Preemptive scheduling, linear programming and network flows. (English) Zbl 0532.90047

Summary: A refinement of the Birkhoff-von Neumann theorem on bistochastic matrices is derived by a simple argument based on network flow theory; this result is then used for solving a problem of preemptive scheduling on unrelated processors with constraints involving subsets of processors and subsets of jobs. A simple construction procedure is given; it generalizes a two- stage method (linear programming \(+\) network flow) developed by E. L. Lawler and J. Labetoulle [J. Assoc. Comput. Mach. 25, 612-619 (1978; Zbl 0388.68027)] and extended by R. Slowinski [RAIRO, Inf. 15, 155-166 (1981; Zbl 0461.68035); Przegl. Stat. 24, 409-416 (1977; Zbl 0374.90076)].


90B35 Deterministic scheduling theory in operations research
15B52 Random matrices (algebraic aspects)
90C05 Linear programming
90B10 Deterministic network models in operations research
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