On Undecidability of Cyclic Scheduling Problems

Cyclic scheduling concerns both kinds of problems relevant to the deductive and inductive ways of reasoning. The first class of problems concentrates on rules aimed at resources assignment so 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 designed so as to guarantee that the assumed qualitative and/or quantitative measures of objective functions can be achieved. The third class of problems can however be seen as integration of the previous ones, 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 account the cyclic scheduling perspective.