Randomization, Approximation, and Combinatorial Optimization. Algorithms and Techniques

Volume 1671 of the series Lecture Notes in Computer Science pp 144-155

Stochastic Machine Scheduling: Performance Guarantees for LP-Based Priority Policies

  • Rolf H. MöhringAffiliated withFachbereich Mathematik, Sekr. MA 6-1, Technische Universität Berlin
  • , Andreas S. SchulzAffiliated withMIT, Sloan School of Management and Operations Research Center
  • , Marc UetzAffiliated withFachbereich Mathematik, Sekr. MA 6-1, Technische Universität Berlin

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We consider the problem to minimize the total weighted completion time of a set of jobs with individual release dates which have to be scheduled on identical parallel machines. The durations of jobs are realized on-line according to given probability distributions, and the aim is to find a scheduling policy that minimizes the objective in expectation. We present a polyhedral relaxation of the corresponding performance space, and then derive the first constant-factor performance guarantees for priority policies which are guided by optimum LP solutions, thus generalizing previous results from deterministic scheduling. In the absence of release dates, our LP-based analysis also yields an additive performance guarantee for the WSEPT rule which implies both a worst-case performance ratio and a result on its asymptotic optimality.