Modeling and Analysis of High Volume Manufacturing Systems

1
Modeling and Analysis of High Volume
Manufacturing Systems
2
Discrete vs. Continuous Flow and Repetitive
Manufacturing Systems(Figures borrowed from
Heizer and Render)
3
Operation Process Chart Example for discrete
part manufacturing(borrowed from Francis et. al.)
4
A typical (logical) Organization of the
Production Activity in Repetitive Manufacturing
Assembly Line 1 Product Family 1
Raw Material Comp. Inventory
Finished Item Inventory
S1,1
S1,n
S1,i
S1,2
Fabrication (or Backend Operations)
Dept. 1
Dept. 2
Dept. k
Dept. j
S2,1
S2,2
S2,m
S2,i
Assembly Line 2 Product Family 2
5
Major Layout Types(borrowed from Francis et. al.)
6
Advantages and Limitations of the various layout
types (borrowed from Francis et. al.)
7
Advantages and Limitations of the various layout
types (cont. - borrowed from Francis et. al.)
8
The product-process matrix
Production volume mix
Low volume, low standardi- zation
Multiple products, low volume
High volume, high standardization, commodities
Few major products, high volume
Process type
Jumbled flow (job Shop)
Commercial printer
Void
Disconnected line flow (batch)
Heavy Equipment
Connected line flow (assembly Line)
Auto assembly
Continuous flow (chemical plants)
Sugar refinery
Void
9
A conceptual characterization of the considered
environments

• Flow line A sequence of workstations supporting
  the production of a single part type.
• Each workstation consists of one or more
  identical servers executing one particular stage
  of the entire production process.
• The part processing time at each workstation
  follows some general distribution which must be
  defined in such a way that accounts for the
  various detractors affecting the station
  operations these detractors will include machine
  downtime, lack of consumables, operator
  unavailability, experienced set-up times,
  preventive maintenance, etc.
• Finished parts could constitute end items or raw
  material for some other downstream process.
• The operation of the line workstations can be
• synchronized through an interconnecting conveyor
  system, or
• decoupled through the installation of some
  buffering capacity between them.

10
Line Performance Measures

• Production rate or throughput, i.e., the number
  of parts produced per unit time
• Line capacity, i.e., the maximum sustainable
  production rate
• Line (expected) cycle time, i.e., the average
  time that is spend by any part into the line
  (this quantity includes both, processing and
  waiting time).
• Average Work-In-Porcess (WIP) accumulated at
  different stations
• Expected utilization of the station servers.
• Remark The above performance measures
  essentially provide a link between the directly
  quantifiable and manageable aspects and
  attributes of the considered operational
  environments and the primary strategic concerns
  of the company, especially those of
  responsiveness and cost efficiency.

11
Production Authorization Mechanisms

• The issue here is to what extent part production
  is triggered from actual orders or from
  forecasted demand.
• In a produce-to-stock scheme, a certain amount
  of end-item inventory is maintained in an effort
  to serve the experienced demand with zero lead
  time.
• Produce-to-stock operation is most appropriate
  for highly commoditized and standardized items.
• A key performance measure for produce-to-stock
  production systems is the fill rate, i.e. the
  percentage of the experienced demand that is
  actually met from stock. A desired fill rate is
  attained by maintaining an appropriate safety
  stock level, that is computed from the statistics
  of the experienced demand and cycle times.
• In a produce-to-order scheme, end items are
  produced in response to particular orders.
• Produce-to-order operation is more appropriate
  for (highly) customized items.
• A key performance measure for produce-to-order
  production is the attained service level, i.e.
  the percentage of orders that are served within
  the quoted lead time. A target service level is
  attained through informed lead time quotation and
  some appropriate capacity buffer.
• Currently, many systems are a hybrid scheme
  consisting of produce-to-stock and
  produce-to-order components. In particular,
  mass customization is supported by an
  assemble-to-order scheme where end-items are
  assembled to order from a number of
  sub-assemblies that are produced to stock.

12
Shop-Floor / Line Control Mechanisms

• Mechanisms that control the part release and
  advancement through the line.
• They are broadly distinguished into push and
  pull mechanisms.
• A push mechanism releases material into the
  line according to a target production rate, and
  material is advanced to downstream stations as
  early as possible.
• Typical instantiations of push systems are the
  asynchronous transfer line and the synchronous
  transfer line.
• A pull system controls the part release and
  advancement in the line taking into consideration
  the status of the various workstations in the
  line.
• Typical instantiations of pull systems are the
  KANBAN and the CONWIP (controlled) production
  lines.
• In general, pull systems reduce congestion,
  since they take into consideration the actual
  shop-floor status in their decision making, but
  the same mechanisms will also make them more
  inert in case of shifts in the production level.
• Both mechanisms are effectively implementable in
  a produce-to-stock or produce-to-order
  context.

