C

n

1

n

C

f1

CmC &

&


Batch size n

Mass of component m

Material cost Cm

Capital write-off time tw o

Load factor L

Overhead rate ohC&

Site-specific, user defined parameters

These are entered by the user via a dialog box

Cost of equipment Cc

Cost of tooling Ct

Production rate

Characteristics of the process

The database has approximate value-ranges for thesen&

++

+

−= oh

wo

ctm Ct.L

C

n

1

n

C

f1

CmC &

&


Cost modelling

Relative cost index (per unit) 5 - 6

Capital cost 2000 - 5000 GBP

Material utilisation factor 0.7 - 0.75

Production rate (units) 20 - 30 per hr.

Tooling cost 300 - 450 GBP

Tooling life 5000 - 10000 units

fx

Dialog box

Capital write-off time two = ….

Component mass m = ….

Load factor L = ….

Material cost Cm =

Overhead rate = ….ohC&

Batch SizeMaterial Cost=2GBP/kg, Com ponent

1 100 10000 1e+006 1e+008

Cost Index (per unit) (G

BP)

10

100

1000

10000

Re

lati

ve

co

st

Batch size

Graph

Case

Rotor

Burst shield

Case study: Flywheels

Specification for a flywheel

Specification

Flywheel

Maximum energy/weight

• Must not disintegrate

• Cost within reason

• Fr. Toughness adequate

• Material

Function

Objectives

Constraints

Free variables

Multiple constraints problem (Overconstrained)

Primary constraint Performance maximizing criteria

Material index and constraints for flywheels

• Maximise energy/unit weight at maximum velocity

Energy

Mass

Must not fail

Energy/mass

Angular velocity

πρ=Ι

ωΙ=

2

tR

2U

42

ρπ= tRm 2

( )y

22R8

3σ≤ωρ

ν+=σ

( )

≈

ν+

ρ

σ≈

2

1

8

3

2m

U y

Density

Strength

Moment of inertia

(1)

(2)

(3)

(4)

Material index and constraints for flywheels

• Maximise energy/unit weight at maximum velocity

Energy

Mass

Must not fail

Energy/mass

Maximise

ρ

σ=

yM

Angular velocity

πρ=Ι

ωΙ=

2

tR

2U

42

ρπ= tRm 2

( )y

22R8

3σ≤ωρ

ν+=σ

( )

≈

ν+

ρ

σ≈

2

1

8

3

2m

U y

Density

Strength

Moment of inertia

Additional constraint: Fracture toughness > 10 MPa.m1/2

(1)

(2)

(3)

(4)

Material for flywheels

ρyσM=

1 Ceramics: But fracture toughness inadequate

2 CFRP, GFRP: The best choice

The selection2

1

Material for flywheels

Density (typical) (Mg/m^3)

1 10

Ela

stic

Lim

it (t

ypic

al)

(M

Pa

)

10

10 0

10 00

CFRPGFRP

Low alloy ste els

Mg alloys

Nickel alloys

Coppe r alloys

Zinc alloys

Low carbon stee l

Al alloys

Al-SiC Composite

Ti alloys

Lead alloys

Density (Mg/m3)

Strength - DensityAdditional constraint:

K1c > 15 MPa.m1/2

Str

eng

th (

MP

a)

ρyσM=

Searchregion

Results

CFRP

• ρ= 1,5 Mg/m3

• σy = 1000 GPa

• m = 0,34 Mg

• M = σy/ρ = 660 MPa.m3/Mg

• Cm = 85 euro/Kg

GFRP

• ρ= 1,8 Mg/m3

• σy = 700 GPa

• m = 0,41 Mg

• M = σy/ρ = 390 MPa.m3/Mg

• Cm = 15 euro/Kg

ρπ= tRm 2

R = 0,5 m t = 0,3 m

Processes selection

CFRP

• ρ= 1,5 Mg/m3

• σy = 1000 GPa

• m = 0,34 Mg

• M = σy/ρ = 660 MPa.m3/Mg

• Cm = 85 euro/Kg

GFRP

• ρ= 1,8 Mg/m3

• σy = 700 GPa

• m = 0,41 Mg

• M = σy/ρ = 390 MPa.m3/Mg

• Cm = 15 euro/Kg

Injection moulding

Compression moulding

Cost modelling: Main parameters

CFRP

• m = 0,34 Mg

• Cm = 85 euro/Kg

GFRP

• m = 0,41 Mg

• Cm = 15 euro/Kg

Component length

Component mass

Material cost

Overhead rate

Capital write-off time

Load factor

0,3 m

0,34 Mg

85 euro/kg

60 euro/h

5 years

0,5

0,3 m

0,41 Mg

15 euro/kg

60 euro/h

5 years

0,5

Cost evaluation: Analysis of results


4000 units



Selecting joining and surface treatment processes

Process

records

Heat treat

Paint/print

Coat

Polish

Texture ...

Electroplate

Anodise

Powder coat

Metallize...

Material

Purpose of treatment

Coating thickness

Surface hardness

Relative cost ...


Material

Purpose of treatment

Coating thickness

Surface hardness

Relative cost ...


Adhesives

Welding

Fasteners

Braze

Solder

Gas

Arc

e -beam ...

Material

Joint geometry

Size Range

Section thickness

Relative cost ...


Material

Joint geometry

Size Range

Section thickness

Relative cost ...


