modli ddeling and solilution issues in discrete event...
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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
400 700 200200 135
200
400 700
T2REPLAN
T5T4T3
T1
200
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190360 400 550 120
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277 43648 120
347 43648 120
390 477648 120
390 477638 120
280 477638 120120
280 477358 120400
43
70
277
110
10
280
Terminal T1
300
400
500
600
Terminal T2
300
400
500
600
190375 400 550 120
190425 400 550 70
70425 400 550 70120
70425 400 550 65125
70425 400 140 65535
70425 400 140600
425 400 140670
425 400 135675
5 1
50
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280 477358 120400
280 477248 120510
280 328248 120659
328248 12044 280659
328248 120280507152
220248 120280507260
220248 120280402260105
6
110
149
44
108
108
105
0
100
200
300
0 48 96 144 192 240 288 336 384 432 480 528 576 624
Tie mpo [h]
P1 P2 P3
0
100
200
300
0 48 96 144 192 240 288 336 384 432 480 528 576 624
Tie mpo [h]P1 P2
Terminal T3
400
500
600
Terminal T4
400
500
600
425 248 135827
425 248 62900
425 248 62900
425 248962
425 1351075
415 1351085
4151220
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248 80190402260455
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90
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13
0
100
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0 48 96 144 192 240 288 336 384 432 480 528 576 624
Tie mpo [h]P1 P2 P3
0
100
200
300
0 48 96 144 192 240 288 336 384 432 480 528 576 624
Tie mpo [h]
P1 P2 P3 P4
Terminal T5
400
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600
2951220120
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295820400 120
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295795425 120
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11
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65
118
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130
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100
200
300
400
0 48 96 144 192 240 288 336 384 432 480 528 576 624
Tie mpo [h]P1 P2 P3 P4
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183 70521301370
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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
Binary VariablesMakespan
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
Binary VariablesMakespan
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
Binary VariablesMakespan
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
Binary VariablesMakespan
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
Binary VariablesMakespan
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
Binary VariablesMakespan
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
Binary VariablesMakespan
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).