design and scheduling of flexible processing systems: an ... · 1 iberian conference in...

1

Iberian Conference in Optimization, Coimbra, Nov. 2006, Ana Póvoa 1

Design and Scheduling of Flexible Processing Systems:

An Optimization Approach

Ana Paula Barbosa Póvoa

Centro de Estudos de Gestão, CEG-ISTInstituto Superior Técnico


Overview

ObjectiveFlexible Processing SystemsProblems & Challenges Systems Approach

Processes, Resources, Operating Conditions

Generic Problems RepresentationsSchedulingDesignSupply ChainsConclusions & Future Work

2

Objective

Develop generic models for the design and scheduling of flexible process systems

Solution of Real Problems

High variety of Products

Low Volumes

Batch and Semi-Continuous Operations

Multipurpose Resources ProductsRaw Materials

Flexible Process Systems

3


Flexible Process Systems

R1

R2

RV1

RV2

ST1 RD2

RD3

RD1

RV1

RV2

FT1

D1

D2

RV1

RV2

RD2

RD1

RD3

RD2RV1

RV2

ProductA

Product B

Product A

Product C

Campaign 1 Campaign 2


Supply Chain Structure

Plants & Distribution Capacities

Resources Requirements inNew Plants /Existing Plants

Maintenance & New Resources

Supply Chain Planning

Production Planning

Production Scheduling and Re-scheduling

Productions Control

Flexible Process Systems : Design + Operation

4


Process Industries: Motivation

Diversity of ApplicationsComplex Production ProcessesImprovement of Processes EfficiencyClient Satisfaction Costs Reduction

Decision Support Systems

Utilities Chemical Oil/Gas Pharma/Fine Metals Enviro Food


Problems & Challenges

How to design these plants?

How to manage the plants resources?

How to design and manage the associated

supply chains?

SYSTEMS APPROCH OPTIMIZATION...

5


The ModelDevelop the model for the problem;

Parameters definitionSets definitionVariables definition

Binary (ex. Use or not the resource ?)Continuous (ex. Batch sizes ?)

Constraints definitionsObjective definition

Complex Optimization ProblemsMixed Integer Linear/Non-Linear

Formulations(MILPs & MINLPs)


Solution Methods

r

Heuristics – generic rules used to evaluate alternatives (FIFO, …).

Meta-Heuristics – algorithms (e.g. simulate annealing, Tabu search, Ant colony, …).

Artificial Intelligence – Ruled based methods, agent methods.

Constraint ProgrammingMathematical Programming – MILPs and MINLPs

models, use of optimization algorithms (e.g. GAMS/CPLEX, XPRESS)

Combination of Methods (Hybrid)

6


Key Components

r

Tasks – activities that transform the materials:ProcessingStorageTransport …

Resources:Processing and storage equipments,TransportMan-powerUtilities …

Time :External - Production versus external demandInternal – Production Planning & Scheduling


Treatment of time

The activities (tasks) must occur such that the problem objectives are attained and no restrictions are violated

The use of the resources by the tasks and its availability along time must be analyzed

1 T2 4 T-2 T-1

0 H

3

Discrete Time Continuous TimeSlot 1 Slot 2 Slot T-2 Slot T-1

0 H

1 T2 3 T-2 T-1

7


Discrete vs. Continuous Time

Discrete TimeTight mathematical formulations Large models – small discretisation of timeProcessing times independent of the batches.

Continuous TimeLoose mathematical formulationsSmaller models – less points within the time gridTime grid points determined by the model Processing times may be dependent of the batches


Problems Representation (Pantelides, 2004)

Problems are very complex and very diverse …need a diverse set of techniques to match problem characteristics

OR

Distinctions between different industrial design & scheduling problems are not really sharp …uniform representations can be used

8


Scheduling

Optimize an objective functionMin. Delays / Max. Prod./ Min Makespan

Process descriptionPlant flow-sheetResources suitability –tasks / materialsOperating constraintsProduction demandsCosts/ValuesTimes of operation

Optimal operation: scheduling

So as to:

Determine:

Given:


Process Description

State-Task Network, STN (Kondili, Sargent & Pantelides, 1988, 1993)

Non ambiguities in the process description:Sharing of intermediate products;Different processing alternatives;Recycles.

