icpse: supply chain research
DESCRIPTION
iCPSE: Supply Chain Research. Dr Matthew J. Realff (GT) Dr. Nilay Shah (IC) Dr. L. Papageorgiou (UCL). Process industries. Very broad Many companies do not operate at “customer-facing” end of chain Affects supply chain performance significantly. Chemical. Oil/Gas. Pharma/Fine. Energy. - PowerPoint PPT PresentationTRANSCRIPT
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iCPSE: Supply Chain Research
Dr Matthew J. Realff (GT)
Dr. Nilay Shah (IC)
Dr. L. Papageorgiou (UCL)
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Process industries
• Very broad
• Many companies do not operate at “customer-facing” end of chain– Affects supply chain performance significantly
Energy Chemical Oil/Gas Pharma/Fine Metals Enviro Food/FMCG
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iCPSE: Application of “systems” approaches through the chemical supply/value chain
Time scale
month
week
day
h
min
s
ms
ns
ps
1 pm 1nm 1 um 1mm 1m 1km
molecules
molecule cluster
particles, thin films
single and multi-phase systems
process units
plants
site
enterprise
Length scale
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Process v discrete
• Process industries often compared unfavourably with other (e.g. automobile, computer, aerospace)
• Some issues/differences– Different “Bill-of-Materials”
• “Inverted”, with co-production and recycles• Open supply chains – intermediates (“sub-assemblies”) may be
bought or sold– Many make-or-buy decisions
– Order of magnitude more complexity in knowledge of transformation processes required
– Asset base age/legacy manufacturing concepts– Manipulation length scale product length scale
Process manufacturing aspects significantly affect supply chain performance
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BOM: part of petrochemical chain
Many tradable intermediates
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BOM: Flexible polyols
Few RMs, lots of Products
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Complexity in operation
• Process: need to determine values for many operating variables in manufacturing process
– Product properties depend on raw material properties and process operating variables
• relationships between raw materials and products may be complex
– Many continuous degrees of freedom• People are better at “discrete” decisions• Explains prevalence of optimisation-based methods since
1950s, but …
… slows down the rate of innovation
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Asset base: is mass customisation possible?
• Consider pharmaceuticals as an exemplar
– Advances in science (biochemistry, genetics) and medicine mean that customised healthcare is possible in theory
– But existing pharmaceutical supply chains are incorrectly configured for this
– Consider a particular mental health therapeutic drug
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Therapeutic product supply chains
• Primary production processes usually “slow”– lowish yield– labour- and time-intensive – can take 30-200 days from end to end– many QA steps along the way
• Secondary processing often geographically separate from primary– transportation lags
• Slow value chain for new pathogens– Very sequential
• Isolate, identify, test, test, test, seek approval, design facility, build facility, operate …
• Hence no SARS, Bird Flu vaccine yet …
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Secondary manufacturing
One batch (smallest lot size) = 3 million (identical) tablets
Granulation Compression
Coating
QCBlister packing
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Manipulation lengthscale v product lengthscale
• Making a complex chemical:– Start with a backbone…
Cl
… and add groups in a sequence
OH
NH2
CH3
Molecular length scale product with O(1m) length scale manipulations
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Manifestation in symptoms
• Pharmaceuticals and related: poor material efficiencies– Process chemistry, solvent and catalyst choices result
in• Low material efficiencies (of order 1% of material entering
supply chain ends up as product)
Incidentally ….– Sub-optimal design of drug delivery systems results in
• Low bio-availability where required (of order 1% for traditional formulations e.g. pills)
– 1mg delivered to target area:• may require 10kg of materials overall…
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Symptom 1: material inefficiency
Recovery/recycle 29%
Incineration 6%
Material in 100% Product 10%Manufacture
Effluent 42%
Landfill 9%
Solvent ‘loss’ 2%
By-product sold 2%Typical fine chemical batch process single stage mass balance
(Source: Britest partners)
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Symptom 2: low responsiveness
• Low manufacturing/supply chain velocities• High stocks
– Pipeline stocks typically 30-90% of annual demand in quantity, usually 4-24 weeks’ worth of finished good stocks
