Article 1: Stochastic Modelling of Manufacturing Systems - Role of Performance Modelli... Page 1 of 3
Imperial College London
ISE-2 Surprise 97 Project
Stochastic Modelling of Manufacturing Systems Role of Performance Modelling in Automated
Manufacturing Systems
Written by Nick Chapman
Ever since the first production line was implemented by Henry Ford in 1913 to
produce an engine in 84 stages, their use as a method of manufacture has
become the dominant approach for mass production. The emergence of high
performance automated manufacturing systems (AMSs), has lead to the need
for methods of modelling these types of system in order to maximise
throughput, flexibility and competitiveness. This article intends to provide an
insight into the area of performance modelling and the methods used in
achieving their optimisation.
An AMS is a complex network of processing, inspecting and buffering nodes
connected by system of transportation mechanisms. For an AMS to be
considered viable as capital outlay it must be flexible in the product that it can
produce, so it should be able to last for several different product life cycles. It
must also have a level of fault tolerance to avoid costly breaks in the production
line in the case of sub system failure. It is also desirable that the line is capable
of increasing or decreasing output with the rise and fall of demand.
All of these specifications show the complexity of decision making in the field
of AMSs and the need for concise and accurate modelling methods. AMSs
belong to the domain of discrete event dynamic systems (DEDS) in which the
evolution of the system depends on the complex interactions of various discrete
events such as the arrival of raw materials, departure of finished goods, failure
of equipment etc. The state of DEDS changes only at these discrete points in
time instead of continuously. Over the last decade several models have come
about to describe DEDS and these can be grouped into two distinct areas.
„ Qualitative models are concerned with the logical aspects of system
evolution such as controllability, stability and the existence of deadlocks
in system operation, etc. This category also includes Petri Nets, extended
state machines and finitely recursive processes.
„ Quantitative models are concerned with the quantitative system
performance in terms of throughput and lead time. This category also
includes discrete event simulation, min-max algebra, Markov Chains,
stochastic Petri nets, queues, and queuing networks.
Quantitative models are a general term including performance modelling which
is the area of interest to this article.
Within the life cycle of an AMS various decisions are made concerning
implementation, design and operation of the system. The role of performance
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Article 1: Stochastic Modelling of Manufacturing Systems - Role of Performance Modelli... Page 2 of 3
modelling is to assist in these decisions in an affective way as possible. Typical
decisions at the planing stage include number and type of machines, number of
material handling devices, number of buffers, size of pallet pool and number of
fixtures, best possible layout, tool storage capacity, evaluate candidate AMS
configurations, part type selection, machine grouping, batching and balancing
decisions, and scheduling policies.
During the operational phase of an AMS performance modelling can be used to
assist decisions about how to cope with in the event of a breakdown, removal
or addition of resources and parts, optimal scheduling in the event of machine
failure or sudden changes in the product or its demand and in the avoidance of
unstable situations such as deadlocks.
Performance modelling is also used in the design stage of the system. It is used
in decisions such as whether to use central versus local storage, push
production versus pull production, shared versus distributed resources, the
effect of flexibility, etc. Performance predictions obtained using faithful models
can be used to convince customers or investors and also give the designer
another perspective on the design enabling better designs.
The performance of an AMS can be measured by a set of generic measures.
These are : manufacturing lead time, work in progress, throughput, machine
utilisation, capacity, flexibility, performance, and quality. Using performance
measuring these values can be evaluated and used to compare AMS
performances. The measures are quite dependant on each other and each is
important in its own right. Some typical questions that are asked and can be
answered using performance modelling are:
1. What is the probability that a particular product can be delivered before
the deadline?
2. What is the minimum number of working machines required so that the
average throughput of finished parts just exceeds the targeted
production?
3. How many fixtures/pallets are to be used in order to increase the average
machine utilisation beyond 80%?
4. Does the given AMS configuration have enough capacity to deliver the
required amounts of products in the set deadlines?
5. Which of the candidate layouts offers the best flexibility to part-mix
changes?
6. What is the minimum number of resources in the system (machines,
transporters, buffers) that would ensure that the probability of producing
at least 100 parts in a shift of 8 hours, in the presence of unscheduled
downtime, exceeds 95%?
7. What is the effect of machine blocking on throughput and manufacturing
lead time? Should we add one more buffer?
8. What are the potential bottleneck resources and congestion points in the
system?
9. Are there deadlocks in the system? What is the mean time to deadlock?
10. How do throughput and lead time change when we have one less
machine? One more machine? One more transporter? Some more
buffers?
11. Is there a spare capacity in the system to undertake some low-priority
jobs?
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Article 1: Stochastic Modelling of Manufacturing Systems - Role of Performance Modelli... Page 3 of 3
Performance evaluation falls into two broad categories; performance
measurement and performance modelling. Performance measurement is
primarily for existing systems and is most commonly used to monitor key
systems to enable re-configuration. Performance modelling can be split itself in
to two sub types; simulation modelling and analytical modelling. Simulation is
the original method of modelling and is still commonly used, there are many
computer based programs design solely for manufacturing simulations.
Analytical modelling is becoming more widely used and is a strong alternative
to simulation, there are many accepted models for manufacturing purposes such
as stochastic Petri nets, Markov chains and queuing theory. Both systems are
commonly used and each has its advantages and disadvantages which are two
deep to be explored within this article.
Performance modelling has become a very important part of automated
manufacturing system design and is equally important for maintaining the
system at its peak of ability. The manufacturing methods in use by companies
has change dramatically in recent years with the use of advance robotics and
computer control to optimise production, this in tern has lead to reduced prices
and higher quality of product. The production lines can only get better with
more modelling and investment and this is best achieved with the use of
performance modelling.
Bibliography
Stochastic Models of Manufacturing Systems, John A Buzacott, George
Shanthikumar
Usefulness: 6
Readability: 5
Comments: Designed for mainly for post-graduates and specialist level. A
strong knowledge of Statistics is require to appreciate fully the book.
Performance Modelling of Automated Manufacturing Systems,
N.Viswanadham, Y.Narahari
Usefulness: 6
Readability: 5
Comments: A good introductory book with a reasonable level of previous
knowledge required.
Last Updated 20th May, 1997
http://www.doc.ic.ac.uk/~nd/surprise_97/journal/vol1/njc1/
7/30/2005