13
Asynchronous Transfer Lines
W1
W2
W3
TH
TH
TH
TH
B1
B2
B3
M1
M2
M3

• Some important issues
• What is the maximum throughput that is
  sustainable through this line?
• What is the expected cycle time through the
  line?
• What is the expected WIP at the different
  stations of the line?
• What is the expected utilization of the
  different machines?
• How does the adopted batch size affect the
  performance of the line?
• How do different detractors, like machine
  breakdowns, setups, and maintenance, affect the
  performance of the line?

14
Synchronous Transfer Lines

• The key issue Assembly Line Balancing (ALB)
• Given
• a set of tasks to be supported by the line
  stations
• each possessing a nominal processing time,
• a number of precedence constraints among these
  tasks,
• and a target throughput,
• determine
• a partitioning of these tasks to a number of
  stations that observes the aforementioned
  specifications, while it minimizes the resulting
  number of stations (and therefore, the resulting
  labor cost).

15
KANBAN-based production lines

• Some important issues
• What is the throughput attainable by a certain
  selection of KANBAN levels?
• What is the resulting cycle time?
• How do we select the KANBAN levels that will
  attain a desired production rate?
• How do we introduce the various operational
  detractors into the model?

16
CONWIP-based production lines

• Some important issues
• Same as those for the KANBAN model, plus
• How can we compare the performance of such a
  system to that of an asynchronous transfer line
  and/or a KANBAN-based system?

17
Module Objectives

• Provide an analytical characterization of the
  operation of HVM systems and their performance,
  based on queueing-theoretic models
• Derive qualitative insights and quantitative
  results on the attributes and factors that shape
  the behavior and performance of these systems.
• Demonstrate the application of these results to
  the design and control of the considered class of
  systems
• Focus primarily on flow lines, since they are the
  main layout used in the context of high-volume,
  repetitive manufacturing.
• Also, flow line dynamics are easier to trace and
  analyze, and therefore, more enlightening in
  terms of qualitative and quantitative insights.
• However, many of the derived insights and results
  are extensible to more complex environments
  either directly or through some appropriate
  decomposition.

18
Plan for the remaining part of the module

• Modeling and Performance Analysis of Asynchronous
  Transfer Lines through a Series of G/G/m queues
• Modeling the impact of operational detractors
• Employing the above results in line diagnostics
• Design of Asynchronous Transfer Lines
• Design of Synchronous Transfer Lines (cf. the ALB
  problem in the module on Sequencing, Dispatching
  and Scheduling of HVM systems)
• Modeling and Performance Analysis of CONWIP-based
  production lines through Closed Queueing Networks
• An integrating framework for bounding and shaping
  the performance of a production line
• Analyzing the impact of batching on the system
  performance and designing optimized batching
  policies
• Understanding the relative advantages and
  disadvantages of the various push and
  pull-based production systems

19
The G/G/1 model

• Modeling Assumptions
• Part release rate Target throughput rate TH
• Infinite Buffering Capacity
• m identical servers
• Server mean processing time te
• St. deviation of processing time ?e
• Coefficient of variation (CV) of processing
  time ce ?e / te
• Coefficient of variation of inter-arrival times
  ca

20
Performance measures for the G/G/1 station

• Server utilization
• Expected cycle time in the buffer
  (Kingmans
  approx.)
• Expected cycle time in the station
• Average WIP in the buffer
  (by Littles law)
• Average WIP in the station
• Squared CV of the inter-departure times