– Supply chain cycle times can lie between 50-300 days
– Poor responsiveness to changes in demand– Value-added times of 0.3-5% overall
– Molecules are idle for long periods
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Statistical data from plant operating records
0:00:00
2:00:00
4:00:00
6:00:00
8:00:00
10:00:00
12:00:00
14:00:00
16:00:00
18:00:00
20:00:00
22:00:00
24:00:00
26:00:00
28:00:00
Time
Holding material while waitingfor something else
“Useful” operations
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Pressures faced by the sector• Global competition …• Cost pressures• Desire to enhance service/IP component of products
– e.g. reconfigure supply chain to modify “delivery” aspects
• Shorter product lifecycles– e.g. “me-too” drugs
• Drive towards mass customisation– “Specialty” products at “commodity” prices
• Stakeholder pressures– End of life product management– Supply chain sustainability– Environmental regulation
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The pharmaceutical value chain: relative
costs
Research & development 15%
Primary manufacturing 5 - 10%
Secondary mfg/packaging 15 - 20%
Marketing/distribution 30 - 35%
General administration 5%
Profit 20%
Total 100% (Shott, 2002)
“There is a welcome move away from viewing the supply chain as merely having to deliver security of supply at minimum cost, to a recognition of its ability to generate value for the customer and the shareholder” (Booth, 1999)
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Implications for quick response to (anticipated) release of pathogens
• Standard supply chain cannot work if it must start from scratch
• Need to devise an appropriate strategy and supporting infrastructure– Activities:
• develop potential scenarios• devise a strategy that is robust against these• provide necessary infrastructure• Needs to be “anticipatory”• Need new, more concurrent value-chain engineering
approach• Need flexible discovery, screening and manufacturing
facilities for faster response (i.e. not designed for particular pathogen)
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Capacity planning under clinical trials uncertainty
materialsentering CT- outcome unknown
promisingCT results
current products
time
dem
and
successfulproduct life-cycle
How to:• allocate capacity between products ?• plan capacity investment ?
•Extreme cases
pessimistic: no investment and many successful products: severe capacity limitations
optimistic: investment plenty of capacity but no new products
• Need for systematic way to balance risks
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Clinical trials – one productcl
inic
al tr
ials
Phase II (~2 year)Stage 1
Phase III 3-5yearsStage 2 & 3
Registration(1 year)
Success
Failure
0.9
0.1
High
Target
Minimum
Failure
0.10
0.10
0.30
0.50
0.40
0.60
Success
Failure
0.95
0.05
LaunchHigh
Low
Deterministic stage
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Alternative investments for company
Many options considered (e.g.) Expand existing site(s)
Alternative process technologies
Invest in new tax haven site
Multi-disciplinary approach with input from Taxation Production planners/process engineers Logistics Marketing and demand management
Model optimises investment and production decisions to maximise expected NPV within risk constraints
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NPV Distribution – Example
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
-200
-100 0
100
200
300
400
500
600
700
NPV
Pro
bab
ilit
y %
Break Even
Expected/Average NPV =
239
Prob. of loss 30%
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NPV Distributions – two options
0
5
10
15
20
-200 0
200
400
600
800
1000
1200
1400
1600
1800
2000
NPV
Pro
b [%
]
lower risk
higher risk
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Results for different optionsOption Capacity
Expansione(NPV)(scaled)
Probability ofLosses
[%]
Worst CaseNPV
A(a) Wait 106 16 -98A(b) Now 108 18 -122B(a) Wait 64 18 -98B(b) Now 106 19 -123B(c) Now 98 18 -120
C Now x2 87 23 -135D Wait 107 7 -86
E(a) Wait 122 16 -98E(b) Now 131 17 -123F(a) Wait 84 17 -98F(b) Now 88 22 -135
G Wait 70 27 -86H Wait 90 16 -98
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Probability of a loss
Wo
rst C
ase
Exp
osu
re m
£ N
PV
s
0%15%30%
(INCREASING RISK)
Risk analysis
Option chosen
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Upside analysisB
est
Cas
e N
PV
s m
£
100%70%Probability (breakeven at least)
Option chosen
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iCPSE: Application of “systems” approaches Pharmaceutical supply/value chain
Time scale
month
week
day
h
min
s
ms
ns
ps
1 pm 1nm 1 um 1mm 1m 1km
molecules
molecule cluster
particles, thin films
single and multi-phase systems
process units
plants
site
enterprise
Length scale
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Reverse Production Systems
The system for taking back and using products at their end of life.
