modli ddeling and solilution issues in discrete event...

d li d l iModeling and Solution Issues in Discrete Event Simulationin Discrete Event Simulation

Applications in Pipeline and Wet-etch Scheduling ProblemsScheduling Problems

CARLOS A MENDEZ CARLOS A. MENDEZ

Process of developing a dynamic model with the goal of p g y gstudying and evaluating the behavior of a real system.Simulation helps to predict performance test ideas eliminateSimulation helps to predict performance, test ideas, eliminate or reduce risks, and deliver superior performance.

Simulations are used as an aid in the Design Emulation andSimulations are used as an aid in the Design, Emulation, and Operation of complex systems.

Computer simulations are done with the aid of appropriate software.

System behavior is typically dominated by randomness.

A simulation model is a description of the systemA simulation model is a description of the system

in sufficient detail to compute the state over time.

Simulation software uses the model to compute the

state of the system as time moves forward.state of the system as time moves forward.

Models are categorized by the type of state

changes that occur.

Deterministic / Stochastic

Continuous4

2

4

00 2 4

Discrete0 2 4

4

0

2

0 2 4

Differential equationsDifferential equations

x’(t) = a x(t) − b x(t) y(t)y’(t) = −c y(t) + d x(t) y(t)

Systems DynamicsSystems Dynamics

Event

Event

ProcessProcess

Object

Process

jObject

Agent

Agent

Entities cause changes in the state of the system.

Attributes are available to a represent the particular features of every entity at allAttributes are available to a represent the particular features of every entity at all times

Activities are processes and logic in the simulationp g

Events are conditions that occur at a point in time which cause a change in the state of the system.

Resources represent anything with restricted capacity

Global variables are available to the entire model at all times

Random number generator are used to model probability distributions

Calendar is a list of events that are scheduled to occur in the future

System state variables are updated every time an event is performed from theSystem state variables are updated every time an event is performed from the calendar

Statistics collectors are used to evaluate system performancey p

Manufacturing Systems. Design/Operation (planning, h d li )scheduling)

Supply Chain Management. Logistics/Design/OperationTransportation Systems. Design/RoutingComputer Systems. (Design/Protocols)Services (Healthcare, Gastronomy, Airports, Train/bus stations)Military (Defense strategies) y gEnvironmental Sciences (Climate change, Global warming)Operator training, model validation (computational pilot plant)Operator training, model validation (computational pilot plant)

Generate random samples.

Schedule and execute events.Schedule and execute events.

Define and track state changes.

Record statistics on state changes.

Di l ltDisplay results.

◦ Interactive animation.

◦ Reports.

SimulationSimulation SoftwareSoftwareGeneral P rpose Leng ages Fortran C++ Pascal etcGeneral Purpose Lenguages: Fortran, C++, Pascal, etc.

MATLAB: (Simulink)

GPSS: General Purpose Simulation Systemp y

SIMAN V, SIMPSCRIPT II.5 y SLAM II:

Enterprise Dynamics: http://www.incontrol.nl/

SIMUL8: http://www.simul8.com/

ARENA: http://www.arenasimulation.com/

SIMIO: http://www simio com/index htmlSIMIO: http://www.simio.com/index.htmlAutoMod: http://www.automod.com/

Quest: http://www.delmia.com/Q p // /

Flexsim: http://www.flexsim.com/

Witness: http://www.witness-for-simulation.com/

ProModel: http://www.promodel.com/

Micro Saint: http://www.maad.com/

Extend: http://www.imaginethatinc.com/

OptimizationOptimization byby simulationsimulationOptimizationOptimization byby simulationsimulation

OptQuest: combines scatter search, tabu search, linear and integerprogramming and neural networksprogramming and neural networks.

http://www.opttek.com/products/index.html

Si C bi i l i h d l iSimrunner: Combines genetic algorithms and evolutionarystrategies.

http://www promodel com/products/simrunner/http://www.promodel.com/products/simrunner/

First developments started in 2003.

Complex system and a need to predict or improve theComplex system and a need to predict or improve the performance.One or more system elements that exhibit variability.The real system does not exist or cannot be easily manipulated.The system cannot be effectively analyzed by theThe system cannot be effectively analyzed by the other methods. Final users closely participating in modelFinal users closely participating in model development, validation and use.

Accurately predict performance.Dynamic behavior evaluation.Some complex systems better representedTest ideas - make better decisions with low costEliminate or reduce risk and uncertaintiesEliminate or reduce risk and uncertainties.Avoid/eliminate unnecessary costs.Validate process improvement.Improve customer service.pGraphical interfaces easier to validate by final users

I. Define the objective of the study.

II. Understand the system.

III. Determine the modeling scope and level of detail.III. Determine the modeling scope and level of detail.

IV. Data collection

B ild h d l (i i )V. Build the model (iterative).