A

B

Reactions C

Mixture 1

Mixture 2

P1

P2

Add3h

2h

1h

80% 20%

75% 25%

“States”

“Tasks”

9


Process + Resources + Production

320 t400t

125 t

A

B

Reaction C

Mixture 1

Mixture 2

P1

P2

Add3h

2h

1h

80% 20%

75% 25%

“States”

“Tasks”

600t

1450t

How long it takes to produce ?

(adapted, Shah, 2004)


Global Model (Kondili et al, 1988, Shah et al 1993)

Process Tasks, States, STNMultipurpose Resources Capacity & Suitability Time representation Discrete, Fixed TimesOperating Costs Batch linear functionOperating modes Periodic e non periodicOperating constraints Cleaning, etc. …Demand Intervals, Fixed Values

Constraints & Objective Function Linear

MILPProblem

10


Scheduling

Batch de P2 Batch de P1

Answer : 26 hours(adapted, Shah, 2003)


STN Restrictions

Tasks are always associated to materials that suffer transformation.

Tasks associated to a dingle equipment.

Each resource is treated independently and non uniformly

Generalizations implies the addition of constraints

Generic Models but with some complexity

11


Resource -Task Network, RTN (Pantelides, 1994)

• Classified accordingly to its functionality• All resources of the same class have the same functionality

Resources Tasks

• Abstract operation that consumes & produces resources

• Uniform treatment of all resources- Materials- Processing & Storage equipment- Utilities & Man-power- Connections - Transport resources …


Resource-Task Network, RTN (Pantelides, 1994)

A BReaction

ReactorReaction A B

A BReaction

Cleaning

Reactor dirtyReactor clean

Reaction A B with cleaning

GENERIC & SIMPLE MODELS

12


Formulations: STN versus RTN

( ). .,, 1 ,0MaxPR S S v D vs ss ts H s ts SP = − +∑ ∑ + ∈

s.t.

1 ,t 1,...,H 1 1

tW ji, j,t'i I t' t pj i

≤ ∀ =∑ ∑∈ = − + ≥

0 , 1,..., st sS C s t H≤ ≤ ∀ =

min max , , 1,..., ij ijt ijt ijV W B W V i j K t Hijt i≤ ≤ ⋅ ∀ ∈ =

, , ,, , , ,, 1

, 1,...,H 1s i s i

is isii T j K i T j K

S S B B D Rs t s t s ti j t i j ts t

s t

ρ ρτ∈ ∈ ∈ ∈

= + + − +∑−−

∀ = +

∑ ∑ ∑ ∑

, , , ,st ijt ijt st stS W B D R

( ). .,, 1 ,0 rMaxPR R R vr vr tr H s tr RP = − + Π∑ ∑ + ∈

s.t.

min max , , 1,..., kr kt kt kt kr kV N N V k r PE t Hξ≤ ≤ ⋅ ∀ ∈ =

( ), ,0

, , 1

, 1,...,H 1

k

kr k t kr k t rtk

R R Nr t s t

r t

τ

θ θ θ θθ

µ υ ξ− −=

= + + +Π−

∀ = +

∑∑

max0 , 1, ..., rt rtR R r t H≤ ≤ ∀ =

, , ,rt kt kt rtR N ξ Π

( ) , 1,...,i

ut ui ijt ui ijti j k

U W B u t Hα β∈

= + ∀ =∑∑

max0 , 1,...,ut uU U u t H≤ ≤ ∀ =


Scheduling: Caima Pulp Mill

(Castro, Barbosa-Póvoa e Matos, 2002)

Dig

este

r

S plitter

Heat E xchangerStream 1

Stream 2

Stream 4

Stream 3

• Four Digesters operating in batch mode(D3, D4, D5 e D6)

• Vapor resource limitation

What is the optimal digesters sequence that maximizes production while account for vaporlimitations?

