Design and Scheduling of Flexible Processing Systems: An ...
Transcript of Design and Scheduling of Flexible Processing Systems: An ...
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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
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Overview
ObjectiveFlexible Processing SystemsProblems & Challenges Systems Approach
Processes, Resources, Operating Conditions
Generic Problems RepresentationsSchedulingDesignSupply ChainsConclusions & Future Work
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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
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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
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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
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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
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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...
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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)
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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)
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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
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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
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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
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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
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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:
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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”
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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)
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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
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Scheduling
Batch de P2 Batch de P1
Answer : 26 hours(adapted, Shah, 2003)
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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
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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 …
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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
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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≤ ≤ ∀ =
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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?
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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
Scheduling: Caima Pulp Mill
(Castro, Barbosa-Póvoa e Matos, 2002)
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Detailed Model (gPROMS) Cooking Operation modeling
RTN Model – Scheduling Time Discretisation
Optimal Sequence
Scheduling: Caima Pulp Mill
(Castro, Barbosa-Póvoa e Matos, 2002)
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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
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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)
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595605Cycle Time (min.)
D3-D6-D4-D5D3-D4-D5-D6Optimal Sequence
14 t/h13 t/h
Scenarios Study
Optimal Sequence
Scheduling: Caima Pulp Mill
(Castro, Barbosa-Póvoa e Matos, 2002)
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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
(Castro, Barbosa-Póvoa e Matos, 2002)
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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)
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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:
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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
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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)
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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*
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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
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Retrofit: Example (Barbosa-Póvoa, 1994)
Expand Existence Capacity ???
If Profitable???
• How to expand ???
• How much it costs ???
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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
Retrofit: Example (Barbosa-Póvoa, 1994)
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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
Retrofit: Example (Barbosa-Póvoa, 1994)
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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%)
Retrofit: Example (Barbosa-Póvoa, 1994)
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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
Retrofit: Example (Barbosa-Póvoa, 1994)
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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
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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)
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Supply Chain
Demand
Distribution
Return
Production
Supply
Integration
Optimization
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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
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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
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++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)
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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
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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.
Closed Loop Supply Chain with return of non-conform products: Pharmaceutical Industry (Amaro e Barbosa-Póvoa, 2006)
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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)
Closed Loop Supply Chain with return of non-conform products: Pharmaceutical Industry (Amaro e Barbosa-Póvoa, 2006)
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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”.
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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
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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
Design of a recovery network of an industrial polluted waste (Duque, Barbosa-Póvoa e Novais, 2005, 2006)
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Operation
Design of a recovery network of an industrial polluted waste (Duque, Barbosa-Póvoa e Novais, 2005, 2006)
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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)
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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
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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
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Iberian Conference in Optimization, Coimbra, Nov. 2006, Ana Póvoa 59
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
Iberian Conference in Optimization, Coimbra, Nov. 2006, Ana Póvoa 60
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
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Iberian Conference in Optimization, Coimbra, Nov. 2006, Ana Póvoa 61
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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