Preemptive scheduling with staircase and piecewise linear resource availability

Some variations are presented for the preemptive scheduling problem on unrelated processors, one shows how nonrenewable resources with a time-varying supply may be taken into account in an extension of the two-phase method; phase 1 consists in solving an LP problem and phase 2 is the construction of the schedule; such a construction reduces to the determination of integral vectors in polyhedra defined by totally unimodular matrices. In special cases, this is simply a compatible flow problem.