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APPLICATION OF GENETIC
ALGORITHM TO FLOWSHOP
SCHEDULING PROBLEM
OFOLUWANYO, Clement Oghenovo.
First Viva Submission in partial fulfillment of
the requirement for the award of
Post Graduate Diploma in Production
Engineering
Faculty of Engineering
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University of Benin, Benin City
June 2011
CHAPTER ONE
INTRODUCTION
1.1 RESEARCH BACKGROUND
A flow shop is a manufacturing facility that produces one
or two similar products using high volume specialized
equipments. It is characterized by unidirectional flow of
work with a variety of jobs being processed sequentially in
a one pass manner; for example an assembly line. In a
flow shop the system flows continuously through a linear
process.
Arising from this definition, is a flow shop scheduling
problem in which all jobs must visit all machines or work
centre in the same sequence.
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Processing of a job must be completed on a current
machine before processing of the job is started on a
succeeding machine. Often the operation must be done on
all jobs in the same order. The machines are assumed to
be set up in a series and such a processing environment is
referred to as a flow shop (Baker, 1974). This means that
all jobs are initially available and that each machine is
restricted to processing one job at any particular time. In
assembly line mentioned earlier, as well as other
manufacturing facilities a number of operations need to be
done on every job.
Flow shop sequencing problems (FSP) has been well
studied in the field of combinational optimization. Stutzle
(1998) posited that a combinational optimization problem
is either a maximization problem or minimization problem
with an associated set of instances. FSP is a problem
normally faced by the Managers in production operations.
As Managers, they need to make decisions on each
activity that will maximize profit to the company.
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In FSPs, a set of n-jobs are programmed to be processed
with the same flow pattern on m-machine. The sequence
of job processing on all machines is the same hence there
is the permutation flow shop sequencing production
environment with no passing job. The number of possible
schedule for the n-job is n! A job that takes 0.01 sec for
instance to complete on one machine will require more
than two centuries for the job completion in m-machine,
where m is fifty for example in its job schedule analysis.
It is however true that the main objective of any
production facility is to maintain a continuous flow of
processing task with minimum idle time and minimum of
waiting time. This process minimizes the production time
or makes span and cost of production. The overall
objectives therefore of this process maximize the
efficiency of the operations reducing cost and maximizing
output or profit. Flow shop sequencing problem (FSP) is
similar to traveling salesman problem (TSP). TSP was first
published in a paper in 1954 by Johnson (Colin 1995) it is
also a combinatorial optimization problem.
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The idea of TSP is to find a tour of a given number of cities
visiting each city exactly once and returning to the
starting city where the length of this tour is minimized.
Flow shop is this similar to TSP in that the number of cities
represents the number of machines and the length of tour
represent time taken to produce a certain product on a
particular machine.
Flow shop sequencing problems are modeled on the
following assumptions in order to achieve its objective of
maximization output or profit.
i. The operation processing time on the machine are known
and fixed.
ii Setup times are included in the processing time and they
are independent of the job position in the sequence of
jobs.
iii At a time every job in processed on only one machine and
every machine process only one job.
iv. The job operation on the machine may not be preempted
(Marcel Seido Nazano 2002).
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From the foregoing, FSPs are seen as problems that has
no known fast solution. The time to solve the problem
using currently known algorithm, increases very quickly as
the size of the job to be done and the number of machines
grows. The problem have is to specify the order and
timing of the processing of the jobs on the machines with
an objective or objectives respecting the assumptions
stated above. This reason of difficult in solving FSP
problem makes must author to refer to FSPs as an N.P-
Hard problem or non-deterministic polynomial time
problem.
1.2 PROBLEM STATEMENTS
The main aim of setting up a production factory is to make
profit. This is obtained by maximization of productivity and
minimization of cost and makes span.
This goal can be achieved by optimal or almost optimal
scheduling of jobs in the production process. This project
intends to solve this optimization problem using the
genetic algorithm method. The objective function here is
to minimize completion time or make span.
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Sequencing problems are boarding divided into job shop,
assembly or flow shop and open shop.
In the job shop schedule, operation sequencing is on
multiple machines subject to some precedence constraints
among the operations.
The flow shop scheduling problem is a set of job that flows
through multiple stages in the same order.
In the open shop scheduling problem, the workshop has
several resources and routing of all the operation is free.
(Wikipedia).
This project is focused on assembly line problems or flow
shop problem.
Genetic algorithm method is the tool that will used to
solve job sequencing and optimization problem in this
thesis. The thesis will focus on finding the advantages and
limitations of genetic algorithm in solving optimization
problems.
1.3 RESEARCH OBJECTIVES
The objectives of this research work are,
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1. Application of genetic algorithm to determine the
sequence of jobs in order to minimize the flow time or
completion time also called make span.
