Cyclic scheduling and diophantine problems

Cyclic scheduling concerns both kinds of questions following the deductive and inductive ways of reasoning. First class of problems concentrates on rules aimed at resources assignment as to minimize a given objective function, e.g. the cycle time, the flow time of a job. In turn, the second class focuses on a system structure designing as to guarantee the assumed qualitative and/or quantitative measures of objective functions can be achieved. The third class of problems can be seen, however as integration of earlier mentioned, i.e. treating design and scheduling or design and planning simultaneously. The complexity of these problems stems from the fact that system configuration must be determined for the purpose of processes scheduling, yet scheduling must be done to devise the system configuration. In that context, the contribution provides discussion of some Diophantine problems solubility issues, taking into