Formulation of fuzzy flowshop scheduling problems with fuzzy processing time

First we explain how to calculate the completion time of each job in fuzzy flowshop scheduling, where the processing time of each job at each machine is given by a fuzzy number. For calculating the completion time, we use fuzzy arithmetic on fuzzy numbers. Next we explain how scheduling criteria (e.g., makespan, maximum delay and total delay) can be defined in our fuzzy flowshop scheduling problems. Because the processing time is given as a fuzzy number these scheduling criteria are also calculated as fuzzy numbers. Then we define the concept of non-dominated solutions based on an inequality relation between fuzzy numbers. Using a small size example, we illustrate that a fuzzy flowshop scheduling problem with a single scheduling criterion has multiple non-dominated solutions. Finally we suggest the use of a multi-objective genetic algorithm as a heuristic method for large size fuzzy flowshop scheduling problems