2 Determination of the limitation of genetic algorithm in
solving flow shop sequencing problem.
1.4. RESEARCH SCOPES
Genetic algorithm is a research instrument. They are
usually random search strategies which have been used
successfully to find near optimal solution to complex
problems.
In implementation of genetic algorithm (GA) in solving
problems, certain information in particular problem is
overlooked. To make use of this information, one need to
modify the coding of the search space and of the
operators that constitutes genetic algorithm. This is a
specific problem task.
This project intends to address this issue with regards to
solving the permutation flow shop problem (FSP).
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A permutation flow shop, is a job processing facility which
consists of several machines and several jobs on the
machines. In this arrangement, all jobs follow the same
machine or processing order. The flow shop by definition
implies the job processing is not intercepted once it is
started. The objective hence is to find a sequence for the
jobs so that the make span or the completion time is
minimized. This is however a difficult problem to solve in a
reasonable amount of line.
1.5 RESEARCH METHODOLOGY
Three main steps are used in this research work. The first
step is the literature review. In literature review, previous
methods that were used to solve flow sequencing problem
are modeled and simulated to ensure the algorithm are
working as reported in scientific books. The limitations of
these algorithms then identified.
From the identified limitations, a new sequencing pattern
is developed as the propose solution to the flow shop
sequencing problem. To prove the efficiency of genetic
algorithm in solving flow shop problem, various kinds of
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problem will be performed. The results of the performance
will be analyzed as the final step of this research.
Numerical analysis of flow shop sequencing problem will
also be performed.
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CHAPTER TWO
2.1 INTRODUCTION
This chapter presents an overview of related previous
work in the area of genetic algorithms and its application
mainly in relations to solving flow shop problem. There is
an attempt at explanation of the term genetic algorithm
(GA) and the steps that are taken to solve the FSP
problem using genetic algorithm method.
2.2 GENETIC ALGORITHM
Genetic Algorithm (G.A) is a research instrument that has
been evolved from the Darwinian theory of biological
evolution. It mimics this theory to evolve solutions to real
world problems. It is an optimization technique based on
natural evolution.
Genetic algorithm was introduced by John Holland in 1975
(Othman 2002). It works on the concept of survival of the
fittest and provides a method of searching which does not
need to explore every possible solution in the feasible
region to obtain a good result (Othman 2002)
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Genetic algorithm is one of the most representative
members of modern heuristic techniques (Holland 1975)
G.A. maintains a pool of tentative solutions for the
problem under consideration and uses the principles of
natural evolution namely adaptation and survival of the
fittest to guide the generation of new promising
selections. These solutions are constructed using some
reproductive operators. These operators are,
recombination and mutation operators. The former is
intended to combine the positive features of two solutions
to create a new solution and it has been traditionally given
a central role in the functioning of the algorithm. For the
later, its mission is to preserve the diversity in the solution
pool (Carless Cotta et al, 1978).
G.A is therefore a consciously developed instrument for
solving machine component grouping problem in
manufacturing systems or industries. It provides a
collection of satisfactory solutions for a two objective
environment allowing the decision maker to select the
best alternatives.
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2.3 PRINCIPLES OF GENETIC ALGORITHM
Genetic algorithm (G.A) follows the evolution theory of
Darwin. It is an adaptation of evolution to solving basic
human problems. In his works on G.A John Holland of the
Michigan University published his adaptation of natural
process to design artificial systems having properties
similar to natural systems.
G.A. is a computerized iterative search optimization
technique that is based on the mechanics of natural
selection and natural genetics. It deals with population of
solutions rather than a single solution. It provides near
optimal schedules. The optimal value depends on the
operators like cross-over, mutation, number of iteration
(i.e. generations), encoding etc. In every generation, a
new set of artificial individual (strings) are created. This
algorithm combines survival of the fittest amongst string
structure. These operators listed above are genetic
principles that are applied in programs when G.A. is
applied to other human endeavour such as aircraft design,
criminology, neural networks, construction, traveling
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salesman problem, flow shop problem, turbine blade
design etc.
2.3.1 BASIC ELEMENTS OF GENETIC ALGORITHM
The basic elements of genetic algorithm are:-
1. ENCODING
Encoding is of various types .For example we have binary
encoding, permutation encoding, value encoding, tree
encoding etc. However, the focus of this project work is on
permutation encoding.
Encoding means changing of information into a form that
can be processed by a computer. In permutation
encoding, every chromosomes is a string of numbers
which represents number in a sequence. For example a
chromosome A and B can be encoded.
Chromosome A 1 5 3 2 6 4 7 9 8
Chromosome B 8 5 6 7 2 3 1 4 9
Permutation encoding is used for ordering problems as in
flow shop or traveling salesman problems.
