A selection method of reasonable non-dominated schedules on scheduling

A selection method for non-dominated schedules for a bi-objective open shop scheduling problem are considered. We treat an open shop scheduling problem on two machines with fuzzy processing times of jobs and with fuzzy due dates of machines. We introduce a possibility distribution function of the processing time for each job and a membership function of the due date of the machine. Thus the processing times and due dates are not constants as in ordinary scheduling problems but decision variables reflecting the fuzzy circumstance of job processing. We propose algorithms for the selection method of reasonable schedules from non-dominated schedules to maximize minimum degree of possibility for the job processing and maximum satisfaction level for the job completion, simultaneously.