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AN OPTIMAL PROCEDURE FOR THE PREEMPTIVE CMAX SCHEDULING OF DEPENDENT TASKS ON PARALLEL IDENTICAL MACHINES

We consider the problem of scheduling preemptable, dependent tasks on parallel, identical machines to minimize the makespan. In this paper a branch-and-bound procedure for solving the problem is described. This procedure is based on a depthfirst strategy where each vertex in the search tree corresponds to a subset of precedence feasible orderings of nodes in the precedence graph. We have performed preliminary computational experiments in order to verify the effectiveness of branching and bounding rules we had applied.