Refining
MaterialManufacturing
ComponentManufacturing Final
Assembly
of Sale
Increase in Manufactured Value
Collection&
SortingDemanufacturing
Decrease in Manufactured Value
ChemicalRecycling Material
Compounding
Forward Logistics Arcs
Point
Reverse Logistics Arcs
Raw Material
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State Task Representations of Process SystemsSuperstructure of Logistic Network
Robust Optimization Formulations and Solution Methods For Large Scale MILP’s
Reservoir Estimation Methods Using GIS
Overall Methodology
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SF1
SF2
FF1
FF2
ES2
ES1
A
B
C
D
E
A mix of 5 plastics
Superstructure based methods for process design under uncertainty
+-
y
x
-V+ V
b 1 b 2
Feeder
L
d2
d
a
+V
Trajectory-based Separation System Modeling & Analysis
Overall Methodology
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“Reservoir Engineering”
Business GovernmentResidential
Product Retirement (Failure, Obsolescence)
Organization Behaviour (Stockpile, Recycle, Dispose)
Transportation Costs (Distance,Frequency, Modes)
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Joint work with N. G. Leigh, S. French, C. Ross
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Robust Optimization Formulations and Solution Methods For Large Scale MILP’s
State Task Representations of Process Systems
Reservoir Estimation Methods Using GIS
Superstructure of Logistic Network
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Robust Problem Formulation
.
.
scenariounder solution robust for the aluefunction v objective therepresent and
scenariounder aluefunction v objective optimal therepresent Let *
R
O
Robust Measure : Minimize the maximum deviation from optimality
minimize > O
* _ R for all
))*
RO (max(miny,x
or
Continuous Variables: Network Flows in each scenario
Discrete Variables: Network Structure, where the materials are collected and processed
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• How to effectively solve the problem with finitely large number of scenarios when scenarios are nicely designed?
The design of scenarios is a full factorial design. (Each uncertain parameter independently takes its values from a finite set of discrete real values.)
Research Question?
up1
up2
Possible value
Two uncertain parameters: up1 and up2
Possible value
12 scenarios
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Full Factorial Robust Algorithm
MILP1 and MILP2 Models (Relaxation Problem)
FFBLPP Model
Scenario with max regret possible for the candidate solution
and
Upper Bound (UB) on Min-Max Regret Value
Is this solution
feasible for all in?
Candidate Robust Solution
Lower Bound (LB) on Min-Max Regret Value
and
Candidate Robust Solution
Infeasible Scenario
FFBLLP ModelNo
Yes
What is the worst scenario
for this solution?
What is the best solution for these
scenarios?
