OCTOBER 19-20, 2012 - YMCA University of Science & Technology

Proceedings of the National Conference on
Trends and Advances in Mechanical Engineering,
YMCA University of Science & Technology, Faridabad, Haryana, Oct 19-20, 2012
cycle time. Low et al. [2] investigated the benefits of lot splitting in job shop scheduling with setup. The objective is
to determine a lot splitting strategy so that an optimal schedule can be obtained with the minimized make span.
3. Problem Statement:
We have considered a Static and Deterministic job shop scheduling problem with sequence dependent setup
times .The objective is to minimize the make span (C max ) i.e. completion time of the last job including determine
best job sequence for the problem using an asexual reproduction genetic algorithm, completion time of the jobs on
each machine, machines loading time, idle time for each machine, percentage of machine utilization, illustrate the
critical machines for the job shop problems.
3.1 Assumptions
• Machines never break down and are available throughout the scheduling period.
• All the jobs and machines are available at time zero.
• All processing time on the machine are known, deterministic and finite.
• Setup times for operations are sequence dependent and are not included in processing times
• Pre-emption is not allowed.
• Each machine is continuously available for assignment, without significant division of the scale into
shifts or days and without any breakdown or maintenance. The first machine is assumed to be ready
whichever and whatever job is to be processed on it first.
• Machines may be idle.
• Splitting of job or job cancellation is not allowed.
3.2 Parameter
i =Index for machines i=1,2,3…m Cj=Completion time of job ‘j’
j=Index for jobs j=1,2,3….n
4. Genetic algorithm:
Genetic Algorithm was introduced by John
Holland. A genetic algorithm is a problem solving method that uses genetics as its model of problem solving [1]. It
is a search technique to find approximate solutions for optimization and search problems. Genetic Algorithm (GA)
is Just like as a machine which derives its behavior from the image of the processes in growth of nature [1]. GA
handles a population of possible solutions. Each solution is represented through a chromosome coding and all the
possible solutions into a chromosome. A reproduction operator is determined. Reproduction operators are applied
directly on the chromosomes. Selection is done by using a fitness function. Selection is able to compare each
individual in the population. Each chromosome has an associated value corresponding to the fitness function and
used to perform mutations and recombinations over solutions [8].
Genetic algorithm loop over an iteration process to develop the new population. Each iteration process consists of
the following steps:
• Selection: The first step is consisting of selecting individuals for reproduction. This selection is done
randomly with a probability depending on the relative fitness of the individuals so that best ones are chosen
for reproduction than the poor ones.
• Reproduction: In the second step, children are produced by the selected individuals. For generating new
chromosomes, the algorithm can use both recombination and mutation.
• Evaluation: Then the fitness of the new chromosomes is evaluated.
• Replacement: During the last step, individuals from the old population are killed and replaced by the new
ones.
Genetic algorithm differs from other optimization and search procedures in following ways:
• Working of genetic algorithm is according to the parameter set with the help of codes, not the parameters it
selves.
• Searching is takes place in genetic algorithm from a population of points, not for a single one.
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