Intermediate Modeling and Steady-State Statistical AnalysisWhat We’ll Do ...Model 7-1: A Small Manufacturing SystemA Small Manufacturing System (cont’d.)New Arena ConceptsThe Modeling ApproachSequence Data ModuleSequence Data Module (cont’d.)Expression Data ModuleVariable Data ModuleSet Data ModuleAdvanced Set Data ModuleRun > Setup and Edit > Entity PicturesPart ArrivalsRelease Arriving Entity into SystemLogic for Cell 1Logic for Cells 2 and 4Logic for Cell 3Digression: Data StructuresLogic for Exiting the SystemAnimationVerificationVerification (cont’d.)Statistical Analysis of Output from Steady-State SimulationsWarm Up and Run LengthWarm Up and Run Length (cont’d.)Warm Up and Run Length (cont’d.)Warm Up and Run Length (cont’d.)Warm Up and Run Length (cont’d.)Truncated ReplicationsTruncated Replications (cont’d.)Batching in a Single RunBatching in a Single Run (cont’d.)Batching in a Single Run (cont’d.)Batching in a Single Run (cont’d.)Batching in a Single Run (cont’d.)What To Do?Simulation with Arena, 3rded. Chapter 7 – Intermediate Modeling & Steady-State Stat. Analysis Slide 1 of 37Intermediate Modeling and Steady-State Statistical AnalysisChapter 7Last revision June 9, 2003Simulation with Arena, 3rded. Chapter 7 – Intermediate Modeling & Steady-State Stat. Analysis Slide 2 of 37What We’ll Do ...• Model 7-1: A small manufacturing system Entity-dependent Sequences Data requirements and availability Verification (debugging)• Statistical analysis of steady-state simulations Warmup and run length Truncated replications Batching Other methods and goalsSimulation with Arena, 3rded. Chapter 7 – Intermediate Modeling & Steady-State Stat. Analysis Slide 3 of 37Model 7-1:A Small Manufacturing System• Part arrivals, four cells, part departures• Cells 1, 2, and 4: single machine each• Cell 3: two machines — newer one 20% faster Need: way to model non-identical resource units• Circular layout of cells• Parts enter at left, exit at right, travel only clockwise, all transfer times = 2 min. (realistic?)Simulation with Arena, 3rded. Chapter 7 – Intermediate Modeling & Steady-State Stat. Analysis Slide 4 of 37A Small Manufacturing System(cont’d.)• Three separate part types Interarrivals (all types merged) ~ expo(13) minutes 26% type 1, 48% type 2, 26% type 3• Different part types follow different routes, have different (triangular) processing times:• Observe utilizations, time/number in queues, cycle times (times in system) by part type• Run for 32 hoursParameters are for the slow machine at Cell 3.Simulation with Arena, 3rded. Chapter 7 – Intermediate Modeling & Steady-State Stat. Analysis Slide 5 of 37New Arena Concepts• Non-identical machines at Cell 3• Different entity types follow different process plans Previous models – all entities went through same sequence of stations, maybe with Decides for branching Now, need process plan with automatic routing by entity type – different Sequence assigned to each entity (like an attribute), and entity follows its own sequence Won’t use direct Connect or Routes … instead we tell entities departing from modules to follow their own Sequence Arena internally keeps track of where entity is, where it will go nextSimulation with Arena, 3rded. Chapter 7 – Intermediate Modeling & Steady-State Stat. Analysis Slide 6 of 37The Modeling Approach• Usually there are many ways to build a (correct) Arena model And also many ways to do so incorrectly …• Important to think about data structures What data are available? How will they be stored in the model?• For this model … Use Sequence for part transfer (described below) As part of Sequence definition, can define Attributes– Do for processing times at all cells but Cell 1 Use an Expression for processing times at Cell 1 Use Variables for new-machine speedup at Cell 3, part transfer timesSimulation with Arena, 3rded. Chapter 7 – Intermediate Modeling & Steady-State Stat. Analysis Slide 7 of 37Sequence Data Module• Advanced Transfer panel• Double-click for new row for each process plan Name for each Sequence Open Steps column for subdialog– Define ordered sequence of Stations to be visited in the Sequence … must have Station Names already defined– Double-click to add a new Station to the bottom of the Sequence list; right-click to insert/delete a row– Name for each step– Possible Assignments of Attribute, Variable, Pictures, etc. at each station in the Sequence … this is done before transferring the entity to this step in the sequence– In this model, Attribute assignment used to attach Process TimeAttribute to entity for the next Cell (except for Cell 1)Simulation with Arena, 3rded. Chapter 7 – Intermediate Modeling & Steady-State Stat. Analysis Slide 8 of 37Sequence Data Module(cont’d.)• Assign Sequence Name to entities that follow it• In Route modules, select Sequence as Destination Type (rather than Station) Departing entity looks in its own sequence to know where to go next• Arena tracks Sequence-following entities via automatic attributes Sequence name, NS (or Entity.Sequence) Station (where entity is or is going to), M (or Entity.Station) JobStep along the sequence, IS (or Entity.JobStep)• Normally, entity is assigned a Sequence, travels its route, then exits Can interrupt this sequence, jump forward/backward (tricky)• Remember to define the “exit” stationSimulation with Arena, 3rded. Chapter 7 – Intermediate Modeling & Steady-State Stat. Analysis Slide 9 of 37Expression Data Module• Advanced Process panel• Use for processing times at Cell 1 Could have done in Sequences, as for other Cells … done this way mostly to illustrate its use• Three different part types at Cell 1, so use a vector-valued Expression with three rows Name for the expression, Cell 1 Times Rows, 3 Expression Values subdialog– Cell 1 processing times for the three part types– Order matters, since index is part type … will reference asCell 1 Times(Part Index) in modelSimulation with Arena, 3rded. Chapter 7 – Intermediate Modeling & Steady-State Stat. Analysis Slide 10 of 37Variable Data Module• Basic Process panel• Factor variable Speed factor at Cell 3 – need a two-row vector– Assume new (faster) machine is #1, old (slower) machine is #2– Set to 0.8 for index 1; set to 1.0 for index 2•