VI. Verify the model logic and data.

VII. Validate the results.

VIII. Design and execute experiments.g p

IX. Analyze and interpret the results.

D t d t th ltX. Document and present the results.

PROCESS SIMULATION (ASPEN GPROMS )PROCESS SIMULATION (ASPEN, GPROMS, …)

MATHEMATICAL OPTIMIZATION (GAMS AIMMS )MATHEMATICAL OPTIMIZATION (GAMS, AIMMS, …)

CONSTRAINT PROGRAMMING (ILOG)

META-HEURISTICS (GA, SA, TS, …)

HEURISTICS (EDD, SPT, … )

PROCEDURES (PINCH, …)

WHAT ABOUT DISCRETE EVENT SIMULATION ?

SITUATION IN THE PAST …

LIMITED AND BASIC SOFTWARE ( t i kill )• LIMITED AND BASIC SOFTWARE (computer science skills)

• ONLY DISCRETE-EVENT ORIENTEDONLY DISCRETE EVENT ORIENTED

• HIGH COMPUTATIONAL COST

• UNATTRACTIVE FOR THE FINAL USER

WHAT ABOUT DISCRETE EVENT SIMULATION ?

CURRENT SITUATIONCURRENT SITUATION …

• FLEXIBLE AND HIGHLY-ADAPTED SOFTWARE

• HYBRID PROCESS ORIENTED (DISCRETE AND CONTINUOUS)

• LOW COMPUTATIONAL COST

• VERY ATTRACTIVE FOR THE END USER (3-D and 2-D

GRAPHICAL INTERFASE)GRAPHICAL INTERFASE)

•• STOCHASTIC OPTIMIZATION (OPTQUEST)STOCHASTIC OPTIMIZATION (OPTQUEST)

Pipeline scheduling T2 T5T4T3T1

REPLANT2 T5T4T3 T1

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Tie mpo [h]

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Tie mpo [h]P1 P2

Terminal T3

400

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Terminal T4

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P1 P2 P3 P4

Terminal T5

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254

ApplicationsWet-etching scheduling

Oil pipelines represent the most reliable and costthe most reliable and cost--efficient efficient way to transport large amounts of liquid fuels over long distancesamounts of liquid fuels over long distances.SchedulingScheduling multiproduct pipelines is a very difficult task with many constraints to be considered.

The scheduling process is usually solved in two stagestwo stages:

AGGREGATE

(2) Output Schedule

(1) Input Schedule Discrete- Event

Simulator

DETAILED SCHEDULING

AGGREGATEPLANNING

sequence of batch injections (lot sizes & pumping run times)

Sequence of product deliveries to distribution terminalsto distribution terminals

DiscreteDiscrete--Event Simulator Event Simulator of multiproduct pipeline operations is particularly useful for generating more efficient, realistic and robust schedules

Product demands at every depot and their due‐dates

Production schedule at the refinery (production rates and run time intervals)

AGGREGATE

Initial stocks at refinery and depots tanks

Sequence of batches in transit along the pipeline and their volumes

D3D2D1

B1B4 B3 B2Refinery

Aggregate Delivery Operations

Sequence of batch injections

AGGREGATEPLANNING

UPPER LEVEL

0 50 100 150 200 250 300 350 400

Start‐End [h]

0.00 ‐ 8.00 400

100 100 100 100

50

100

400

50

50

50

100B5

Sequence of batch injections

Batch features (product, batch size, mean pump rate)

Aggregate product deliveries to depots during every batch injection

Volume [102m3]

00

100 100 100 100

D3D2D1

B1B4 B3 B2Refinery

Detailed Delivery Operations

DETAILED SCHEDULING LOWER LEVEL

0.0

1.00

2.00

4.00

0.00

1.00

2.00

50

100

200

100

100

100

100

100

50

50

100

100

100

100

100

50

50

50

P1

P2

50

100

50

50

50

100

0

B5

Detailed sequence of individual lots leaving the pipeline and their assigned depots

Times at which pumps should be turned on/off, and valves must be open/closed

Flow set points for pumps and valves at every instant of the

5.00

6.00

7.00

8.00

4.00

5.00

6.00

7.00

250

300

350

400

50 50

50

50

50

50

P3

P450

50

50

50

50

50

50

50Flow set points for pumps and valves at every instant of the time horizon

0 50 100 150 200 250 300 350 400

Volume [102 m3]

TimeInterval [h]

• This work introduces an efficient discrete-event simulation modeldeveloped on Arena® Software.