13


Process:

1 – Chip filling;2 – Acid filling3 – Heating ( 55ºC to 130ºC)4 – Cooking5 – Degasification (high & low pressure)6 - Blowing

Cyclic Operation – sequence that is repeated




Detailed Model (gPROMS) Cooking Operation modeling

RTN Model – Scheduling Time Discretisation

Optimal Sequence



14


Cooking Process, RTN (Castro, Barbosa-Póvoa e Matos, 2002)

Heating phase simplification K=3-10

k=1S1 S2

R1

k=1S1 S2

k=1S1 S2

k=1S1 S2

k=2

k=2

k=2

k=2

S3

S3

S3

S3

R2

k=3-10

k=3-10

k=3-10

k=3-10

S8

S8

S8

S8

R3

k=11

k=11

k=11

k=11

S9

S9

S9

S9

k=12

k=12

k=12

k=12

S10

S10

S10

S10

R4

k=13

k=13

k=13

k=13

k=14

k=14

k=14

k=13

S11

S11

S11

S11

R5R6

D3

D4

D5

D6

D3

D4

D5

D6


H 0 (3,3)

S3 S4 S8

H 1 (3,3)

H 0 (3,4)

H 0 (3,5)

H 0 (3,6)

H 1 (3,4)

H 1 (3,5)

H 1 (3,6)

S5

S6

S7

H 1 (4,3)

H 1 (5,3)

H 1 (6,3)D3

H 0 (4,4)

S3 S4 S8

H 1 (4,4)

H 0 (4,3)

H 0 (4,5)

H 0 (4,6)

H 1 (4,3)

H 1 (4,5)

H 1 (4,6)

S5

S6

S7

H 1 (3,4)

H 1 (5,4)

H 1 (6,4)D4

H 0 (5,5)S3

S4 S8

H 1 (5,5)

H 0 (5,3)

H 0 (5,4)

H 0 (5,6)

H 1 (5,3)

H 1 (5,4)

H 1 (5,6)

S5

S6

S7

H 1 (3,5)

H 1 (4,5)

H 1 (6,5)

D5

H 0 (6,6)

S3S4 S8

H 1 (6,6)

H 0 (6,3)

H 0 (6,4)

H 0 (6,5)

H 1 (6,3)

H 1 (6,4)

H 1 (6,5)

S5

S6

S7

H 1 (3,6)

H 1 (4,6)

H 1 (5,6)

D6

Heating Phase, RTN (Castro, Barbosa-Póvoa e Matos, 2002)

15


595605Cycle Time (min.)

D3-D6-D4-D5D3-D4-D5-D6Optimal Sequence

14 t/h13 t/h

Scenarios Study

Optimal Sequence




Optimal Scheduling for 14 ton/hr

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000

D3

D4

D5

D6

Time (min)

Chip filling Acid filling Steam sharing Heating till 90ºC (H0) Final heating (H1) Cooking HP Degassing LP Degassing Blowing


16


Flexible Systems Scheduling

Generic & Flexible Representations Detailed Models

BUT IS MISSING ….

