Harendra Kumar1, Pankaj Kumar1* and Manisha Sharma2
Author Address :
1Department of Mathematics and Statistics, Gurukula Kangri University, Hardwar-249404, Uttarakhand, India.
2Department of Mathematics, Panjab University, Chandigarh-160014, Punjab, India.
A flow shop is a production system in which machines are arranged in the order in which operations are performed on jobs. The flow shop is characterized by a flow of work that is unidirectional. In this paper, a new hybrid optimization (NHO) algorithm combining branch and bound (B&B) technique with genetic algorithm (GA) is proposed for solving flow shop scheduling problem (FSSP). Triangular and trapezoidal fuzzy numbers are used to represent processing times of jobs on each machines which are more realistic and general in nature. The present algorithm is divided into two phases. In the first phase, an initial schedule is constructed by using branch and bound technique. The processing times have been defuzzified into crisp one. The second phase finds the best schedule of the jobs by genetic algorithm for fuzzy processing times. The performance of a genetic algorithm depends very much on the selection of the proper genetic operators. In this paper, partially matched crossover operator for crossover and shift mutation operator for mutation are used. Numerous examples are illustrated to explain the proposed approach. Finally, the experimental results show the suitability and efficiency of the present NHO algorithm for optimal flow shop scheduling problem.
Flow shop scheduling, branch and bound technique, genetic algorithm, fuzzy numbers, fuzzy processing times.
Article Info :
Received : December 24, 2017; Accepted : January 21, 2018.