Sequencing in an assembly line with blocking to minimize cycle time
Operations Research
Annals of Operations Research
Compact cylindrical chromatic scheduling
SIAM Journal on Discrete Mathematics
Cyclic schedules for job shops with identical jobs
Mathematics of Operations Research
Flowshop scheduling with limited temporary storage
Journal of the ACM (JACM)
Periodic schedules for linear precedence constraints
Discrete Applied Mathematics
Survey: Complexity of cyclic scheduling problems: A state-of-the-art survey
Computers and Industrial Engineering
High-multiplicity cyclic job shop scheduling
Operations Research Letters
CROSS cyclic resource-constrained scheduling solver
Artificial Intelligence
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In this paper, we investigate the complexity of various cyclic scheduling 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-hard, and in the process, we give a polynomial transformation of generic makespan minimization problems in static scheduling to cycle time minimization in cyclic scheduling problems. Secondly, we show that when we try to schedule a single job type in a cyclic, reentrant flow shop, even 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.