Dynamic Scheduling treatmentUncertainty study Explore more efficient solution methods – complex problems

Real cases solution

(Shah, 1998, Floudas & Lin, 2004, Mendez et al., 2005)


Design / Retrofit

Optimize and Objective FunctionMin. Costs / Max. Profit

Process DescriptionPlant Superstructure : Equipment & TopologyEquipment Suitability –Tasks/MaterialsOperational constraintsDemandsOperating & Investment Costs/ValuesOperation times

Plant design : Equipment & TopologyOptimal Operation : scheduling

So as to:

Determine:

Given:

17


Design / Retrofit (Barbosa-Póvoa e Macchietto, 1994)

maximal State-Task Network, mSTN

V1 R1

V2 V4R3

V5

V6

Equipment Network, Flowsheet

S6/V6

S1/V1

S2/V2

T1/R1

T2/R1

T4/R3

S5/V5

S4/V4

T3/R3

S1

S2

S3

S4 S5

T1

T2 T3

0.6

0.4

0.6

0.4

2 h

T4 S6

2 h 4 h

2 h

State-Task Network, STN

R1

• Only feasible configurations

• Precise representation of :

- all transfers- all material locations- any storage policies


Equipment-Process Modeling (Barbosa-Póvoa & Macchietto, 1997)

Representing:-precedence constraints-sequence dependencies-cleaning requirements

( i.e. Reactor R1)

R1_Sujo_S3

T1

R1_Sujo_S4

Limpeza

T2

R1_Limpo

- eTask (process, storage, services & Transfers)

- eState (connections / units)

C_Limpa

( i.e. Connection)

C_Suja

tr_S4

tr_S3

tr_água

Equipment State- Task Network (eSTN)

• Define allowable states of each piece of equipment / connection (eStates)

• Define allowable transformations between equipmentstates caused by process, transfers, storage and cleaning tasks (eSTN Tasks)

18


Design - Modeling (Barbosa-Póvoa, 1994)

* - generated automatically

Process Networksproducts recipes (ex. make A)ancillary operations (ex. clean)

STN

Equipment Network- Units- Connections

Operational Pre-conditions- Equipment States- Product precedence orders- Cleaning needs

eSTN*

Flow-sheet

Equipment / Process• Units / Tasks-States (Suitability)• Connections / States

mSTN*


Model Characteristics (Barbosa-Póvoa and Machietto, 1994)

Process Representation, STN;Resources with Discrete & Continuous Capacity;Plant TopologyTime Discretisation;Short-term & Periodic Operation;Multipurpose Resources Fixed Processing Times;Non-preemptive Operations;Generic Storage Policies;Operating demands;Utility circuits;Multi-product operation.

MILPProblem

Objective Function

19


Retrofit: Example (Barbosa-Póvoa, 1994)

Expand Existence Capacity ???

If Profitable???

• How to expand ???

• How much it costs ???


Process Representation (STN)

RMP

RMD

R_INTA IMPA SEP_A

WA

INTA0.2

R_INTB IMPB WASH_B R_INTCINTC

RML RMA

WB

PROC

WC

IMPC

WASH_C0.1

0.9

RMW

0.2

0.1

0.9

0.20.2

0.2

0.4

0.1

0.8

0.1

0.9

0.34

0.33

0.330.8

0.5

0.5

10 h 15 h 10 h 5 h10 h

5 h


20


Superstructure – Flowsheet(in black existing plant – in red possible additions)

F_RMD

VwA

VA1

VA2

Sep2

Sep3

Sep1

F_RMP

RA1

RA2RA3

RA4

RA5

RB1

RB2WB2

WB1

VB1

VB2

VwB VwC

RC5

WC2

RC4

WC1

VC1VC2

RC3

RC2

RC1

F_RML

F_RMW

F_RMA



Optimal Structure

F_RMD

VwA

VA1

Sep1

F_RMP

RA1

RA2

RB1WB1

VB1

VwB VwC

RC5

RC4WC1

VC1VC2

RC3

RC2

RC1F_RML

F_RMW

F_RMA

F_RMD

Profit = (> 20%)


21


Tempo de Cycle (hr)

