Scheduling tasks with exponential duration on unrelated parallel machines
This paper introduces a stochastic scheduling problem. In this problem a directed acyclic graphs (DAG) represents the precedence relations among m m tasks that n n workers are scheduled to execute. The question is to find a schedule ? ? such that if tasks are assigned to workers according to ? ? , the expected time needed to execute all the tasks is minimized. The time needed to execute task t t by worker w w is a random variable expressed by a negative exponential distribution with parameter ?wt ? w t and each task can be executed by more than one worker at a time. In this paper, we will prove that the problem in its general form is NP-hard, but when the DAG width is constant, we will show that the optimum schedules can be found in polynomial time.
stochastic parallel scheduling multiple choice hyperbolic 01 programming