Soft Computing for Problem Solving 2019 pp 171-183 | Cite as

# Flow Shop Scheduling Problem of Minimizing Makespan with Bounded Processing Parameters

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## Abstract

A three-machine flow shop scheduling problem of minimum makespan is addressed in this paper. The setup time and transportation time are considered as independent parameters of processing. Further, setup time, processing time and transportation time are considered to be stochastic rather than deterministic. It is observed that the actual value of these cannot be estimated in advance unless the processing of jobs is completed on each of the available machines and only prior information of lower and upper bounds is available. Since the exact value of the time required is not known in advance, there may not exist a unique optimal schedule of jobs. Therefore, it is desired to obtain the set of all dominating schedules and reduce the cardinality of solution set. To meet the claimed objective, the local and global dominance relations have been developed and the use of these relations is represented by numerical illustration.

## Keywords

Flow shop scheduling Dominance relation Bounded processing time Bounded setup and transportation time Makespan## Notes

### Acknowledgements

One of authors (Meenakshi Sharma) acknowledges the financial support provided by council of scientific and industrial research, New Delhi, India, in the form of SRF through grant number 09/135(0766)/2017-EMR-I.

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