Bi-criteria Three Stage Fuzzy Flowshop Scheduling with Transportation Time and Job Block Criteria

Scheduling is an enduring process where the existence of real time information frequently forces the review and modification of pre-established schedules. The real world is complex and complexity generally arises from uncertainty. From this prospective the concept of fuzziness is introduced in the field of scheduling. The present paper pertains to a bi-criterion in n-jobs, three machines flowshop scheduling to minimize the makespan and the rental cost of the machines taken on rent under a specified rental policy in which processing time, transportation time are in fuzzy environment and are represented by triangular fuzzy membership function. Further, the concept of job block to represent the relative importance of some jobs over other is also introduced. A heuristic algorithm to find optimal or near optimal sequence optimizing the bi-criteria is discussed. A numerical illustration is given to demonstrate the computational efficiency of proposed algorithm.