0 5 10 15 20 25 30 35 40 45 50 55 60

Tank VB10

1500

250Filter WC

Reactor RC1

Filter WB

Reactor RA1

Reactor RA2

Separator Sep1

Reactor RC2

Reactor RC3

R_INTA100

R_INTA100

R_INTA100

SEP_A SEP_A SEP_A200200

375WASH_B WASH_B WASH_B WASH_B WASH_B

375 200350R_INTC

100R_INTC

30R_INTC

100R_INTC

100R_INTC

100

R_INTC100

R_INTC100

R_INTC100

R_INTC100

R_INTC100

R_INTC100

Reactor RC5

Reactor RC4R_INTC

230R_INTC

230R_INTC

230R_INTC

230R_INTC

230R_INTC

230WASH_CWASH_C WASH_C WASH_C WASH_C WASH_C WASH_C WASH_C WASH_C WASH_C WASH_C WASH_C

333400400400400267 222 222 222 222 222 367

IMPA100

R_INTA100

R_INTA78

R_INTA100

178

Reactor RB R_INTB R_INTB R_INTB R_INTB300300160300

R_INTB300

R_INTC100

R_INTC100

R_INTC100

R_INTC100

R_INTC100

R_INTC100

IMPA78

SEP_A

375

R_INTC30

R_INTC100

R_INTC30

R_INTC30

R_INTC100

R_INTC100

Tank VA1



Design & Retrofit - RTN

Generic ModelsPlants TopologyMultipurpose Resources Operating ConstraintsDiscrete & Continuous CapacitiesCyclic & Short Term Operation

TimeDiscrete (Pinto, Barbosa-Póvoa e Novais, 2005)

Continuous (Castro, Barbosa-Póvoa e Novais, 2005)

Investment in the models applications

22


Design of Flexible Systems

Details models but exists space for much more :

Multi-level models (design, planning & scheduling)Multi-objective models Uncertainty modelingExplore more efficient solution methods

Explore the solutions of real cases

(Barbosa-Póvoa, 2006)


Supply Chain

Demand

Distribution

Return

Production

Supply

Integration

Optimization

23


Optimization Opportunities

The supply chains are difficult to understandDecisions are frequently based on common sense

Optimization tools allow the possibility of looking in an integrated form to:

Design & Operational decisions


Supply Chains

Previous representations can be extended to the supply chain

Knowledge obtained within the design and scheduling problems should be used.

ModelsDetailed and able to capture interactionsDeal with uncertaintyDynamic & FlexibleExtensible

24


++Model(MILP)ModelModel(MILP)(MILP)

TOPOLOGYTOPOLOGY

OPERATIONOPERATION

++MARKET ASPECTSMARKET ASPECTS

Chain StructureTransportation Network

Supply/DemandConstraints

TasksMaterials flows

ChainSTN

Supply Chains Operation(Amaro e Barbosa-Póvoa, 2004, 2006)


Closed Loop Supply Chain with return of non-conform products: Pharmaceutical Industry (Amaro e Barbosa-Póvoa, 2006)

AP

SP

I1

WH2

WH1

WH3

I2

I3

WSH1

WSH2

BC1

BC2Plants: I1, I2, I3

Airport and Sea Port

Burning Centers

Distribution Sites

Ii

Forward flows(white/ final Products)

ProductsWhite Final

PC SC EC

.

.

.

Reverse flows(Recycle, Remanufacturing, Burning)

Africa

Europe Europe

Europe

IP1

IP2

IP3

IP4

25


Main OperationsProduction Production – intermediate medicines production (not for sale)

involves essentially operations like:sterilization, components calibration, mixing, etc.

Customization Customization – considers operations as:filling, blistering, packing, etc.

Distribution and Supply Distribution and Supply – considers operations as:storing, distribution.



