Identical Parallel Machines Vs . Unit - Time Shops , Preemptions Vs . Chains , and Other Offsets in Scheduling

نویسندگان

  • Vadim G. Timkovsky
  • VADIM G. TIMKOVSKY
چکیده

This paper studies the complexity variations of scheduling problems in diierent machine environments when replacing operations with arbitrary processing times by the chains of operations with unit processing times. Special attention is paid to polynomial-time algorithms for chain-like precedence-constrained problems with unit processing times and transformations of their solutions to each other. Due to the small size, the problems of this type cannot be solved in polynomial time by the algorithms solving in polynomial time their extensions with tree-like or general precedence constraints. There are also considered reductions of preemptive problems with arbitrary processing times to nonpreemptive problems with unit processing times in cross or equal machine environments involving parallel machines, a ow shop and an open shop. The complexity status of several problems that were open before is clariied.

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تاریخ انتشار 1998