environmentally conscious design & manufacturing...

s Design & Manufacturing

nscious turing

for ng

dit

Environmentally ConsciouDate: April 7, 2000 slide1

Environmentally CoDesign & Manufac

Class 15: ToolsDecision Maki

Prof. S. M. Pan


ossible

hniquesmization


Steps

● Setting up the problem» Objective

–Create one metric if p» Constraints

● Using optimization tec» Linear / Non-linear mini


l

tors

jective Function


Problem-Genera

Multiple Manufacturing / Environment Fac

Cost Implications Ob

Optimization


em

mix produced}

Effort

Cost


Example Probl

Manufactured product{fraction reprocessed & Number

Reuse

Remanufacture

Recycling

Design & Production

Materials


g

design variables,ctive, .

at limit the design

Z


Decision-makin

• Simple case: select values for , that optimize some obje

• Of course, often have restrictions thspace.

x1 x2 … xn, , ,

Z f x1 x2 … xn, , ,( )=

b1 g1 x1 x2 … xn, , ,( )≤

b2 g2 x1 x2 … xn, , ,( )≤

b3 g3 x1 x2 … xn, , ,( )≤


ont.)

e Z.

Z


Decision-making (c

• How to do this?- Linear programming- Nonlinear programming- Quadratic programming- Genetic optimization

Use numerical procedure to optimiz

Performancex1, x2,... Model

+ Constraints on x’s


e models):

, waste, time

vice life, potential modularity


Examples

• Objectives (think also of performanc

• Minimize: Cost, materials, energy

•

• Maximize: Product function, serfor reuse/remanufacture/recycle,


hold)

e/ recycle


Constraints

• Product demand

• Design & production set-up time lag

• Environmental hazard (Dosage thres

• Exposure to toxic by-products

• Energy use

• Potential for reuse/ remanufactur


zation

nce measures orneously optimize:


Multi-Criteria Optimi

• Let’s say we have several performaobjectives that we wish to simulta

Z1 Z2 … Zm, , ,

Design Variable 1

Des

ign

Var

iab

le 2


on (cont.)

s are conflicting.

tive:

portance on eachiverse metrics ont (e.g., Max).

he constraints on


Multi-Criteria Optimizati

• As we might expect, the objectiveWhat to do???

One approach: use a weighted objec

Select weights to place different imperformance measure and to put dequal footing. P’s must be consisten

Optimize Y!! Subject, of course, to tthe design variables.

Y W1Z1 W2Z2 …+ +=


on (cont.)


Multi-Criteria Optimizati

Other ideas:

• Goal programming• Non-dominated sets

Design Variable 1

Des

ign

Var

iab

le 2


ts

eems promising..

onverted into thers) this may help.lem that we mayers, e.g., product

nalytic Hierarchywise Comparison

2 … Wm, ,


Selecting Weigh

• The weighted objective approach sHow do we pick the weights??

• If all the objectives are somehow csame units (say dollars or eco-dollaBut, this does not address the probvalue some objectives more than othcost vs. energy cost.

• Saaty (1990) in his text, The AProcess, propose the use of a PairApproach to obtain the weights.

W1 W,


ons

a decision-maker.ria of interest.ed product

used product product materiald in dealing with a

./modules in a

riteria - maybe wed be placed.


Pairwise Comparis

• For a given circumstance interview Rank the relative importance of crite• Time: time reqd. to deal with a us• Cost: dollars reqd. to deal with a• Matls.: difficulty associated used• Energy: amt. of energy consume

used product• Modularity: Imp. of sub-assem

product• In the absence of models for these c

can identify where our efforts shoul


(cont.)

left side (i)

ergy Modularity

4 7.33 0.504 51 2.50 1

m

2 m!

2! m 2–( )!-------------------------=


Pairwise Comparisons

• For m criteria, no. of comp.:

• Imp. of factor on top (j) to factor on

Time Cost Matl. En

Time 1 3 7Cost 0.33 1 0.20 0Matl. 0.14 5 1Energy 0.25 3 0.25Modularity 0.14 2 0.20 0

k =


lysis (PCA)

e want to find!

e elements within

rnally consistent

h to solve for the.


Pairwise Comparison Ana

• Global Importance, gi - this is what w

• Relative Importance, rij - these are ththe Pairwise Comparison matrix

• The r values are not necessarily inte

• Saaty proposes a heuristic approacelements within g, given the matrix R

gi rij gj=


o find the g’s

h

ates of g2

1

2


PCA (cont.)

• We will use an analytical approach t(Whitmer, et al., 1995)

• What do we know....

and so fort

or,

many estim

g1 r1 1, g1= g3 r1 3, g=

g2 r1 2, g1=

g2 r1 2, g1= g2 r2 2, g=

g2 r3 2, g3=


values (g’s) that

, that describeise comparison

modified form of

lect values for theat make the error


PCA (cont.)

• We can use least squares to findminimize inconsistencies in r’s.

• Define a vector of errors, einconsistencies within the pairwmatrix, R. Actually, Whitmer uses aR --- F.

• Least squares problem -- want to seelements of g (global importance) thvector small.


so, since we can’s to zero, must

nge multipliers tores problem.


PCA (cont.)

• Want to minimize this quantity. Alactually minimize this by send gintroduce the requirement that

• We can employ the method of Lagraincorporate this into the Least Squa

eTe1

k2----- gTFTFg=

gTg 1=


with eigenvalue

is eigenvector

)


PCA (cont.)

• After taking the derivative, end upproblem:

where, , v is eigenvalue, g

Min L g v,( ) 1

k2----- gTFTFg v gTg 1–(–=

A vI–( )g 0=

A1

k2----- FTF=


solution with all

g to obtain W’s


PCA (cont.)

• We are looking for the eigenvectorpositive values.

Square the elements in g

0.200.440.480.410.61

=


n

Matl.23%

Cost19%


PCA - conclusio

Mod.37%

Time4%

Energy17%


roaches

)


Other Optimization App

• Markov decision processes (MDP

• Input/output modeling

• Hybrid models

• Fuzzy concepts


ng with air quality

.

rticles affect thesystem?

e motion of theed in determining


Homework #5

1. a) What are the EPA standards dealiin terms of particulate matter?b) How are they being revised?c) Give the rationale for the revision

2. How do the coarse and fine padifferent regions for the respiratory

3. What are the forces affecting thaerosol particles? How are they ustheir settling velocity?


hich an aerosol

out the processentration level ofdity based on the

the cutting fluidransfer function

at can be used inre the parameters


4. What are the mechanisms by wparticle can be deposited on a fiber?

5. State the primary conclusions abconditions affecting the mass conccutting fluid mist. Discuss their valimechanics of mist formation.

6. Sketch block diagrams showing maintenance scheme and its timplementation.

7. Show typical data based models ththe maintenance procedure. How aof these models estimated.

environmentally conscious design & manufacturing...

Documents