• The simulator works in combination with a continuous-timescheduling framework.

• The main objectives are:

the validation of the pipeline schedule provided by the optimization moduleand the generation of detailed output schedules.

• It permits to adopt alternative detailed schedules by using differentoperational criteria and evaluating them through simulation runs.

The proposed model permits to visualize the pipeline operations by means of a friendly animation interface showing the dynamics of the pipeline system over time. p p y

Pipeline: Single Origin / Multiple Distribution

Terminals Distribution Centers

D2D1 D4D3 D53 5

Head Terminal

P4P3P1P2

The trunk line is made up of a

Refinery

psequence of pipes, each one

connecting either an input to an output terminal or just a pair of

From the discrete simulation viewpoint, the pipeline can be regarded as a

coordinated non-traditional multi-server distribution terminals between

themselves.queuing system.

The servers perform their tasks in a synchronizedmanner, with each one having its own queue of fixed-

sized batch elements (entities).

Every pipe should be permanently full of liquid and has a constant volume the length of any server queue willa constant volume, the length of any server queue will

remain fixed throughout the whole time horizon.

There is a server at the end of each pipe and its queue is composed by the sequence of batch elements

contained in that pipe.

Refinery PIPELINE SEGMENT Modeled as FIFO queue Batch Element

(entity) Batch

?

INPUT STATION

PRODUCT SUPPLIES According to the Production Schedule

INPUT STATION Injects product entities from refinery tanks into the pipeline

INPUT SCHEDULE PIPELINE INTERCONNECTION

INPUT SCHEDULE• Pumping Run • Batch • Product Type • Volume • Pump Rate

PIPELINE INTERCONNECTION Decides:

• Move the entity to the next pipe • Dispatch the entity to the terminal• Hold the entity

?To Local Market

RECEIVING TERMINAL • Receiving products from

the pipeline interconnection • Delivering products to

Pump Rate

MARKET DEMANDS • Product Type • Volume • Due Date• Delivering products to

consumer markets • Due-Date

(1) A unidirectionalunidirectional pipeline connecting a single refinery to multiple distribution(1) A unidirectionalunidirectional pipeline connecting a single refinery to multiple distribution terminals is considered.

(2) The pipeline is always full always full of liquid products.

(3) A single batch can have many destinationsmany destinations.

(4) Products are injected into the pipe one after the other, with no separation deviceno separation device.

(5) Due to liquid incompressibility, every time an entity is injectedis injected, another entity already in the line is simultaneously transferredtransferred from the pipeline to a single receiving terminal.

The detailed sequence of batch injections and pumping operations (runs).

The product volume and starting/end time of each run

The product delivered the batch source and the receiving terminal for every

The product, volume and starting/end time of each run.

The product delivered, the batch source and the receiving terminal for every run (Active TerminalActive Terminal).

The product inventory management at the input station by considering discharged production runs from neighboring refineries and product injected

The product inventory management at receiving terminals by considering discharged product lots and client demands on a hourly basis.

Different Priority Rules are Tested

Determine if the Accessible Batch is Still Demanded

Identify if the Batch Transfer is Mandatory

ACTIVATIONLOGIC

ELIGIBLEASSIGN

TERMINAL 1ACTIVE

RESTRICTIVEASSIGN

PRIORITYASSIGN

The Simulator Activates the Terminal

Selection Module

Rules are Tested Batch is Still Demanded Transfer is Mandatory

Identify the Batch to be Transferred

Select the Eligible Terminal with the Highest Priority

PRIOR_ELIGASSIGN

DELIV_BATCHASSIGN

Else

TERMINALSELECT ACTIVE

TERMINAL 2ACTIVE

TERMINAL 3ACTIVE

be Transferred

ERROR

TERMINAL 4ACTIVE

TERMINAL 5ACTIVE

Calculate Priorities of Eligible Terminals

TERMINAL 5

TrueOPERATION?

NEW DELIVERYSTOPPAGEREGISTER

Return Control to the Pipeline Simulator

False

OPERATION? STOPPAGE

END

Identify Changes in Terminal/Batch

Delivery Operations SIGNALRESUME

The sequencesequence in which product deliveries to distribution terminals are accomplished has great impact on the s stem operational costsaccomplished has great impact on the system operational costs.

A pipeline stoppage stoppage occurs whenever a delivery at some terminal is interrupted and a different stripping operation starts at an upstreaminterrupted and a different stripping operation starts at an upstream point.

