Fuzzy scheduling on two-machine flow shop

Scheduling consists mainly of allocating resources to jobs over rime under necessary constraints, In the past, the processing time for each job was us ually assigned or estimated as a fixed value. In many real-world applicatio ns, however, job processing time may vary dynamically with the situation. I n this paper, fuzzy concepts are applied to Johnson algorithm for managing uncertain scheduling. Given a set of jobs, each having two tasks that must be executed on two machines, and their processing time membership functions , the fuzzy Johnson algorithm can yield a scheduling result with a membersh ip function for the final completion time, thus helping managers gain a bro ader overall view of scheduling. Also, the conventional Johnson algorithm i s shown as a special case of the fuzzy Johnson algorithm with special membe rship functions being assigned. The fuzzy Johnson algorithm is thus a feasi ble solution for both deterministic and uncertain scheduling.