The discrete part of the discrete-continuous scheduling problems - new properties

The problems of scheduling of tasks described with dynamic models appear in the real-world situations, where management of the processes described with differential equations is needed. Possible applications contains e.g: refuelling of the feet of the boats in the given critical time, scheduling of tasks in the multiple computer systems and the forging process in the steel plants. The solution for such problems consists of two parts: continuous one (the allocation of the continuously divisible resource) and the discrete one (sequence of task subsets). The research has been done mostly for the former part so far, where the latter one was neglected. In the paper we recollect properties of the discrete part of the solution space and we prove some new properties. These new properties can be used to construct more efficient algorithms for the scheduling problems with the dynamic models of tasks.