Stop when UB – LB <
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Robust RPS Infrastructure for Television Recycle in GA
12 Municipal collection sites
9 Commercial processing sites (A)
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Problem Size without Uncertainty
Model TypeNumber of Constraints
Number of Continuous
Variables
Number of Binary
Variables
MILP1 14,182 11,843 1,180
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Problem Size with Uncertainty
Uncertainty Level
Number of Possible Scenarios
Number of MILP2
Constraints
Number of MILP2
Continuous Variables
Number of MILP2
Binary Variables
1 8 102,396 94,744 1,180
2 64 808,108 757,952 1,180
3 512 6,453,804 6,063,616 1,180
4 4,096 51,619,372 48,508,928 1,180
5 32,768 412,943,916 388,071,424 1,180
6 262,144 3,303,540,268 3,104,571,392 1,180
7 2,097,152 26,428,311,084
24,836,571,136 1,180
For uncertainty level 3-7, the direct method failed to solve the problem using C++ with CPLEX 9.0 on Pentium (R) 4 CPU 3.6 GHz with 2 GB RAM . (Still running after 8 hours)
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Performance of the Proposed Algorithm
Uncertainty Level
Total # Scenarios
# Scenarios Generated
Ratio Between # Scenarios Generated and Total # Scenarios
Min-Max Regret
Time (sec)Proposed Algorithm
Time (sec)Direct Method
1 8 2 25% 5,244.75 58.50 1,186.88
2 64 4 6.25% 42,397.84 506.30 15,504.51
3 512 4 0.78% 42,397.84 516.29 N/A
4 4,096 6 0.15% 46,756.29 1,246.36 N/A
5 32,768 7 0.02% 51,918.70 1,909.99 N/A
6 262,144 5 0.0019% 52,100.33 1,084.43 N/A
7 2,097,152 6 0.0003% 53,864.33 1,947.89 N/A
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Superstructure of Logistic Network
Superstructure of unit operations
Robust Logistics and Process Network
Unit Operations Models
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A Mechanical Separation Process
Size reduction
Ferrous Metals Removal
Non-ferrous Metals Removal
Plastics SeparationPlastics Separation
Post processing
A mix of products
Recycled metals, plastics
Uncertainties:
Feed composition, volume
Uncertainties:
Product prices, demands
Sink-float
Froth flotation
Electrostatic
Spectroscopic
density
wettability
charge
spectrum
Separation by Different mechanisms
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Models from Mineral Processing
H
Hc
dyyC
dyyCR
kCvCyy
CD
yt
C
0
0
2Ep
e1
1R 7525
Ep
0986.150
Theoretical approach Experimental approach
Does not account for the particle distribution
C: concentrationD: diffusion coefficientv: velocityk: rate constant
100
75
50
25
0 75 50 25
Recovery (%)
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Unit Modeling-Free-fall electrostatic separation
BBBmg
Vqxx 1lnarctan
tan
20
d
L
y
x
-V+ V
b 1 b 2
F e e d e r
a
d 2
Distributions:
• Particle entering position:
x0~ uniform distribution U(-a, a)
• Particle charge-to-mass ratio:
qm ~ normal distribution: N (,)
dLBwhere /sin2 ,
Particle horizontal position at the bottom
+-
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The Recovery Model
101 12
bBlnBarctanBtanmg
VqxPrr
Recovery to the left bin is the probability that particle final position is less than the bin position:
0 2
0 1
2
,VL
gd
,BlnBarctanB
V/tang
M
ab
abyM
yzm dzdyz,yfMxbqPr 1101
ab,abU~xbY 1101
,N~qZ m
)gg(
)g()g(
12
12
22
1
21
1
)ab(Mg
22
1
)ab(Mg
21)()( xexerfxx
where
Jing Wei and Matthew J. Realff, 2003, Design and Optimization of free-fall electrostatic separators for plastics recycling, AIChE J., 49(12): 3138-3149
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Transformation from the CDF Model to the Partition Curve Model
Ma5.0Ep1
For 50:
0gg 12 50
22
1 set
12
12 .gg
ggR
150 Mb
For Ep:(1) When the entering position is the only random variable
(2) When the particle charge-to-mass ratio is the only random variable
q2 6745.0Ep
2111
21
Epc
Epb
aEpEpEp
(3) When both random variables exist, fit the data to the empirical model
a=2.8725, b=1.0513, c=2.3784
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Unification of Unit Models
100
50
25
Id e alR e al
50 2575Partic le property
Rec
over
y (%
)
75
Partition curve 50
0986.1
1
1
Epe
R2
7525 Ep
q
.Ma.
q.
.Ma.Ep
3784205131 11
872526745050
For free-fall electrostatic separation
150 Mb
Choose as the charge-to-mass ratio
Ep for the case with only the distribution of particle entering position
Ep for the case with only the distribution of particle size
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Summary of the Unit Models
Random
Variables
Trajectory
Model
Recovery
Model
Ep and 50
Models
Sink-float Settling velocity,
particle size
Analytical N/A Empirical
Froth flotation
Settling velocity, particle size, bubble
coverage
Analytical N/A Empirical
Free-fall
Electro
Initial position,
Particle charge
Analytical Analytical Empirical
Drum-type electro
Particle charge Empirical Analytical Analytical
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A Unified Approach
Step 1: Trajectory modelDo force balance and derive a trajectory model y= f (d, p, ), where d, p and are vectors of design, operating variables and distribution parameters
Step 2: Recovery modelFind the joint probability expression for recovery R=Pr{ y y*} and do a numerical calculation if an analytical solution is not available
Step 3: Partition curve model Derive 50 from the deterministic case Find Ep models for cases where only one random variable exists Fit the Ep data to the empirical model following a multi-stage approach
Jing Wei and Matthew J. Realff, 2003, A unified probabilistic approach for trajectory based solids separations, AIChE J.