21
Some Important Remarks

• The entire analysis of the previous slide is an
  approximation, since it derives from the provided
  approximation for CTq.
• The provided formula for CTq is exact for the
  M/M/m and M/G/1 stations.
• The station operation will be stable only if u
  TH te / m lt 1.0, i.e., only if the effective
  workload released into the station per unit of
  time is less than the available processing time
  of the station. Otherwise WIPq, CTq and CT will
  grow infinitely large.
• Notice that the requirement u lt 1.0 is also
  suggested by the provided expression for CTq
  since only then CTq takes finite positive values.
• The expression for CTq comprises three factors,
  each depending respectively upon (i) the
  variability of the processing and inter-arrival
  times, as expressed by the corresponding SCVs,
  (ii) the server utilization, and (iii) the mean
  processing time. An increase of any of these
  factors results in an increase of CTq, and also
  of CT, WIPq and WIP.
• Assuming a non-zero mean processing time, CTq0.0
  only if ca2 ce20.0 these are essentially the
  conditions of a paced / synchronous production
  line.
• The SCV of the inter-departure times can be
  approximated as a linear function of the SCVs of
  the inter-arrival and processing times.
  Furthermore, for u?1.0, cd2 depends primarily on
  ce2, while for u?0, cd2 depends primarily on
  ca2.

22
Analyzing an entire Production Line
TH

• Key observations
• A target production rate TH is achievable only
  if each station satisfies the stability
  requirement u lt 1.0.
• For a stable system, the average production rate
  of every station will be equal to TH.
• For every pair of stations, the inter-departure
  times of the first constitute the inter-arrival
  times of the second.
• Then, the entire line can be evaluated on a
  station by station basis, working from the first
  station to the last, and using the equations for
  the basic G/G/1 model.

23
Modeling the impact of operational detractors

• Effective processing time time that the part
  occupies the server
• Effective processing time Actual processing
  time
• any additional non-processing time
• Actual or otherwise natural processing time
  typically presents fairly low variability ( SCV lt
  1.0).
• Non-processing time is due to detractors like
  machine breakdowns, setups, operator
  unavailability, lack of consumables, etc.
• Detractors are distinguished to preemptive and
  non-preemptive. Each of these categories requires
  a different analytical treatment.
• Preemptive detractors are outages that take place
  during the actual processing of the part. Typical
  examples are machine breakdowns, lack of
  consumables, operator unavailability, etc.
• Non-preemptive detractors are activities that may
  take place between the processing of two
  consecutive parts. Typical examples are setups,
  preventive maintenance, operator breaks, etc.
• We want to determine the mean, variance and SCV
  of the effective processing time from the
  corresponding attributes of the natural
  processing time and some additional attributes
  characterizing the behavior of the various
  detractors.

24
Modeling the impact of preemptive detractors

• X random variable modeling the natural
  processing time, following a general
  distribution.
• to EX ?o2VarX co?o / to .
• T random variable modeling the effective
  processing time where
• Ui random variable modeling the duration of the
  i-th outage, following a general distribution,
  and
• N random variable modeling the number of
  outages during a the processing of a single
  part.
• mrEUi ?r2VarUi cr ?r / mr
• Time between outages is exponentially distributed
  with mean mf.
• Availability A mf / (mfmr) percentage of
  time the system is up.
• Then,
• te ET to / A or equivalently re 1/te
  A (1/to) A? ro

25
Breakdown Example

• Data Injection molding machine has
• 15 second stroke (to 15 sec)
• 1 second standard deviation (?o 1 sec)
• 8 hour mean time to failure (mf 28800 sec)
• 1 hour repair time (mr 3600 sec)
• Natural variabilityco 1/15 0.067 (which is
  very low)

26
Example Continued

• Effective variability

Which is very high!
27
Example Continued

• Suppose through a preventive maintenance program,
  we can reduce mf to 8 min and mr to 1 min

(the same as before)
Which is low!
28
Modeling the impact of non-preemptive detractors

• X random variable modeling the natural
  processing time, following a general
  distribution.
• to EX ?o2VarX co?o / to .
• NS average number of parts processed between
  two consecutive setups
• It is also assumed that the number of parts
  between two consecutive setups follows a
  geometric distribution, which when combined with
  the previous bullet, it implies that probability
  for a setup after any given job 1/ NS.
• Z random variable modeling the duration of a
  setup
• tS EZ ?S2 VarZ
• S random variable modeling the setup time
  experienced by any given job
• T random variable modeling the effective
  processing time XS
• Then,
• ES tS / NS VarS (?S2 / NS)
  tS2((NS-1) / NS2)
• te ET totS / NS
  
  

29
Setup Example

• Data
• Fast, inflexible machine (2 hr setup every 10
  jobs)
• Slower, flexible machine (no setups)

No difference!
30
Setup Example (cont.)

• Compare mean and variance
• Fast, inflexible machine 2 hr setup every 10
  jobs
• Slower, flexible machine no setups
• Conclusion

Flexibility can reduce variability.
31
Setup Example (cont.)

