Fuzzy Branch and Bound Solution for a Flow-shop Scheduling Problem

N. Selvamalar1 and V. Vinoba2

1Research Scholar, RMK College of Engg. and Tech, Puduvoyal, INDIA. 2Research Guide, K N Govt. Arts College (Autonomous), Thanjavur, INDIA.


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 and trapezoidal fuzzy numbers are used in1,7 to solve fuzzy flow-shop scheduling problems. In this work, octagonal fuzzy numbers are used to represent those vague job processing times in flow-shop production systems. The branch and bound algorithm of Ignall and Scharge which is modified to fuzzy scenario7 is used to solve the m jobs and n machines problem. The Fuzzy makespan and fuzzy mean flow times are then calculated for making decisions which can be used for further analysis. Examples are illustrated to explain the approach.MSC 2010 No.:90C70,97M40.

Keywords :Flow-shop scheduling, Branch and bound, Octagonal fuzzy numbers, Ranking methods.

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