Two Stage Flow Shop Scheduling under Fuzzy Environment

Abstract

Background/Objectives: The real life applications are complex in nature and demand the uncertainty as key characteristic in the problem. An algorithm incorporating the uncertain processing time and setup time of n-jobs on two machines to minimize rental cost of machines is described. The jobs to be processed as block and the transportation time between different units of production under particular rental situation is an addition to the existing problem. Methods/Statistical Analysis: The main characteristic as uncertainty in processing time and setup time is depicted with fuzzy triangular membership function. The basic set operations on fuzzy set theory are applied to obtain the mathematical solutions. A comprehensive defuzzification technique known as Yager’ formula is used in the proposed algorithm. The algorithm uses a heuristic approach to obtain the desired objective with constraints of job-block, transportation time under definite rental situation. Results/Findings: The sequence obtained using the proposed heuristic in the sample numerical problem minimizes the total rental cost of machines by minimizing the operation time of machines. The Johnson technique used in the algorithm minimizes total elapsed time and hence ensures the total minimum operational cost of machines. Conclusion/Findings: The algorithm put forward minimizes the operation time and therefore the rental cost of machines using the concept of processing of jobs as block called equivalent job-block along with the time taken in transporting a job from one machine to another in fuzzy environment. This algorithm allows the dynamical nature of the processing times using fuzzy triangular membership function which is easy to understand and straight in its approach.Keywords: Average High Ranking, Fuzzy Processing Time, Fuzzy Setup Time, Operation Time, Rental Cost