Both the energy cost energy cost and the maintenance cost maintenance cost increase with the number of stoppages, since the time between pump repairs strongly depends on the number of shutdownsnumber of shutdowns.

To measuremeasure the quality of the resulting output schedule, the so called accumulated idle volume accumulated idle volume is defined.

This variable is computed by addingadding the product volumes in new idle new idle pipes throughout the complete horizon.

Terminal 1 Terminal 2 Terminal 3 Terminal 4 Terminal 5Input Station

ACTIVE SEGMENT

IDLE VOLUMEACTIVE SEGMENT

ACTIVE SEGMENT

It should be established the detailed delivery scheduledetailed delivery schedule, including:

The sequence of batch portions to be pumped into the pipeline;

The size of every portion and the starting/end times of the related injections;

The amount and type of product delivered to a storage tank from a batch arriving to an output terminal, during every injection;

The time at which a batch portion has been completely loaded in the terminal tank

The product inventory management at the delivery terminals by considering discharged product lots and client demands on a hourly basis

OSBRA pipeline transports almost 20% of the total Brazilian oil derivatives.

OSBRA is the most important Brazilian pipeline

PIPE Capacity [m3]

OSBRA is the most important Brazilian pipeline

p y [ ]

REPLAN ‐ Riberão Preto 39.759

Riberão Preto – Uberaba 25.279

Uberaba – Uberlândia 25.321

Uberlândia – Senador Canedo 59.766

Senador Canedo‐ Brasilia 13.739

OSBRA pipeline owned by the Petrobras Company

Senador CanedoUberlândiaUberabaRibeão Preto Brasília

Monthly horizon

Priority Rule Cut Operations Accumulated Idle Volume[ 2 3 ][102 m3 ]

Nearest First (NF) 65 14.045

Farthest First (FF) 63 14.725

Nearest to the Current (NC) 55 8.350

P1: Gasoline P4: Jet FuelP2: Diesel P3: LPGFirst Week Delivery Schedule

B6 B7

D3

D4

D5

Injected BatchB6 B7

D4

D5

Injected Batch

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170

D1

D2

D3

Time [hs]

FF Rule

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170

D1

D2

D3

NF Rule

20 cutsIdle Volume: 1.410 [10 2 m3 ]

20 cutsIdle Volume: 2.860 [10 2 m3 ]

Time [hs]

B6 B7

D3

D4

D5

INJECTED BATCH

16 cuts

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170

D1

D2

D3

Time [hs]

NC Rule

Idle Volume: 1.005 [10 2 m3 ]

d The procedure of reading and writingReading The procedure of reading and writing data dynamically, is used to generate a

solution schedule

Processing

Writing

• Pipelines networks are critical components in the petroleump p psupply chain. An advanced discrete event simulation model formultiproduct pipelines has been developed.

• The novel approach is very useful for validating operationalThe novel approach is very useful for validating operationalpipeline schedules provided by rigorous optimizationtechniques.

• It allows to generate and test alternative monthly product• It allows to generate and test alternative monthly productdelivery schedules in less than one minute of CPU time.

• In addition, it allows the visualization of the dynamic evolutionof the pipeline system over time using a friendly animatedof the pipeline system over time, using a friendly animatedinterface.

• The proposed approach can be easily extended to permit thef i l ti b d ti i ti t l i d t iuse of simulation-based optimization tools in order to improve

pipeline operations performance.

AutomatedAutomated WetWet--EtchEtch StationStation (AWS)(AWS) is one of the most important operation carried

out in SemiconductorSemiconductor ManufacturingManufacturing SystemsSystems (SMS)(SMS)out in SemiconductorSemiconductor ManufacturingManufacturing SystemsSystems (SMS)(SMS)

This stationstation represents a complex flowshopflowshop operationoperation processprocess inin whichwhich semiconductorsemiconductor

wafer'swafer's lotslots have to be processedprocessed andand transferredtransferred throughoutthroughout sequentialsequential stagesstages by using

automatedautomated transportationtransportation devicesdevices..

AWSAWS tt ll lti d tlti d t lti tlti t b t hb t h f t if t i I thi t tiAWSAWS representsrepresents aa complexcomplex multiproductmultiproduct multistagemultistage batchbatch manufacturingmanufacturing processprocess.. In this station,

a set of jobsjobs oror waferwafer lotslots ((ii==11,,......,N),N) must be produced in severalseveral stages,stages, bathsbaths oror units,units,

(j=(j=11,,......,M),M) of the process followingfollowing thethe samesame manufacturingmanufacturing reciperecipe.

