Improved makespan of the branch and bound solution for a fuzzy flow-shop scheduling problem using the maximization operator

V. Vinoba; N. Selvamalar

doi:10.26637/MJM0701/0018

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

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

V. Vinoba Department of Mathematics, KN Government Arts College (Autonomous), Thanjavur, India.
N. Selvamalar Department of Humanities and Basic Sciences, Aditya Engineering College, Andhra Pradesh, India.

Pages: 91-95
Date Published: 01-01-2019
Vol. 7 No. 01 (2019): Malaya Journal of Matematik (MJM)

G. Ambika and G. Uthra, Branch and bound technique in flow-shop scheduling using fuzzy processing times, Ann. Pure Appl. Math., 8(2)(2014), 37-42.

V. Dhanalakshmi and Felbin C. Kennedy, Some aggregation operations on octagonal fuzzy numbers and its applications to decision making, Int. J. Math. Sci. Comput., 5(1)(2015), 52-57.

E.J. Ignall and L.E. Scharge, Applications of the branch and bound technique for flow-shop Scheduling problems, Oper. Res., 13(1965), 400-412.

Izzettin Temiz and Serpil Erol, Fuzzy branch and bound algorithm for flowshop scheduling, J. Intell. Manuf., 15(2004), 449-454.

A. Kaufmann and M.M. Gupta, Introduction to Fuzzy Arithmetic, Van Nostrand-Reinhold, New York, 1985.

S.U. Malini and Felbin C. Kennedy, An Approach for solving Fuzzy transportation problem using octagonal fuzzy numbers, Appl. Math. Sci., 7(54)(2013), 26612673.

C.S. McCahon and E.S. Lee, Job Sequencing with fuzzy processing times, Comput. Math. Appl., 19(7)(1990), 3141.

Michael L. Pinedo, Scheduling, Theory, Algorithms and Systems, Springer, Fourth Edition, 2003.

V. Vinoba and N. Selvamalar, Fuzzy CDS Algorithm For A Flowshop Scheduling Problem, International Journal of Mathematical Archive, 8(9)(2017), 1-6

V. Vinoba and N. Selvamalar, Fuzzy Branch and bound solution for a flow-shop scheduling problem, J. Comp. & Math. Sci., 8(3)(2017), 85-95.

V. Vinoba and N. Selvamalar, Fuzzy Johnson Algorithm for a flow-shop scheduling problem with octagonal fuzzy processing times, presented in ICCSPAM 2018, Coimbatore, India.

V. Vinoba and N. Selvamalar, Nawaz-Enscore-Ham Algorithm for a Permutation Flowshop Scheduling Problem in Fuzzy Environment, Journal of Applied Science and Computations 5(9)(2018), 1010-1022.