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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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