2. CROSSOVER
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Crossover occurs in genetic algorithm and programs when
two member of a population (chromosomes) are selected
for reproduction. The selection of any particular
chromosome is dependent on the relative fitness of such
chromosome to solving the problem being tackled.
Sometimes called recombination, crossover entails the
process of combining the attributes of two chromosomes
to produce one or more new ones that inherit some or all
of the attributes of the parent chromosomes. There are
different types of crossover. They include, one point
crossover, two point crossovers, uniform cross over,
arithmetic crossover, partially mapped crossover, cycle
crossover etc.
3.FITTNESS AND SELECTION
Fitness is one of the main concepts in Darwinian theory of
evolution. It gives direction to genetic algorithm in its
pursuit of improvement in problem solving. Fitness refers
to an individuals ability to compete within an environment
for available resources.
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In genetic algorithm, the fitness function determines the
extent to which the system must go with a particular
problem.
Selection technique adopted in genetic algorithm
determines the efficiency of G.A in solving a problem. It
entails the process of choosing a fit chromosome from the
population. The primary task of any adopted selector is to
measure the relative fitness of each chromosome. The
Roulette wheel is one method in use for selection in
genetic algorithm applications.
4. MUTATION
Mutation is change in the genetic structure of an organism
that distinguished it from others of the same type.
Mutation results in a new trait which can be inherited.
In G.A, mutation represents random element in creation of
new solution and ensures movement in search space
independent of existing solutions and helps in decreasing
the probability of a solution being trapped in local
extreme. Mutation operation randomly changes the
offspring resulting from cross over.
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2.3 FLOWSHOP SCHEDULING PROBLEM (FSP)
A Flow Shop is a manufacturing facility that produces one
or two similar products using high volume specialize
equipment; for example an assembly line. The system
flows continually through a linear process.
A flow shop schedule is one in which all jobs must visit
machines or work centre in the same sequence.
Processing of a job must be complete in a current machine
before processing of the job is started on a succeeding
machine. This means that initially all jobs are available
and that each machine is restricted to processing only one
job at any particular time. Since the first machine is the
facility machine, all jobs must necessarily start procession
from there before moving on to the next machine. The
objective of all production industry is to complete the
production process within the shortest possible time or
make span.
Many researchers have looked into the efficient operation
of transfer lines. Different methods have been dealt with.
Most of them have dealt with the effect of buffer
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capacities and equipment reliability on line performance.
For example, Buzacott (1972), Ignall and Silker (1977),
Elsayed and Turley (1980), Grover (1982), Gershwin and
Schink (1983), Savsar and Biles (1984) and EL Tamini and
Savsar (1987) have all done some work in this regard.
Others such as Gershin ans Schink have developed
analytical model for three stage transfer lines with
machine failures.Commault and Dallery (1990) proposed
models to determine the production rate of transfer lines
without buffer storage. They developed heuristics rules to
estimate the amount of storage space required to reduce
the effect of machine break downs. Bolat et al (1984)
addressed the issue of assembly line scheduling without
considering the possibility of duplicate stations on the line.
Inman and Leon (1984) considered the analysis of serial
duplicate stations on automated production lines. They
posited that duplicate stations are generally useful for
smoothening out production if some stations are slower
than the others or if they are subject to failures more
often than others. This position however have the
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disadvantage of want of large space which results in
additional cost of employing material handling system and
possibly re-sequencing of the products if the entry
sequence is to be maintained.
From the foregoing analysis it is pertinent to state that
performance of a flow shop having duplicate stations is
affected by the job scheduling policy adopted by the
Managers. For this reason, Inman and Leon (1994)
stimulated a complete line using duplicate stations under
the following assumptions. They assumed that the
sequence of arriving jobs is fixed, i.e. the job are released
to the stations in the order they arrived, thus the only
decision to be made is the allocation of the jobs to the
stations. They also assumed that the processing time is
constant. With these assumptions, they tested for
different policies under which jobs are alternately sent to
the two duplicate stations.
Job scheduling is developed with respect to certain
objectives or goals such as; meeting due dates,
minimizing flow time and work- in-process minimizing
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makes span (the completion time for last job to leave the
system) minimizing the idle time or maximizing
throughput and resource utilization. This shows that
problems arising in production scheduling are difficult in
the technical sense. In general flow shop scheduling
problem are combinational and complex (Gavey and John
1979). Production scheduling involves a large number of
jobs and machines subject to a set of constraints and
objectives (Lee et al 1993).
Job scheduling problems are also classified on various
schemes. These are static or dynamic single-product or
multiple-product, single processor or multiple processor
facilities etc. This research work seeks to concern itself
with single product flow shop problem (FSP).
