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
s Design & Manufacturing
ossible
hniquesmization
Environmentally ConsciouDate: April 7, 2000 slide2
Steps
● Setting up the problem» Objective
–Create one metric if p» Constraints
● Using optimization tec» Linear / Non-linear mini
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l
tors
jective Function
Environmentally ConsciouDate: April 7, 2000 slide3
Problem-Genera
Multiple Manufacturing / Environment Fac
Cost Implications Ob
Optimization
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em
mix produced}
Effort
Cost
Environmentally ConsciouDate: April 7, 2000 slide4
Example Probl
Manufactured product{fraction reprocessed & Number
Reuse
Remanufacture
Recycling
Design & Production
Materials
s Design & Manufacturing
g
design variables,ctive, .
at limit the design
Z
Environmentally ConsciouDate: April 7, 2000 slide5
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, , ,( )≤
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ont.)
e Z.
Z
Environmentally ConsciouDate: April 7, 2000 slide6
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
s Design & Manufacturing
e models):
, waste, time
vice life, potential modularity
Environmentally ConsciouDate: April 7, 2000 slide7
Examples
• Objectives (think also of performanc
• Minimize: Cost, materials, energy
•
• Maximize: Product function, serfor reuse/remanufacture/recycle,
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hold)
e/ recycle
Environmentally ConsciouDate: April 7, 2000 slide8
Constraints
• Product demand
• Design & production set-up time lag
• Environmental hazard (Dosage thres
• Exposure to toxic by-products
• Energy use
• Potential for reuse/ remanufactur
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zation
nce measures orneously optimize:
Environmentally ConsciouDate: April 7, 2000 slide9
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
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on (cont.)
s are conflicting.
tive:
portance on eachiverse metrics ont (e.g., Max).
he constraints on
Environmentally ConsciouDate: April 7, 2000 slide10
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 …+ +=
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on (cont.)
Environmentally ConsciouDate: April 7, 2000 slide11
Multi-Criteria Optimizati
Other ideas:
• Goal programming• Non-dominated sets
Design Variable 1
Des
ign
Var
iab
le 2
s Design & Manufacturing
ts
eems promising..
onverted into thers) this may help.lem that we mayers, e.g., product
nalytic Hierarchywise Comparison
2 … Wm, ,
Environmentally ConsciouDate: April 7, 2000 slide12
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,
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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.
Environmentally ConsciouDate: April 7, 2000 slide13
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
s Design & Manufacturing
(cont.)
left side (i)
ergy Modularity
4 7.33 0.504 51 2.50 1
m
2 m!
2! m 2–( )!-------------------------=
Environmentally ConsciouDate: April 7, 2000 slide14
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 =
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lysis (PCA)
e want to find!
e elements within
rnally consistent
h to solve for the.
Environmentally ConsciouDate: April 7, 2000 slide15
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=
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o find the g’s
h
ates of g2
1
2
Environmentally ConsciouDate: April 7, 2000 slide16
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=
s Design & Manufacturing
values (g’s) that
, that describeise comparison
modified form of
lect values for theat make the error
Environmentally ConsciouDate: April 7, 2000 slide17
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.
s Design & Manufacturing
so, since we can’s to zero, must
nge multipliers tores problem.
Environmentally ConsciouDate: April 7, 2000 slide18
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=
s Design & Manufacturing
with eigenvalue
is eigenvector
)
Environmentally ConsciouDate: April 7, 2000 slide19
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=
s Design & Manufacturing
solution with all
g to obtain W’s
Environmentally ConsciouDate: April 7, 2000 slide20
PCA (cont.)
• We are looking for the eigenvectorpositive values.
Square the elements in g
0.200.440.480.410.61
=
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n
Matl.23%
Cost19%
Environmentally ConsciouDate: April 7, 2000 slide21
PCA - conclusio
Mod.37%
Time4%
Energy17%
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roaches
)
Environmentally ConsciouDate: April 7, 2000 slide22
Other Optimization App
• Markov decision processes (MDP
• Input/output modeling
• Hybrid models
• Fuzzy concepts
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ng with air quality
.
rticles affect thesystem?
e motion of theed in determining
Environmentally ConsciouDate: April 7, 2000 slide23
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?
s Design & Manufacturing
hich an aerosol
out the processentration level ofdity based on the
the cutting fluidransfer function
at can be used inre the parameters
Environmentally ConsciouDate: April 7, 2000 slide24
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.