Preemptive Scheduling, Linear Programming and Network Flows

Abstract

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 [J. Assoc. Comput. Mach., 25 (1978), pp. 612–619] and extended by R. Slowinski [Przeglad Statyst., 24 (1977), pp. 409–415, RAIRO Inform., 15 (1981), pp. 155–166].