A Comparative Study on Optimal Solutions of Flow Shop Scheduling Problems under Fuzzy and Intuitionistic Fuzzy Environment

G. Uthra, K. Thangavelu, S. Shunmugapriya

Abstract


This paper deals with the comparative study on the optimal solutions of flow shop scheduling problem under fuzzy and intuitionistic fuzzy environment. The processing times are represented as generalized intuitionistic triangular and trapezoidal fuzzy numbers which are then defuzzified into crisp values by the efficient centroid ranking method. This paper concludes that problems under intuitionistic environment yields better results and the approach is illustrated with numerical examples. 

Keywords: Fuzzy flow shop scheduling problem, Generalized Intuitionistic Trapezoidal Fuzzy Number, Branch and Bound, job block criteria.


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Amit Kumar, Pushpinder Singh, Parampreet Kaur and Amarpreetkaur(2010), A new approach for ranking of GTFN, International journal of computer, Electrical, Automation, Control and Information Engineering, vol:4,no.8.

G. Ambika and G.Uthra , Branch and Bound Technique in flow shop scheduling using fuzzy processing times, vol 8, No. 2, 2014,37-42.

A.P.G.Brown and Z.A.Lominicki (1966), Some applications of the branch and bound algorithm to the machine scheduling problem, Operational Research Quarterly, 17 (1966) 173-182.

D.Gupta (2011), Application of branch and bound technique for n x 3 flow shop scheduling in which processing time associated with their respective probabilities, MathematicalModeling and Theory, 2(1) (2011) 31-36.

D.Gupta, S.Sharma and S.Bala,(2012). Specially structured two stage flow shop scheduling to minimize the rental cost, International Journal of Emerging trends in Engineering and Development,vol 2, no.1, pp. 206-215.

T.Hong, and T.Chuang,(1999). New triangular fuzzy Johnson algorithm, Computer and Industrial Engineering, 36(1), 179-200.

E.Ignall and L.Schrage(1965), Application of the branch and bound technique to some flow shop scheduling problem, perations Research, 13(3) (1965) 400-412.

H.Ishibuchi, and K.H.Lee,(1996), Formulation of fuzzy flow shop scheduling with fuzzy processing time, In Proceeding of IEEE International Conference on Fuzzy system, 199-205.

T.Izzettin and S.Erol, Fuzzy branch and bound algorithm for flow shop scheduling,Journal of Intelligent Manufacturing, 15 (2004) 449-454.

Jing – Shing Yao and FrengTsc Lin,(2002), constructing a fuzzy flow shop sequencing model based on statistical data, International Journal of Appropriate Reasoning, 29(3), 215-234.

S.M.Johnson(1954), Optimal two and three stage production schedules with setup times include, Naval Research Logistics Quarterly, 1(1) (1954) 61-68.

L. Martin, and T. Roberto (2001). Fuzzy scheduling with application to real time system, Fuzzy sets and Systems, 121(3), 523-535.

S. McCahon and E.S.Lee,(1990). Job sequencing with fuzzy processing times. Computer and Mathematics with applications, 19(7), 31-41.

P. Sanuja and S. Xueyan, A new approach to two machine flow shop problem with uncertain processing time. Optimization and Engineering 2006, 7(3), 329-343.

T.P.Singh, D.Gupta,(2005), Minimizing rental cost in two stage flow shop, the processing time associated with probabilities including job block Reflections de ERA, 1(2),107-120.

T.P.Singh, Sunita and P.Allawalia,(2009). Fuzzy flow shop problem on two machines with single transport facility- An heuristic approach, Arya Bhatta journal of mathematics and informatics, 1(1-2), 38-46.

S. Aggarwal, D. Gupta, S. Sharma, (2013) ,Bi-criteria Three Stage Fuzzy Flowshop Scheduling with TransportationTime and Job Block Criteria, International Journal of Applied Operational Research, Vol. 2, No. 4, pp. 41-53

K.Thangavelu, G.Uthra, S.Shunmugapriya(2016) , Optimal Solution of Three Stage Fuzzy flow Shop Scheduling Problem Using Branch and Bound Technique, Global Journal of Pure and Applied Mathematics(GJPAM) ISSN 0973-1768 volume 12, Number 1.

. G.Uthra, K.Thangavelu, S.Shunmugapriya(2018), Ranking Generalized Intuitionistic Fuzzy Numbers, Internationa Journal of Mathematics Trends and Technology(IJMTT), volume 56 Issue 7.

K.Atanasssov, Instutionistic Fuzzy sets, Fuzzy sets and Systems, Vol.20(1986) pp. 87-96.

.K.Atanasssov, More on Instutionistic Fuzzy sets, Fuzzy sets and systems, Vol.33(1989) pp. 37-46.

.A. Nagoor Gani and V.N. Mohamed, A method of Ranking Generalized Trapezoidal Institutionistic Fuzzy Number, International Journal of Applied Engineering Research, ISSN 0973- 4562 Volume 10(2015) pp 25465-73.


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