Inman and Leon (1994) with an intention to finding
solution to FSP simulated a complete line with assumption
that the sequence of arrival of jobs is fixed and that the
processing time is constant. In their test they used four
different policies for operating the serial duplicate
stations.
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The first policy is the alternating policy in which jobs are
alternately sent to the two duplicate stations.
In the second policy called Tandem, jobs are released to
the duplicate stations in tandem. In other words the only
time jobs are allowed to enter the pair of duplicate station
is when both stations are empty and also at least two jobs
are on queue. They discovered that these two policies
cause throughput inefficiencies.
Other policies also investigated by Inman and Leon
includes, the greedy assignment policy which assigns jobs
that are arriving to the farthest accessible station. This
policy resulted in blocking of the downstream duplicate
station by the upstream one. The time left policy which
considers the expected processing time left on jobs that
are already in the duplicates stations. This policy attempts
to improve on the greedy algorithms short comings.
In their conclusion, Inman and Leon (1994) concluded that
the time left policy is optimal for simple problems.
Ng (1995), studied the problem of determining the optimal
number of duplicate process tanks with the objective of
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maximizing the throughput for a given tank configuration
of a single host circuit board production line. He
formulated the problem as a mixed integer program and
derived the properties of the optimal solution. Ng (1995)
developed an algorithm to determine the optimal number
of duplicate stations that maximizes the productivity of
the system.
Savsar and Allahvedi (1999) addressed the problems of
duplicate station scheduling with respect to three
objectives functions; minimizing mean flow time, make
span and station idle time. The work was the first
analytical attempt to solve the problem. In their works,
they assumed that all jobs are available at time zero to be
scheduled and hence two decisions needed to be made.
One was how to allocate the job to the stations and the
other was how to sequence the jobs. Other methods have
also been used in a attempted at solving FSP. Meta
heuristics is one of those methods that have been used to
solve FSP problems or complex combinational optimization
problems. Holland (1975), Osman and Laporte (1995) and
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Reeves (1995) have all applied this method. Traditional
techniques at finding solution to FSPs have provided exact
analytical solution to highly specific and restricted
problems or approximate solutions to fairly general
classes of problems. Modern approaches to the problem
have involved techniques such as simulated annealing and
tabu search with improved results. Genetic algorithm is
one of such modern approaches introduced by Holland
(1975) but whose potential for solving combinational
optimization problem was only latterly well explored. Mott
(1991) discussed how G.A. can be used to drive suitable
schedule for a serial flow shop.
Bolat et al (2005) provided a persuasive evidence of the
power of G.A. to generate high quality solutions and
showed that G.A. compares favourably with modern
approaches with respect to efficiency. As an extension of
these previous works examined above this research work
seeks to consider the application of G.A. in serial stations
with n-jobs. The objective is to minimize total complete
time otherwise called make span and maximize production
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or profit. In this regard the GA optimal returns will be
considered visa vice that of the orthodox Johnson
algorithm.
REFERENCES
1. ADUSUMILLI KUMAR, et al. A Genetic Algorithm for
the Two Machine Flow shop Problems. International
Journal of Computers, Communications & Controls.
2. BAUDET, P et al, A Genetic Algorithm for Batch
Chemical Plant Scheduling.
3. BOUKEF, HELA. et al (2007). A Proposed Genetic
Algorithm Coding for Flow Shop Scheduling Problems.
International Journal of Computers, Communications &
Controls. Vol 1 pp 229-240.
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4. DIPAK LAHA and SAGAR U. (2011). An Efficient
Heuristic Algorithm for m-Machine No-Wait Flow Shop.
Proceeding of the International Multi-Conference of
Engineers and Computer Scientist. VI
5. GUPTA KUMAR PREM & HIRA, D.S, (2009).
Operations Research. S Chand & Company Limited. Ram
Nagar, New Delhi. Pp 404-446.
6. LING WANG, et al. (2005). An Effective Hybrid
Genetic Algorithm for flow shop Scheduling with Limited
Buffers, Journal of Computer & Operation Research.
7. MARCELO SEIDO NAGANO, (2002). A ConstructiveGenetic Algorithm for Permutation Flow shop
Scheduling. Journal of the Operation Research Society.
8. RAJASEKARAN, & VIJAYALAKSHMI, G.A,
(2004).Neural Networks, Fuzzy logic, and Genetic
Algorithms; Synthetic and Applications. Prentice Hall of
India Private Limited. New Delhi, pp 225-293.
9. SAUVEY, C and SAUER N. (2011).An EfficientGenetic Algorithm for permutation Flow shop Problem
with Particular Blocking. 8th International Conference of
modeling and Simulation.
10. SHARMA, J.K, (2009). Operations Research, Theory
and Applications. MacMillan Publishers India Ltd. New
Delhi. pp 723-740.
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