I 1 I 3I 2

BF1 BF2 BF3 BF4 BF1 BF2 BF3 BF4BF3 BF4

BC 1 BC 2

Scenario 1 – no recover, Burning (SC1)

BF1 BF2 BF3 BF4RF1 RF2 RF3 RF4

BF3 BF4RF3 RF4

I 1

BC 1 BC 2

BFi RFi

Ws RC RM

I 1 Produção

BFi RFi

Mercado(Outras Indústrias)

BFi RFi

Transporte Transporte

I 2

BF1 BF2 BF3 BF4RF1 RF2 RF3 RF4

I 3

Valência-U

Scenario 2 – recover,without minimums (SC2)with minimums (SC3)


26


Return with and without Recover (Amaro e Barbosa-Póvoa, 2006)

Glob al P lan n in g P ro fit

17713

18093 180731783717882

17296

16 5 0 0

17 0 0 0

17 5 0 0

18 0 0 0

18 5 0 0

S c1 S c2a S c2b

Operatio na l S cenarios

Prof

it (th

ousa

nds

of m

.u.)

Ca se I - 5% P rio r T rim e stre

Ca se I I - 10% P rior T rim e stre

Reverse Logistic - Global "Profit"

-800000

-600000

-400000

-200000

0Sc1 Sc2a Sc2b

Operational Scenarios

Cos

ts

Case I - 5% Prior Trimestre

Case II - 10% Prior Trimestre

Recovery of medicines is more favourable than the non-recovery situation.

The increase of non conform products recovery reduces the chain “profit”.


IP1 IP2Formulação: PF1, EECF1, EF1

PF2, EECF2

Scheduling Scheduling –– 5 days5 days

Costumização:

Planning & Scheduling (Amaro e Barbosa-Póvoa, 2006)

Planning (Antibiotics) Planning (Antibiotics) –– 3 months3 months

27

Design of a recovery network of an industrial polluted waste (Duque, Barbosa-Póvoa e Novais, 2005, 2006)

Optimize the network maximizing the profit accounting for :- Demands within intervals - Environmental Impacts (CTAM, CTWM, SMD…)

Process

Super-estructure

+ Environmental data

S1Diluição, T1

(1 dia) S3

WT1

1%

99%

S2

57%

38%

Utilidade 1Electricidade

Utilidade 2Água

5%

S1Secagem, T2

(2 dias) S4

WT2

1%

99%

S2

25%

75%

Utilidade 1Electricidade

Simplified super-structure Optimal Network


28

Operation



Supply Chains

Area with a great potential.There is some work done but there is space for much more:

Improve existing structures Integrated different decision levelsExplore environmental impactsEconomic details UncertaintyDeal with complexity & different scales….

(Goetschalckx et al. 2002, Shah, 2004)

29

Optimization is a possible Solution

Products demands Resources Characteristics

ObjectivesStructural / Operational

Economic Parameters

+mSTNs

STNs

eSTNs

Topological CharacteristicsRTNs

Operational Characteristics

MathematicalFormulation

Flexible Systems

….

ChainNetDesign

+Retrofit

+Scheduling


Conclusions

Design & SchedulingDetailed modelsSolutions of some real cases There is space for more …

Supply Chains Detail models are appearingGreat complexity in the modeling & solution There is space for more …

Optimization Possible Solution

30


Future

Fill the “GAP” between research & its applicationExplore solution methods more efficiently :

Hybrid methodsHeuristics + MILPsMeta-Heuristics + MILPSConstraint Programming + MILPs

Integrated different decision levelsExplore environmental impactsUncertainty


Thanks

Augusto Novais, INETIHenrique Matos, DEQB, IST

MScsAna MestreFernando Miranda, MScJoão TelesJosé Matos, MScNuno Saúde, MScPedro OliveiraRicardo Mateus, MScSofia Pinheiro, MScVerónica Becken

PhDsCarlos Vieira, MScCristina Amaro, MScElisa Cunha, PhDIsabel Salema, MScJoaquim DuqueMarta Gomes, MScPedro Castro, PhDSusana RelvasTânia Pinto, MSc

31


Design and Scheduling of Flexible Processing Systems:

An Optimization Approach

Ana Paula Barbosa Póvoa

Centro de Estudos de Gestão, CEG-IST


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