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.