No intermediate No intermediate

buffer exists between buffer exists between ZeroZero WaitWait mustmust bebe

f llf ll i i dddd b hb h buffer exists between buffer exists between

consecutive bathsconsecutive bathsfollowfollow in in oddodd bathsbaths

Holding time in Holding time in

even baths are even baths are

allowedallowed

Many related works have been developed up to now to provide reliablereliable resultsresults for

the schedulingscheduling of processingprocessing and transferringtransferring operationsoperations in this stationstation.

ExactExact MathematicalMathematical formulationsformulations ((BhushanBhushan andand KarimiKarimi,, 20032003;; Aguirre,Aguirre, MéndezMéndez andand Castro,Castro,

20112011;; ZeballosZeballos etet alal..,, 20112011;; CastroCastro etet alal..,, 20112011),),

i ii i dd h i ih i i dd (G i(G i ll 9999 h hh h dd i ii i 200200 ))HeuristicsHeuristics andand MetaMeta--heuristicheuristic proceduresprocedures (Geiger(Geiger etet alal..,, 19971997;; BhushanBhushan andand KarimiKarimi,, 20042004),),

HybridHybrid methodsmethods (Castro,(Castro, Aguirre,Aguirre, ZeballosZeballos andand MéndezMéndez,, 20112011),),

SimulationSimulation toolstools ??????SimulationSimulation toolstools ???,???,

But efficientefficient systematicsystematic solutionsolution methodsmethods that represent and evaluate the complexcomplex dynamicdynamicBut, efficientefficient systematicsystematic solutionsolution methodsmethods that represent and evaluate the complexcomplex dynamicdynamic

behaviourbehaviour of the AWS for any system size are still needed.

In this work, a modelling,modelling, simulationsimulation and optimizationoptimization--basedbased approachapproach isIn this work, a modelling,modelling, simulationsimulation and optimizationoptimization basedbased approachapproach is

proposed to faithfullyfaithfully representsrepresents the dailydaily operationoperation of the AWSAWS.

To do this, a discretediscrete--eventevent simulationsimulation modelmodel was developed by using most of the toolstools

and capabilitiescapabilities that are available in ArenaArena simulationsimulation environmentenvironment..

The principalprincipal aimaim is to provide a systematicsystematic computercomputer--aidedaided tooltool to improveimprove

the dynamicdynamic operationoperation of this criticalcritical manufacturingmanufacturing stationstation.yy pp gg

TheThe AWSAWS schedulingscheduling problemproblem providesprovides aa complexcomplex interplayinterplay betweenbetween materialmaterial--TheThe AWSAWS schedulingscheduling problemproblem providesprovides aa complexcomplex interplayinterplay betweenbetween materialmaterial

handlinghandling limitationslimitations,, processingprocessing constraintsconstraints andand stringentstringent mixedmixed intermediateintermediate

storagestorage policiespolicies..

robot schedulerobot schedulerobot schedulerobot schedule

bath schedulebath schedule

The aim of our work aim of our work is to find the best schedule of processing and transfer activities best schedule of processing and transfer activities in a single robot a single robot that

minimizeminimize the residence time residence time of all the jobs in the system, which is widely known as Makespan (MK)(MK).

OnlyOnly aa singlesingle processingprocessing unitunit (Bath)(Bath) isis availableavailable inin eacheach productionproduction stagestage..

MaterialMaterial--handlinghandling devicesdevices (Robots)(Robots) can only move oneone waferwafer lotlot atat aa timetime.

WaitingWaiting timestimes areare notnot allowedallowed during the transportationtransportation of a waferwafer lotlot.

NISNIS is applied because nono intermediateintermediate bufferbuffer exist betweenbetween consecutiveconsecutive bathsbaths.

RobotsRobots and BathsBaths are failurefailure--freefree and setupsetup timestimes areare notnot requiredrequired inin themthem..

BathsBaths can only processprocess oneone waferwafer lotlot atat aa timetime.

ProcessingProcessing and transfertransfer timestimes are consideredconsidered knownknown and deterministicdeterministic.

ZWZW policypolicy must be ensured in chemicalchemical bathsbaths whereas LSLS is allowed in waterwater bathsbaths

The problemproblem to be faced corresponds to the corresponds to the schedulingscheduling of N jobsjobs in M bathsbaths, in a

serial multiproduct serial multiproduct flowshopflowshop, , under ZW/LS/NISZW/LS/NIS policiespolicies, in where a single shared a single shared

robotrobot with finite load capacity finite load capacity is explicitly considered explicitly considered for the wafer movementwafer movement.