Class AttributesMember

Surface

treat

Joining

Family

Shaping

Kingdom

Processes


Gas Tungsten Arc (TIG)Tungsten inert-gas (TIG) welding, the third of the Big Three (the

others are MMA and MIG) is the cleanest and most precise, but also the most expensive. In one regard it is very like MIG

welding: an arc is struck between a non-consumable tungsten electrode and the work piece, shielded by inert gas (argon, helium, carbon dioxide) to protect the molten metal from

contamination. But, in this case, the tungsten electrode is not consumed because of its extremely high melting temperature.

Filler material is supplied separately as wire or rod. TIG welding works well with thin sheet and can be used manually, but is easily automated.

Physical AttributesComponent size non-restricted

Watertight/airtight TrueProcessing temperature 870 - 2250 K

Section thickness 0.7 - 8 mm

Joint geometryLap True

Butt TrueSleeve True

Scarf TrueTee True

Materials Ferrous metals

Economic AttributesRelative tooling cost low

Relative equipment cost mediumLabor intensity low

Typical usesTIG welding is one of the most commonly used processes for dedicated automatic welding in the automobile, aerospace, nuclear, power generation, process plant, electrical and domestic equipment

markets.



Induction and flame hardeningTake a medium or high carbon steel -- cheap, easily formed and

machined -- and flash its surface temperature up into the austenitic

phase-region, from which it is rapidly cooled from a gas or liquid jet,

giving a martensit ic surface layer. The result is a tough body with a

hard, wear and fatigue resistant, surface skin. Both processes allow the

surface of carbon steels to be hardened with minimum distortion or

oxidation. In induction hardening, a high frequency (up to 50kHz)

electromagnetic f ield induces eddy-currents in the surface of the work-

piece, locally heating it; the depth of hardening depends on the

frequency. In flame hardening, heat is applied instead by high-

temperature gas burners, followed, as before, by rapid cooling. Both

processes are versatile and can be applied to work pieces that cannot

readily be furnace treated or case hardened in the normal way.

Physical AttributesCoating thickness 300 - 3e+003 µm

Component area restricted

Processing temperature 727 - 794 K

Surface hardness 420 - 720 Vickers

Economic AttributesRelative tooling cost low

Relative equipment cost medium

Labor intensity low

Typical usesThe processes are used to harden gear teeth, splines, crankshafts, connecting rods, camshafts, sprockets and gears,

shear blades and bearing surfaces.

MaterialCarbon steel

Purpose of treatmentFatigue resistance

Friction control

W ear resistance

Hardness



Joining -- the most important criteria are:

� The material(s) to be joined

� The geometry of the joint

Apply these first, then add other constraints

Surface treatment -- the most important criteria are:

� The purpose of the treatment

� The material to which it will be applied

Apply these first,

then add other constraints

Assessing potential: Cost, price and value

Technical performance

Technical performance

Estimates for cost, C

Estimates for cost, C

Potential viability

Is there profit in it?

Potential viability

Is there profit in it?

Market assessment

Value V, adoption time ta

Market assessment

Value V, adoption time ta

Successful implementation

Successful implementation

� The real requirement is

Cost < Price < Value

C < P < V

Cost C = what it actually costs to make the part or product

Price P = the sum you sell it for

Value V = the worth the consumer puts on the product

The ultimate economic objective is not so much to minimize cost as to maximize the difference between cost and value – the worth the consumer perceives the product to have.

If, by using more expensive materials and processes value is increased more than cost, the difference V-C increases, allowing the profit P-C to be maximized.


A product has a cost C the true cost of manufacture, marketing etc.

a price P the price at which it is offered to the consumer

a value V what the consumer thinks it is worth

Product success requires thatC < P < V

What determines cost? Technical design, materials, processes

What determines value? Both technical and industrial design;

-- aesthetics, associations, perceptions

My Parker pens,

8 euros eachParker special

edition 3000 euros

Do they write 375 times better?

Improve potential: Technical, industrial and product design

Technical design

Industrial design

Product design

Aesthetics

Associations

PerceptionsSatis-

factionProduct must be

life-enhancing

UsabilityProduct must be easy

understand and use

FunctionalityProduct must work, be safe, economical

Improve potential: Industrial Design

• As products mature and markets saturate, the products of competing manufacturers converge technically -- hardly differ in performance or cost

ID allows differentiation, enhanced value

Product maturity and market saturation

• Corporate and product identity are partly created and largely maintained through innovative industrial design

ID creates corporate image

Corporate identity

• Products are part of our environment. Products that give no sensual satisfaction damage the environment.

ID contributes to quality of life

The environment, in the broadest sense

Improve potential: Product character

Product “psychology”

Aestheticsassociations

Personalityperceptions

Biometrics

UsabilityBio-mechanics

Product “physiology”

Metals, ceramics

Materialspolymers, composites

Shapingjoining

Processessurface

treatment

Product

“character”What, who

Contextwhere, when

why

Function

ProductFeatures


Market assessment: size Smax and adoption time ta of the potential market

Time (Years)

Ma

rke

t vo

lum

e S

Anticipated volume,

Smax

Adoption

time, ta

Production

starts

Revenue

Investment

Investmentstarts

First +valuecash flow

First

profit

Net cash flow

Ca

sh

flo

w

Time

• Production volume (batch size)

• Cash flow projection

The main points

� To maximize profit: minimize cost C (economics of manufacture) and maximize value V (technical performance and product image)

� Cost can be modeled at several levels -- depends on purpose

� To rank process options, approximate modeling is adequate

� A cost-model for this uses “generic” inputs (Resource-based

approach): material, time, capital etc

� More precise analysis must be based on information from suppliers or (if out-sourcing) contractors.

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