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

Energy Chemical Oil/Gas Pharma/Fine Metals Enviro Food/FMCG

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

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

BOM: part of petrochemical chain

Many tradable intermediates

BOM: Flexible polyols

Few RMs, lots of Products

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

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

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 …

Secondary manufacturing

One batch (smallest lot size) = 3 million (identical) tablets

Granulation Compression

Coating

QCBlister packing

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

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…

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)

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

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

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

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)

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)

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

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

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

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%

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

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

Probability of a loss

Wo

rst C

ase

Exp

osu

re m

£ N

PV

s

0%15%30%

(INCREASING RISK)

Risk analysis

Option chosen

Upside analysisB

est

Cas

e N

PV

s m

£

100%70%Probability (breakeven at least)

Option chosen

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

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

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

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

“Reservoir Engineering”

Business GovernmentResidential

Product Retirement (Failure, Obsolescence)

Organization Behaviour (Stockpile, Recycle, Dispose)

Transportation Costs (Distance,Frequency, Modes)

Joint work with N. G. Leigh, S. French, C. Ross

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

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

• 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

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 <

Robust RPS Infrastructure for Television Recycle in GA

12 Municipal collection sites

9 Commercial processing sites (A)

Problem Size without Uncertainty

Model TypeNumber of Constraints

Number of Continuous

Variables

Number of Binary

Variables

MILP1 14,182 11,843 1,180

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)

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

Superstructure of Logistic Network

Superstructure of unit operations

Robust Logistics and Process Network

Unit Operations Models

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

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 (%)

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

+-

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

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

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

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

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.

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 (%)

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

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

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

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

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

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

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