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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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slide1

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

slide2

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

operational features
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

design of production lines resource allocation problems
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

performance measures of interest
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

example a packaging line

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

packaging line arena model
Packaging Line Arena Model

Altiok / Melamed Simulation Modeling and Analysis with Arena

Chapter 11

slide8

Queue Statistics

Altiok / Melamed Simulation Modeling and Analysis with Arena

Chapter 11

slide9

Queue Statistics (Cont.)

Altiok / Melamed Simulation Modeling and Analysis with Arena

Chapter 11

slide10

Queue Statistics (Cont.)

Altiok / Melamed Simulation Modeling and Analysis with Arena

Chapter 11

slide11

Queue Statistics (Cont.)

Altiok / Melamed Simulation Modeling and Analysis with Arena

Chapter 11

slide12

Resources Statistics

Altiok / Melamed Simulation Modeling and Analysis with Arena

Chapter 11

slide13

User Specified Statistics

Altiok / Melamed Simulation Modeling and Analysis with Arena

Chapter 11

slide14

User Specified Statistics (Cont.)

Altiok / Melamed Simulation Modeling and Analysis with Arena

Chapter 11

slide15

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

understanding system behavior
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

slide17

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

slide18

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

modeling blocking phenomena
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

alternative modeling of blocking
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

modeling machine failures
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

slide22

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

failure rules
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

slide24

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

slide25

Linking States to Resources

Dialog box for failure declarations in the Resource module

Altiok / Melamed Simulation Modeling and Analysis with Arena

Chapter 11

impact of buffers in case of failures
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

estimating sojourn time distributions
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

batch processing
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

batch modified packaging line
Batch-Modified Packaging Line

Altiok / Melamed Simulation Modeling and Analysis with Arena

Chapter 11

slide32

Batch-Modified Packaging Line (Cont.)

Altiok / Melamed Simulation Modeling and Analysis with Arena

Chapter 11

slide33

Batch-Modified Packaging Line (Cont.)

Altiok / Melamed Simulation Modeling and Analysis with Arena

Chapter 11

synchronization and assembly

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

assembly operations
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