Stochastic Machine Scheduling: Performance Guarantees for LP-Based Priority Policies
- Cite this paper as:
- Möhring R.H., Schulz A.S., Uetz M. (1999) Stochastic Machine Scheduling: Performance Guarantees for LP-Based Priority Policies. In: Hochbaum D.S., Jansen K., Rolim J.D.P., Sinclair A. (eds) Randomization, Approximation, and Combinatorial Optimization. Algorithms and Techniques. Lecture Notes in Computer Science, vol 1671. Springer, Berlin, Heidelberg
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.
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