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SIMULATION MODELING AND ANALYSIS WITH ARENA T. Altiok and B. Melamed Chapter 11 Modeling of Production Lines

SIMULATION MODELING AND ANALYSIS WITH ARENA T. Altiok and B. Melamed Chapter 11 Modeling of Production Lines. Operator. Outgoing Material Storage. . . . Machinery. Incoming Material Storage. Work station 1. Workstation 2. Workstation K. Production Lines: Push Regime.

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SIMULATION MODELING AND ANALYSIS WITH ARENA T. Altiok and B. Melamed Chapter 11 Modeling of Production Lines

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  1. SIMULATION MODELING AND ANALYSIS WITH ARENA T. Altiok and B. Melamed Chapter 11 Modeling of Production Lines Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  2. Operator Outgoing Material Storage . . . Machinery Incoming Material Storage Workstation 1 Workstation 2 Workstation K Production Lines: Push Regime Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  3. Operational features • Blocking (downstream buffer full) • propagating upstream • Starvation (upstream buffer empty) • propagating downstream • Machines are unproductive (idle) during blocking and starvation Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  4. Design of Production Lines: Resource Allocation Problems • Workload allocation • Amount of work at each workstation • Buffer capacity allocation • Target WIP (work in-process) levels at each workstation Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  5. Performance Measures of Interest • Average throughput (work units/unit time) • Average inventory levels in buffers (work units) • Downtime probabilities • Blocking probabilities at bottleneck workstations • Average system flow times (time units/job) • Manufacturing lead times (time units/job) Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  6. Filling 6.5 seconds Capping 5 seconds Labeling 8 seconds Sealing 5 seconds Carton Packing 6 seconds Example: A Packaging Line • System parameters: • Buffers are 5 units of capacity • Processing times are fixed (deterministic) • Consequently, • Labeling is the slowest workstation • Workstations upstream of labeling will experience blocking • Workstations downstream of labeling will experience no blocking and jobs will not wait in the buffer after labeling • We expect that the throughput will be 1/8, that is, the rate of slowest workstation Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  7. Packaging Line Arena Model Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  8. Queue Statistics Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  9. Queue Statistics (Cont.) Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  10. Queue Statistics (Cont.) Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  11. Queue Statistics (Cont.) Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  12. Resources Statistics Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  13. User Specified Statistics Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  14. User Specified Statistics (Cont.) Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  15. Model Verification for Production Lines • Probabilities of machine status • is the probability that is idle • is the probability that is blocked • is the probability that is down • is the probability that is up (producing) • Then, the utilization of is given by • this indicating that is in the up state when it is neither idle nor blocked nor down • during the up state, produces at rate , resulting in throughput Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  16. Understanding System Behavior • The line throughput should be the same for all workstations, and equal to the slowest workstation, namely, 1/8 = 0.525 units/second • The throughput of the capping stationisunits/second Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  17. Verification Via Little’s formula • For the entire system, the average total number of jobs in the buffers and in service is given by • Little’s formula is given by • The two values are sufficiently close Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  18. Sensitivity Analysis SinceLabeling is the slowest and Capping is the one blocked most of the time, let us increase their buffers • Consequently, system throughput does not change, buffer content keeps increasing and system flow time keeps increasing • Conclusion: When processing times are fixed and there is no randomness in the system, increasing the buffer is of no value Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  19. Modeling Blocking Phenomena • Sequence of actions: • seize Filler • delay for Filling Time • hold NQ(Capping Process.queue) < 5 • block job waits in the Hold queue Filler Blocked.Queue • release Filler • seize Capper • The estimate of the time-average probabilityPr(Filler is blocked) = total time Filler blocked queue is occupied total stimulation time is obtained by the Time Persistent statistic NQ(Filler Blocked. Queue) Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  20. Alternative Modeling of Blocking • Model an intermediate buffer as a resource, i.e. • seize Capper • delay • seize Labeling Buffer (resource cap = 5) • seize a unit of buffer • blocked job remains in the queue • release Capper • seize Labeler • release Labeling Buffer • a unit of buffer is released when Labeler is seized Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  21. Modeling Machine Failures • Failure Types: • operation-dependent failures • operation-independent failures • Auto-states of an Arena Resource • Idle, Busy, Failed, Inactive • Long-run probabilities are collected via the Frequency option in the Statistics module Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  22. Modeling Machine Failures (Cont.) • Failure module • Time-based failures (timed) • Count-based stoppage (count) • Uptime • Downtime • Uptime in this state (aging takes place in this state) • States option of State Set links states to auto-states • and to failures/stoppages Dialog box for the Failure module Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  23. Failure Rules • The Preempt option starts a downtime by suspending the resource immediately on failure arrival, so that the remaining processing of the current unit will resume once the downtime is over • The Wait option allows the current unit to finish processing, following which the resource is suspended and downtime begins • The Ignore option starts the downtime after the current unit finishes processing, but only that portion of the downtime following unit completion is recorded (in contrast, the Wait option records the full downtime) Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  24. Linking Failures to States Dialog boxes for the StateSet module (left) and Filler resource States module (right) Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  25. Linking States to Resources Dialog box for failure declarations in the Resource module Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  26. Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  27. Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  28. Impact of Buffers in Case of Failures • Buffers are particularly useful in case of machine failures as “shock absorbers” • buffering absorbs some of the negative impact of machine failure, by permitting continued processing for a while • On the other hand, buffering is not all that useful in high-speed manufacturing lines, where buffers may fill up quickly Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  29. Estimating Sojourn Time Distributions Arena fragment for estimating delay time probabilities in the Packer buffer Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  30. Batch Processing • Batch serving resources are modeled using the Batch and Separate modules. • Batching can be permanent or temporary Dialog boxes for the Batch module (left) and Separate module (right) Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  31. Batch-Modified Packaging Line Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  32. Batch-Modified Packaging Line (Cont.) Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  33. Batch-Modified Packaging Line (Cont.) Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  34. Assembly Station Matching Buffers Synchronization and Assembly • The main purpose of the Match module is to synchronize the movements of Arena entities • It is also used for assembly by terminating all other departing entities from a Match module, except for one entity Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

  35. Assembly Operations • Assembly operations are modeled using the Match module A Match module (top) and its dialog box (bottom) Altiok / Melamed Simulation Modeling and Analysis with Arena Chapter 11

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