Queueing Analysis in Manufacturing Systems

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Queueing Analysis in Manufacturing Systems

• Dr. Quan-Lin Li
• School of Mathematics and Statistics
• Carleton University
• Ottawa,Ontario, Canada K1S 5B6

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Outline of This Talk

• Simple introduction to manufacturing systems
• Modeling analysis
• 1. Product-form manufacturing networks
• 2. Non- product-form manufacturing networks
• Summary

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Simple introduction

• Manufacturing processes
• Manufacturing and market

Factory
Factory
Source of raw materials
Market for goods
4
Classification of manufacturing systems
Simple introduction

• Based on manufacturing transformation process
• 1. Continuous type Chemical, oil, food
  industries
• 2. Discrete type Electronics, computer and
  goods industries.
• 1). Assembly
• 2). Non-assembly.
• Based on volume of production
• 1. Mass manufacturing systems
• 2. Batch manufacturing systems.

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Volume of production
Simple introduction
Mass
Batch
Job shop
Transfer line
Production line
FMS
FAS
1. Automation and production volume
decrease 2. The flexibility of the system
increases.
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The role of Market
Simple introduction
Market changes are the driving force that
manufacturing is moving away from mass
manufacturing systems to low volume and high
flexible systems.
Past
Factory
Buffer
Customer
Now
Factory
Customer
Product
Order
1. The marketplace has change dramatically in
the last twenty or so years 2. Customers have
become more discerning, requesting a wide variety
of highly quality product at competitive
price 3. The manufacturer tries to interact
more closely with the customer 4. The life
period of product becomes relatively short in
some setting.
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The role of Market
Simple introduction
Mass
Batch
Jobshop
ETO
ATO
MTO
MTS
To illustrate the evolution of the market
role, we see the following four types of
manufacturing environments 1. Make to stock
(MTS) 2. Assemble to order (ATO) 3. Make to
order (MTO) 4. Engineering to order (ETO).
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Mass manufacturing systems
Simple introduction
--Workstation
--Buffer
1. Simple routines 2. Fewer type 3. High
production rate 4. Low flexibility 5.
Emphasis on efficiency and economy of scale in
market 6. Used in assemble to order (ATO) An
order-driven part and a forecast-driven
part.
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Classification of mass manufacturing systems
Simple introduction
Production-flow-layout
Transfer line
Production line
Fluid line
Single
Multiple
Single
Multiple
Mixed
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Batch manufacturing systems
Simple introduction

• Batch manufacturing systems are a very important
  sector within the entire manufacturing industry,
  and will become more and more important in the
  future.
• Batch manufacturing systems contains two crucial
  types
• 1. Flexible manufacturing systems (FMS)
• 1). Flexible manufacturing cell (FMC)
• 2). FMS
• 3). Flexible manufacturing line (FML).
• 2. Flexible assemble systems (FAS).

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Flexible manufacturing systems
Simple introduction
Material handling system
Tool delivery system
1. Computer-controlled configuration of
semi-independent work-stations 2. Material
handling system designed to efficiently
manufacture several types of parts at low to
medium volume.
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Flexible manufacturing systems
Simple introduction
Volume
FML
High
FMS
Medium
1. Reduced set-up time 2. Reduced production
cycle times 3. Reduced WIP storage
Low
FMC
Flexible
Low
Medium
High
4. Increased machine utilization 5. Increased
flexibility.
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Flexible assemble systems
Simple introduction
Carousel
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Modeling analysis
Mathematical tools for manufacturing systems

• Queueing networks
• Maxmin linear algebra
• Petri net
• Stochastic program
• Simulation
• Infinitesimal perturbation analysis
• Singular perturbation

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Introduction to queueing theory
Modeling analysis

• Some distributions
• Markov chains Renewal processes Regenerate
  processes Brown motions Self-similar processes
• Statistics
• Single-server queues
• multi-server queues
• Product-form queueing networks
• non-product-form queueing networks

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Performances of manufacturing systems
Modeling analysis

• Stationary production rate
• Production variance
• Main delay times
• Satisfied probability
• Reliability indices
• Occupied rate of machines
• Others

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Production lines
Modeling analysis
1. Decomposition method 2. Flow equilibrium 3.
Approximations
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Product-form manufacturing networks
Modeling analysis

• Close Jackson networks
• Open Jackson networks
• Semi-open Jackson networks
• Time-invertibility conditions
• Product-form networks
• Generalized Product-form networks

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Non-product-form manufacturing networks
Modeling analysis
Methods
Dimension
Comments
More complete
Generating function
2 or 3
Compensation methods
Better
2
Diffusion approximation
OK
2
Matrix-analytic methods
Weak
2
Precedence relation
Special model
n
Power series algorithm
Non-complete
n
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Non-product-form manufacturing networks

• Haight (1958) proposed the shortest queueing
  model with two parallel waiting line
• Kingman (1961), Flatto and Mckean (1977) and
  Knessl et al. (1986, 1987) used two-dimensional
  generating function for studying the model, and
  obtained the asymptotic behavior of joint
  distribution of queue lengths.

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Non-product-form manufacturing networks

• Adan et al. (1990,1991) proposed a compensation
  method, which is effective for some special
  two-dimensional models.
• Adan et al. (1996) studied shortest expected
  delay routine (including M/Er/1).

n
m
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Non-product-form manufacturing networks

• Cohen (1987) considered the longer queueing model
• Cohen described the longer queue (including
  general service time) as a boundary value
  problem. Flatto (1989) applied the method of
  generating function to further discuss this
  model.

server
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Non-product-form manufacturing networks

• Takacs (1968) studied two queue attended by a
  single server
• Eisenberg (1979) used the method of generating
  function for this model.

server
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Non-product-form manufacturing networks

• Hofri (1978) proposed a multiprogramming queueing
  model
• He used the method of generating function to
  study this model. Adan (1993) applied the
  compensation method to discuss the model.

IO
Queue 2
Queue 3
CP
Queue 1
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Non-product-form manufacturing networks

• Flatto and Hahn (1984, 1985) presented the
  queueing model with a arrival putting two demands
• They analyzed the model using the method of
  generating function. Zhang (1990) and Wright
  (1992) further studied this model.

server
server
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Non-product-form manufacturing networks

• For two-dimensional queueing models, there also
  are other models according two classes 1)
  Customers choose a queue and 2) servers choose a
  customer. For example,
• Priority queues
• Tandem queues
• Sharing server queues
• Polling queues

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Non-product-form manufacturing networks

• Model one The two-dimensional Markov chain with
  rate diagram given by

n
m
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Non-product-form manufacturing networks

• Model second The two-dimensional Markov chain
  with rate diagram given by

n
m
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Summary

• All problems remain open if the dimension is
  larger than three. Very limited results for
  higher-dimensional problems are provided by the
  methods of Precedence relation and of power
  series. The method of generating function seems
  more promising in studying higher-dimensional
  models. The other three methods will face more
  theoretic difficulties.

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Summary

• Can the compensation method be generalized to
  deal with two-dimensional Markov chains with
  block-structure?
• Can the method of diffusion approximation be
  generalized to deal with two-dimensional Markov
  chains with block-structure?

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Thanks
Any questions
For any question