• New Machine Consider a third machine same as
  previous machine with setups, but with shorter,
  more frequent setups
• Analysis
• Conclusion

Shorter, more frequent setups induce less
variability.
32
Example Employing the presented results for line
diagnostics
Desired throughput is TH 2.4 jobs / hr but
practical experience has shown that it is not
attainable by this line. We need to understand
why this is not possible.
33
Diagnostics example continuedCapacity analysis
based on mean values
34
Diagnostics example continuedAn analysis based
on the G/G/1 model
i.e., the long outages of M1, combined with the
inadequate capacity of the interconnecting
buffer, starve the bottleneck!
35
Example Designing an asynchronous prod. line

• Design of a new 4-station assembly line for
  circuit board assembly.
• The four consecutive stations and the currently
  considered technology options for them (each
  option defines the processing rate in pieces per
  hour, the CV of the processing time, and the cost
  per unit in thousands of dollars).

• The above data correspond to the effective
  processing times.
• Each station can employ only one technology
  option.
• The maximum production rate to be supported by
  the line is 1000 panels / day.
• The desired average cycle time through the line
  is one day.
• One day is equivalent to one 8-hour shift.
• Workpieces will go through the line in totes of
  50 panels each, which will be released
• into the line at a constant rate determined by
  the target production rate.
• Design task Identify a line configuration that
  meets the above requirements while
• minimizing the equipment cost.
• Also, estimate the expected WIP at every
  station, when the line is operated at
• maximum production rate.

36
A baseline designMeeting the desired prod. rate
with a low cost
37
Reducing the line cycle time by adding capacity
to Station 2
38
Adding capacity at Station 1, the new bottleneck
39
An alternative optionEmploy less variable
machines at Station 1
This option is dominated by the previous one
since it presents a higher CT and also a higher
deployment cost. However, final selection(s) must
be assessed and validated through simulation.
40
Analyzing CONWIP-based flowlines with
single-machine stations as Closed Queueing
Networks (CQNs)

• Mean Value Analysis - the key underlying ideas
• A CONWIP-based flow line with single-machine
  stations and its WIP level set to W, can be
  modeled by a closed queueing network (CQN) with
  general processing distributions, W jobs in it,
  and the following structure
• II. In a CQN with W jobs and exponential
  processing times, the expected number of jobs
  observed at the various stations by a job
  arriving at some station Sj, is equal to the
  expected number of jobs observed at any random
  time at the same stations when the system is
  operated with W-1 jobs in it.
• III. Assuming that this effect applies in an
  approximate sense for more general distributions
  of the processing times, we proceed to develop an
  algorithm that will compute the performance
  measures of interest iteratively, for various W
  levels, starting with W0.

?
?
?
M1
M2
Mn
41
Notation
n number of stations te(j) mean effective
processing time at station j ce2(j) SCV for
effective processing time at station j TH(W)
the line throughput when operated with WIP level
W CT(W) expected job cycle time through the
line CTj(W) expected job cycle time at station
j when the WIP level is W WIPj(W) expected WIP
level at station j when the WIP level is W uj(W)
utilization of the server at station j when the
WIP level is W
42
Deriving the algorithm iteration

• CTj(W) Eremaining processing time for the job
  at the server of Sj
• (Enumber of jobs at station Sj-Enumber of
  jobs in service)te(j)
• te(j)
• But
• Eremaining processing time for the job at the
  server of Sj
• Prob(Server of Sj busy)?Eremaining process time
  busy
• uj(W-1)?Eremaining process time busy ?
• (b) Enumber of jobs at station Sj ? WIPj(W-1)
• Enumber of jobs in service ? uj(W-1)
• (d) uj(W-1) TH(W-1)? te(j)

43
Deriving the algorithm iteration (cont.)
Combining the results of the previous
slide But then, Obviously, for W0, CT(0)
TH(0) WIPj(0) 0 Furthermore, application of
the above formulae for W1 gives
(from Littles law)
44
Bounding the line throughputUpper bounds

