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Scheduling tasks with exponential duration on unrelated parallel machines

Nouri, M ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1016/j.dam.2012.06.010
  3. Publisher: 2012
  4. Abstract:
  5. This paper introduces a stochastic scheduling problem. In this problem a directed acyclic graphs (DAG) represents the precedence relations among m tasks that n workers are scheduled to execute. The question is to find a schedule Σ such that if tasks are assigned to workers according to Σ, the expected time needed to execute all the tasks is minimized. The time needed to execute task t by worker w is a random variable expressed by a negative exponential distribution with parameter λ wt 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
  6. Keywords:
  7. Multiple choice hyperbolic 01 programming ; Stochastic parallel scheduling ; 0-1 programming ; Directed acyclic graph (DAG) ; Expected time ; Negative exponential distribution ; NP-hard ; Optimum schedule ; Parallel scheduling ; Polynomial-time ; Precedence relations ; Scheduling tasks ; Stochastic scheduling ; Unrelated parallel machines ; Polynomial approximation ; Stochastic systems ; Scheduling
  8. Source: Discrete Applied Mathematics ; Volume 160, Issue 16-17 , November , 2012 , Pages 2462-2473 ; 0166218X (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0166218X12002454