I.I. ArenaArena SoftwareSoftware providesprovides anan easyeasy wayway toto representrepresent thethe AWSAWS byby dividingdividing thethe entireentire processprocess inin

specificspecific subsub--modelsmodels ((Initializing,Initializing, Transfer,Transfer, ProcessProcess andand OutputOutput))..

II.II. InIn eacheach subsub--modelmodel,, thethe detaileddetailed operativeoperative rulesrules andand strategicstrategic decisionsdecisions involvedinvolved areare

modelledmodelled..

Input Buffer or Initializing processInput Buffer or Initializing process Transfer moduleTransfer module

Here the jobjob entitiesentities are generatedgenerated and the internalinternalrobot robot logiclogic of the job’sjob’s transferstransfers entitiesentities isis performedperformed. This module is used to simulatesimulate thethe time time spentspent toto

transfer transfer jobsjobs between successivesuccessive bathsbaths and betweenbetween bathsbathsand buffersand buffers. For each transfer a robotrobot isis assignedassigned. . And a transfertransfer is performed only if the nextnext bathbath isis emptyempty and therobot robot isis availableavailable..

Process subProcess sub--model model robot robot isis availableavailable..

Output BufferOutput Buffer

Different subsub--modelsmodels are defined for everyevery typetype of of bathbath((ChemicalChemical oror WaterWater). ). In everyevery bathbath the beginningbeginning and endingending processprocess timestimes are reportedreported and waitingwaiting timestimesare onlyonly availableavailable in waterwater bathsbaths

This is a disposeddisposed stagestage in which thethe final final processingprocessing timetime((MKMK) ) of each job isis reportedreported

III.III. AA setset ofof visualvisual monitoringmonitoring objectsobjects isis usedused toto measuremeasure thethe utilizationutilization performanceperformance ofof allallgg jj pp

bathsbaths andand resourcesresources inin thethe systemsystem..

IV.IV. TheThe modelmodel allowsallows workingworking withwith aa useruser--friendlyfriendly interfaceinterface withwith MicrosoftMicrosoft ExcelExcel forfor

simultaneouslysimultaneously readingreading andand writingwriting differentdifferent datadata..

AA discretediscrete--eventevent simulationsimulation frameworkframework is developed to represents the actualactual operationoperation of

the AWSAWS in the waferwafer fabricationfabrication processprocess.

TheThe proposedproposed simulationsimulation modelmodel representsrepresents thethe sequencesequence ofof successivesuccessive chemicalchemical andand

waterwater bathsbaths,, consideringconsidering thethe automatedautomated transfertransfer ofof jobjob

BasedBased onon aa predefinedpredefined jobjob sequencesequence,, whichwhich isis providedprovided byby anan optimizationoptimization--basedbasedBasedBased onon aa predefinedpredefined jobjob sequencesequence,, whichwhich isis providedprovided byby anan optimizationoptimization basedbased

formulationformulation,, thethe modelmodel structurestructure allowsallows toto generategenerate anan efficientefficient robotrobot scheduleschedule..

ThisThis methodologymethodology allowsallows alsoalso evaluatingevaluating andand improvingimproving thethe operationoperation andand reliabilityreliability ofofThisThis methodologymethodology allowsallows alsoalso evaluatingevaluating andand improvingimproving thethe operationoperation andand reliabilityreliability ofof

bathsbaths andand robotrobot schedulesschedules..

AnAn advancedadvanced internalinternal robotrobot logiclogic isis toto explicitlyexplicitly representrepresent thethe finitefinite capacitycapacity ofofAnAn advancedadvanced internalinternal robotrobot logiclogic isis toto explicitlyexplicitly representrepresent thethe finitefinite capacitycapacity ofof

transportationtransportation resourcesresources forfor transferringtransferring jobsjobs betweenbetween consecutiveconsecutive bathsbaths..

ThisThis complexcomplex internalinternal logiclogic forfor thethe robotrobot waswas embeddedembedded inin thethe simulationsimulation modelmodel toto

generategenerate allall transferstransfers evaluateevaluate itsits attributesattributes andand allocateallocate thesethese inin thethe systemsystemgenerategenerate allall transfers,transfers, evaluateevaluate itsits attributesattributes andand allocateallocate thesethese inin thethe systemsystem..

AA tt tt d itid iti l ithl ith RCURMRCURM ii dd ii dd tt fi dfi d f iblf ibl l til ti ff

Bhushan & Karimi, 2003Bhushan & Karimi, 2003

AA twotwo--stagestage decompositiondecomposition algorithmalgorithm RCURMRCURM isis usedused inin orderorder toto findfind aa feasiblefeasible solutionsolution ofof

thethe entireentire problemproblem inin aa sequentialsequential wayway..