• For W??, TH(W)?rb?minj1/te(j), the bottleneck
  rate of the line.
• rb can also be achieved with finite WIP in a
  deterministic setting, i.e., in a line with
  ce(j) 0, ?j, and synchronized with pace
  tb1/rb.
• However, by Littles law, a line with raw
  process time To, in order to produce at rate rb,
  will need a WIP level of WorbTo this WIP level
  is known as critical WIP.
• An interpretation of Wo is given by the
  following formula
• i.e., Wo is the level of WIP that we must
  maintain in the system in order to maintain the
  bottleneck utilization at 100. Otherwise, the
  bottleneck will starve.
• If WltWo, then in a deterministic setting we can
  pace the jobs through the system in such a way
  that CTTo. Hence, the maximal line throughput
  will be

45
Example Attaining the throughput upper bound
with balanced, deterministically paced line
46
Bounding the line throughputLower bounds (under
global non-idleness)

• Clearly, 1/To is a lower bound to TH(W) under
  global non-idleness, since this is the rate of a
  line with only one job in it, and therefore, no
  parallelism.
• This bound is also achievable under any other
  finite WIP level W, by a non-idling policy that
  moves all W jobs as a single batch from station
  to station. Indeed, for that policy

47
Example Attaining the throughput lower bound
through batching
t1
t2
t3
t4



2.0
W3
T 0
T 6
T 12
T 18
T 24
TH W / (W? To) 3 / 24 1 / 8
48
The W-TH(W) space
TH(W)
Ideal Operational Point
rb
1/To
1/To
1
WorbTo
W
49
The W-CT(W) Space
The depicted curves are induced from those
depicted in the W-TH(W) space, through Littles
law. In particular, upper bounds in the W-TH(W)
space provide lower bounds in the W-CT(W) space,
and vice versa, as follows
50
Practical System Performance

• The ideal performance is attained in an
  optimized, deterministic setting. this
  performance is typically compromised by
• the variability that is inherent in the system
  operations
• the impact of the applied control policies
  (e.g., the batching policy that defines the lower
  bounds for the system throughput - Notice,
  however, that these policies might be justified
  from some broader considerations).
• A benchmark case Maximizing the variability
  inherent in the system operation
• Single-machine stations
• Exponential processing times
• Balanced line, i.e., te(j) t, ?j
• Key feature All feasible states for this line
  are equiprobable.
• Mean Value Analysis (exact, since processing
  times are exponential)

Remarks As expected, TH(1) rb/Wo 1/To and
TH(?) rb. A performance that is worse than that
of the benchmark case is a strong indication of
mismanagement / bad practice.
51
Effective Mechanisms for Improving the System
Performance
The problem Given a line operating at a desired
throughput rate, TH, what are some possible
mechanisms to reduce the expected cycle time
through the line, CT (and through Littles law,
the line WIP, W) ? The key idea We need to
pull the curve describing the line performance
in the W-TH(W) space to the left. (i) Increase
rb (by adding capacity or making more effective
use of the existing capacity at the line
bottleneck(s))
52
Effective Mechanisms for Improving the System
Performance (cont.)
(ii) Add capacity to some non-bottleneck
station(s) (this addition essentially enables the
better catering to the bottleneck needs, but it
can help only to a limited extent)
TH(W)
rbrb
TH
1/To
1/To
1/To
1/To
W
Wo
1
W
Wo
W
(iii) Reduce the inherent variability at the
different stations the corresponding reduction
of the station CVs will pull the performance
curve in the W-TH(W) space closer to the curve
characterizing the upper bound. (iv) Increase
the line flexibility, which essentially enables
the better utilization of the bottleneck capacity
(and takes us back to item (i) above).
53
On the relative advantages of push and
pull-based production systems

• The WIP cap employed by pull systems provides a
  feedback mechanism for reacting to operational
  disruptions and prevents congestion.
• The avoidance of congestion further facilitates
  more flexible and responsive decision making in
  reaction to arising contingencies.
• Another benefit from avoiding congestion is that
  the WIP necessary to elicit a certain throughput,
  TH, from a pull system is typically lower than
  the WIP accumulated in this system when it is
  operated in a push mode and with the feeding
  rate equal to TH.
• WIP as a control variable is more easily
  measurable than throughput.
• The performance attained by a pull system is
  robust to the selection of the WIP level.
• However, this robustness also implies that the
  production rate of a pull system cannot be
  easily controlled through WIP cap adjustments,
  which further implies that effective deployment
  of pull systems necessitates non-volatile
  demand profiles (and raises the issue of active
  demand management).
• CONWIP systems can achieve higher throughput than
  their KANBAN-based counterparts because they
  provide the aforementioned advantages of
  pull-based operation while eliminating the
  negative impact of (internal) blocking that is
  inherent in the KANBAN mechanism.