In this paper, we investigate the complexity of various cyclic schedul
ing problems in flow-shop, job-shop and other environments. We review
existing results and provide Proofs for two new complexity results: we
show that maximizing throughput in a flexible assembly line is NP-har
d, and in the process, we give a polynomial transformation of generic
makespan minimization problems in static scheduling to cycle time mini
mization in cyclic scheduling problems. Secondly, we show that when we
try to schedule a single job type in a cyclic, reentrant flow shop, e
ven if we are given the sequence of operations on each machine, it is
still NP-hard to figure out how to place the operations onto cycles of
a given length so as to minimize flow time (or, equivalently, work in
process). This paper may also be viewed as a classification of cyclic
scheduling research from the perspective of computational complexity.