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Models to Design Method
+-
y
x
-V+ V
b 1 b 2
Feeder
L
d2
d
a
+V
Trajectory-based Separation System Modeling & Analysis
SF1
SF2
FF1
FF2
ES2
ES1
A
B
C
D
E
A mix of 5 plastics
Superstructure based methods for process design under uncertaintyMixed Integer Nonlinear Programming Strategy
75 50 25
Recovery (%)
75 50 25
Recovery (%)
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Formulation for Stochastic MINLPs
,}1 0{ ,
0),,,( ..
)],,,([ min*zy,x,
m,yZzX,x
zyxgts
zyxfvObjective value:Objective value:
Expected value of profit or cost
Constraints:Constraints:
Every constraint in the deterministic case must remain feasible for every realization in the uncertainty space
im
i
iii
iiN
,yZzX,x
Nizyxgts
zyxfv
,10 ,
,,1 ,0),,( ..
),,,( N
1minˆ
,
N
1izy,x, i
Joint confidence region
2
1
Monte Carlo sampling
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Stochastic Approximation Algorithms
Average of the solutions of M replicated problems, each with sample size N
1MM
vv
M
S
M
vv
2M
1mM,N
mN2
M,N
,
M
1m
mN
M,N
Solution of a larger problem with a sample size N’ and fixed decision variables x and y
1'N'N
vf
'N
S
'N
fv
2'N
1i'Ni2
'N
'N
1ii
'N
,
Refs: Norkin et al. (1998), Mak et al (1999), Kleywegt et al (2001)
Lower estimateLower estimate
N=5, M=5
x , y fixed
Upper estimateUpper estimateN’=50
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SAA: Confidence interval of the optimality gap
M
1m
mNM,N v
M
1v
Mean of Upper Estimate
Mean of Lower Estimate
'N
1ii'N f
'N
1v
'N
Stv 'N
,1N'N2
CI of Upper Estimate
'N
Stv 'N
,1N'N2
M
Stv M,N
,1MM,N2
CI of the optimality gap
CI of Lower Estimate
M
Stv M,N
,1MM,N2
Mean of the optimality gap
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Evaluation of Solution QualityCriteria 1: Probability of losing the optimal solution y*
The probability that y* is lost is no greater than 3K, where K is the number
of iterations at which the bounds are updated,
and assume all of variances of upper and lower bounds are bounded by 2.
Criteria 2: Probability of having a “bad” solutionCriteria 2: Probability of having a “bad” solution
With probability at most ’, the difference of two values is greater than 2(K-1)
'
112
2
NMa
'1K2*yv'yvPr 2
2111
a'NMK'
where,
Jing Wei and Matthew J. Realff, 2004, Sample average approximation methods for stochastic MINLPs, Computers and Chemical Engineering, 28(3): 333-346
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Superstructure of Logistic Network
Superstructure of unit operations
Robust Logistics and Process Network
Unit Operations Models
75 50 25
Recovery (%)
•Reservoir Estimation Using GIS
•Robust MILP Formulation“Devils and Angels”
•Trajectory Based Modeling of Particle Separation
•Stochastic MINLP For Process Design
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iCPSE: Application of “systems” approaches Reverse Production System Design
Time scale
month
week
day
h
min
s
ms
ns
ps
1 pm 1nm 1 um 1mm 1m 1km
molecules
molecule cluster
particles, thin films
single and multi-phase systems
process units
plants
site
enterprise
Length scale
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SummarySupply Chain Engineering in Process Industries will require research that:
Intelligently links information at different time and length scales together
Is founded on science and engineering of interacting infrastructures
Is driven by the details of the application domain