URM : URM : UnlimitedUnlimited--Robot Robot ModelModelORM : ORM : OneOne--Robot Robot ModelModelOO O eO e obotobot odeodeRCURM : RobotRCURM : Robot--ConstrainedConstrained UnlimitedUnlimited Robot Robot ModelModel

Finish time & Start time of job Finish time & Start time of job ii in Bath in Bath jj

Proccesing time of jobProccesing time of job ii in Bathin Bath jj

JobsJobs BathsBathsZeroZeroWaitWait & Non& Non‐‐IntermediateIntermediateStorage Storage PoliciesPolicies

Aguirre , Méndez, Castro 2011Aguirre , Méndez, Castro 2011

TimingTiming ConstraintsConstraints

Transfer Time Transfer Time

Proccesing time of job Proccesing time of job ii in Bath in Bath jj

Transfer time Transfer time between Bath between Bath jj‐‐11 & Bath & Bath jj

Job Job sequencingsequencingBinaryBinary VariableVariable

BetweenBetweenConsecutiveConsecutive BathsBaths

SequencingSequencingConstraintsConstraints

BinaryBinary VariableVariableBig M parameterBig M parameter

ConstraintsConstraints

TransfersTransferssequencingsequencing

AssignmentAssignment & & sequencingsequencing of of

Job’s Transfer Job’s Transfer Sequencing Binary Var.Sequencing Binary Var.

Resource AssignmentResource AssignmentBinary Var.Binary Var.

Resources Resources

Objetive Objetive FunctionFunction

q gq g ffalternativealternative transfer transfer resourcesresources

((MakespanMakespan))

Baths x Jobs Statistics Unlimited Robot Model(URM-MILP)

One Robot Model(ORM-MILP)

Resource Constrained Model (RCURM-MILP)

Simulation Model (URM-SIM)

4x8

Binary VariablesMakespan

CPU Time (s)a

Job Sequence p

2895.10.484

58895.6 √11.25

56095.6 √0.091

-95.6 √< 0.5

4-2-8-5-1-7-3-6 4-2-5-8-1-7-3-6 4-2-8-5-1-7-3-6

4x10


CPU Time (s)a

45115.56 785

945115.6 √

488 7

900116 (+0.5%)

0 122

-116 (+0.5%)

< 0 5CPU Time (s)Job Sequence p

6.785 488.7 0.122 < 0.59-2-5-8-10-4-1-7-3-6 9-6-5-4-10-2-8-1-7-3 9-2-5-8-10-4-1-7-3-6

4x14


CPU Time (s)a

Job Sequence p

91154.73600b

1911158.8 (+1.6%)

3600b

1820156.2 √

0.235

-156.2 √

< 0.59-12-5-8-7-11-14-10-2-4-1-13-3-6 9-2-8-12-4-14-10-11-5-1-3-7-13-6 9-12-5-8-7-11-14-10-2-4-1-13-3-6


45149 4

3285154.4 √

3240156.7 (+1 5%)

-166.4 (+7 2%)8x10 Makespan

CPU Time (s)a

Job Sequence p

149.455.07

154.4 √3600b

156.7 (+1.5%)3.42

166.4 (+7.2%)0.5

6-9-2-1-3-4-7-5-10-8 4-9-3-1-2-6-7-5-10-8 6-9-2-1-3-4-7-5-10-8

12x10


CPU Time (s)a

Job Sequence p

45192.2145.5

7065206.3 (+4.5%)

3600b

7020197.2 √152.97

-227.8 (+13%)

0.756-8-3-2-9-5-10-7-4-1 6-1-2-10-5-3-9-7-8-4 6-8-3-2-9-5-10-7-4-1

Binary Variables 66 10362 10296 -

12x12


CPU Time (s)a

Job Sequence p

66210.73600b

10362NFScd

3600b

10296215.8 √2249.7

264.3 (+18%)1.0

4-8-10-3-11-2-9-5-12-1-7-6 - 4-8-10-3-11-2-9-5-12-1-7-6

12x15


CPU Time (s)a

Job Sequence p

105241.96.785

16485NFScd

3600b

16380NFScd

3600b

-334.2 √

1.56-8-3-11-2-13-9-5-14-10-12-1-15-4-7 - 6-8-3-11-2-13-9-5-14-10-12-1-15-4-7Job Sequence p 6 8 3 11 2 13 9 5 14 10 12 1 15 4 7 6 8 3 11 2 13 9 5 14 10 12 1 15 4 7

