iCPSE: Supply Chain Research

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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

Chemical
Oil/Gas
Pharma/Fine
Energy
Metals
Enviro
Food/FMCG
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iCPSE Application of systems approaches
through the chemical supply/value chain
Time scale
enterprise
site
plants
process units
single and multi- phase systems
particles, thin films
molecule cluster
molecules
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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Bills of materials
Polystyrene
Note co-production recycles
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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
Coating
Granulation
Compression
QC
Blister packing
One batch (smallest lot size) 3 million
(identical) tablets
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Manipulation lengthscale v product lengthscale

• Making a complex chemical
• Start with a backbone

and add groups in a sequence
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
Effluent 42
Landfill 9
Incineration 6
Material in 100
Manufacture
Product 10
Recovery/recycle 29
Solvent loss 2
Typical fine chemical batch process single stage
mass balance (Source Britest partners)
By-product sold 2
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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
Holding material while waiting for 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
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)
 
 
(Shott, 2002)
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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
materials entering CT - outcome unknown
promising CT results
current products

• 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

demand
successful product life-cycle
time
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Clinical trials one product
Success
High
Deterministic stage
0.95
0.10
Launch
High
0.40
Failure
Target
Success
Low
0.05
0.60
0.50
0.9
clinical trials
Minimum
0.10
Failure
0.30
Failure
0.1
Phase II (2 year) Stage 1
Phase III 3-5years Stage 2 3
Registration (1 year)
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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
0.16
0.14
Prob. of loss ? 30
0.12
0.1
Probability
0.08
0.06
0.04
0.02
0
0
100
200
300
400
500
600
700
-200
-100
NPV
Break Even
Expected/Average NPV 239
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NPV Distributions two options
lower risk
higher risk
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Results for different options
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Risk analysis
Worst Case Exposure m NPVs
(INCREASING RISK)
30
0
15
Probability of a loss
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Upside analysis
Best Case NPVs m
70
100
Probability (breakeven at least)
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iCPSE Application of systems approaches
Pharmaceutical supply/value chain
Time scale
enterprise
site
plants
process units
single and multi- phase systems
particles, thin films
molecule cluster
molecules
Length scale
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Reverse Production Systems
The system for taking back and using products at
their end of life.
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Overall Methodology
Reservoir Estimation Methods Using GIS
State Task Representations of Process Systems
Superstructure of Logistic Network
Robust Optimization Formulations and Solution
Methods For Large Scale MILPs
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Overall Methodology
Superstructure based methods for process design
under uncertainty
Trajectory-based Separation System Modeling
Analysis
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Reservoir Engineering
Business
Government
Residential
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 MILPs
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Robust Problem Formulation
Robust Measure Minimize the maximum deviation
from optimality
or
minimize d d gt Ow _ Rw
for all w
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Research Question?

• 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.)

Two uncertain parameters up1 and up2
up2
12 scenarios
Possible value
up1
Possible value
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Full Factorial Robust Algorithm
What is the best solution for these scenarios?
Candidate Robust Solution
Is this solution feasible for all w in W?
Scenario with max regret possible for the
candidate solution and
Infeasible Scenario
No
FFBLLP Model
Stop when UB LB lt e
Upper Bound (UB) on Min-Max Regret Value
Yes
Candidate Robust Solution
What is the worst scenario for this solution?
and
Lower Bound (LB) on Min-Max Regret Value
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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 Type Number 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
Robust Logistics and Process Network
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A Mechanical Separation Process
A mix of products
Uncertainties Feed composition, volume
Separation by Different mechanisms
Recycled metals, plastics
Uncertainties Product prices, demands
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Models from Mineral Processing
Theoretical approach
Experimental approach
C concentration D diffusion coefficient v
velocity k rate constant
Does not account for the particle distribution
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Unit Modeling-Free-fall electrostatic separation

• Distributions
• Particle entering position
• x0 uniform distribution U(-a, a)
• Particle charge-to-mass ratio
• qm normal distribution N (?,?)

Particle horizontal position at the bottom
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The Recovery Model
Recovery to the left bin is the probability that
particle final position is less than the bin
position
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
For ?50
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
(3) When both random variables exist, fit the
data to the empirical model
a2.8725, b1.0513, c2.3784
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Unification of Unit Models
Partition curve
For free-fall electrostatic separation
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
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
Mixed Integer Nonlinear Programming Strategy
Trajectory-based Separation System Modeling
Analysis
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Formulation for Stochastic MINLPs
Objective value Expected value of profit or
cost
Constraints Every constraint in the
deterministic case must remain feasible for every
realization in the uncertainty space
Monte Carlo sampling
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Stochastic Approximation Algorithms
Lower estimate
N5, M5
Refs Norkin et al. (1998), Mak et al (1999),
Kleywegt et al (2001)
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SAA Confidence interval of the optimality gap
Mean of Upper Estimate
Mean of Lower Estimate
CI of Lower Estimate
CI of Upper Estimate
CI of the optimality gap
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Evaluation of Solution Quality

• Criteria 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 solution
where,
With probability at most ?, the difference of
two values is greater than 2(K-1)?
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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Robust Logistics and Process Network
Superstructure of Logistic Network

• 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
enterprise
site
plants
process units
single and multi- phase systems
particles, thin films
molecule cluster
molecules
Length scale
58
Summary
Supply 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