Evaluate the fuzzy completion times in the fuzzy flow shop scheduling problems using the virus-evolutionary genetic algorithms

The scheduling problem with fuzzy processing times is concerned in this paper. A computational procedure is proposed to obtain the approximated membership function of fuzzy completion time for each schedule. The possibility and necessity measures will be used to propose the ranking concept of fuzzy numbers. Under this ordering among fuzzy numbers, we plan to minimize the fuzzy makespan and total weighted fuzzy completion time. Two types of formulations will be proposed by considering the different directions of ordering among fuzzy numbers. We shall apply the modified virus-evolutionary genetic algorithms to search for the best schedules. Three numerical examples are also provided to clarify the discussions in this paper using the commercial software MATLAB.