12x25


CPU Time (s)a

Job Sequence p

300357

3600b

47100NFScd

3600b

46800NFScd

3600b

-516.8 √

5.06-16-8-11-20-4-21-18-17-19-5-10-15-22-14-2-12-3-25-13-24-9-23-7-1

(a) MILP models were solved by using GAMS/CPLEX 12 while Arena 12.0 was used for Simulation Models. All results reported were run in a PC Core 2 Quad parallel processing in 4 threads. (b) Termination criterion (3600 CPU s). (c) No feasible solution found after 3600 sec. (d) Upper 2 Quad parallel processing in 4 threads. (b) Termination criterion (3600 CPU s). (c) No feasible solution found after 3600 sec. (d) Upper Bound=1000 units. √ good-quality solutions.

FullFull--spacespace ModelModel--ORMORM SequentialSequential approachapproach--RCURMRCURM SimulationSimulation tooltool--URMURM--SIMSIM

>10000 Bin Var

No Feasible solution found !!!

<10000 Bin. Var.

>10000 Bin. Var.

>10000 Bin. Var.

(a) MILP models were solved by using GAMS/CPLEX 12 while Arena 12.0 was used for Simulation Models. All results reported were run in a PC Core 2 Quad parallel processing in 4 threads. (b) Termination criterion (3600 CPU s). (c) No feasible solution found after 3600 sec. (d) Upper Bound=1000 units.

AA novelnovel discretediscrete eventevent simulationsimulation modelmodel hashas beenbeen developeddeveloped toto simultaneouslysimultaneously addressaddress thethe

integratedintegrated schedulingscheduling problemproblem ofof manufacturingmanufacturing andand materialmaterial--handlinghandling devicesdevices inin thethe AWSAWS inin

thethe semiconductorsemiconductor industryindustry..

TheThe proposedproposed modelmodel cancan bebe easilyeasily usedused toto dynamicallydynamically validatevalidate,, generategenerate andand improveimprove differentdifferent

schedulesschedules..

WW hh d t t dd t t d th tth t thth ddWeWe havehave demonstrateddemonstrated thatthat thethe proposedproposed

solutionsolution algorithmalgorithm forfor thethe robotrobot isis ableable toto

generategenerate veryvery effectiveeffective resultsresults withwith modestmodest

computationalcomputational efforteffortcomputationalcomputational efforteffort..

ForFor largelarge--sizedsized casescases,, onlyonly ourour simulationsimulation

approachapproach foundfound feasiblefeasible solutionssolutions toto thethe problemproblem

ii blbl i li l iiinin aa reasonablereasonable computationalcomputational timetime..

Vanina G. Cafaro and Adrián Vanina G. Cafaro and Adrián M. M. AguirreAguirre–Results & animations shown on this talk

CCenter enter for for AAdvanceddvanced PProcessrocess SSystems ystems EEngineeringngineering (CAPSE),(CAPSE),INTEC (UNLINTEC (UNL--CONICET), Santa Fe, ArgentinaCONICET), Santa Fe, Argentina

http://www.intec.santafe-conicet.gov.ar/capse/p g p

References

• Cafaro V.G., Cafaro, D.C., Méndez, C.A., Cerdá, J. MULTIPRODUCT OPERATIONS: Discrete-event simulation guides pipeline

logistics. Oil & Gas Journal, 109 (15), 98-104, (2011).

• Cafaro V.G., Cafaro, D.C., Méndez, C.A., Cerdá, J. MULTIPRODUCT OPERATIONS -2 (Conclusions) New scheduling rule improves

pipeline efficiency. Oil & Gas Journal, 109 (17), 136-139, (2011).

M F Gleizes G Herrero D C Cafaro C A Méndez J Cerdá “Managing distribution in refined products pipelines using• M.F. Gleizes, G. Herrero, D.C. Cafaro, C. A. Méndez, J. Cerdá, Managing distribution in refined products pipelines using

discrete-event simulation”, International Journal of Information Systems & Supply Chain Management, Special Issue: HybridAlgorithms for Solving Realistic Routing, Scheduling and Availability Problems, Edit. By A.A. Juan, J. Faulin, S. Grasman, D. Riera,

58-79. ISSN: 1935-5726 EISSN: 1935-5734. (2012).

•A. Aguirre, V. Cafaro, C.A. Méndez. “Simulation-based framework to automated wet-etch station scheduling problems in the

semiconductor industry” Proceedings of Winter Simulation Conference 2011, 1821-1833 (2011).

modli ddeling and solilution issues in discrete event...

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