Improved makespan of the branch and bound solution for a fuzzy flow-shop scheduling problem using the maximization operator
Authors :
V. Vinoba 1 and N. Selvamalar 2*
Author Address :
1 Department of Mathematics, KN Government Arts College (Autonomous), Thanjavur, India.
2 Department of Humanities and Basic Sciences, Aditya Engineering College, Andhra Pradesh, India.
*Corresponding author.
Abstract :
In practical situations, the processing times are not known exactly i.e., they are not crisp. They lie in an interval. A fuzzy number is essentially a generalized interval which can represent these processing times naturally. In the literature, Triangular, trapezoidal and octagonal fuzzy numbers are used in to solve fuzzy flow-shop scheduling problems with the objective of minimizing the makespan using the branch and bound algorithm of Ignall and Scharge which is modified to fuzzy scenario. The fuzzy makespan and fuzzy mean flow times are then calculated for making decisions using fuzzy addition and fuzzy subtraction. While calculating the waiting time and completion times of a job on a machine,fuzzy subtraction leads to negative processing times which are not realistic and hence they are neglected for the evaluation of the makespan. In this paper, the makespan is calculated using the fuzzy maximization operator which in turn improves the makespan in comparison with fuzzy subtraction.
Keywords :
Flow-shop scheduling, Branch and bound, Octagonal fuzzy numbers, Ranking methods,Fuzzy maximization.
DOI :
Article Info :
Received : October 27, 2018; Accepted : January 09, 2019.
