Stochastic Machine Scheduling: Performance Guarantees for LP-Based Priority Policies
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.
Unable to display preview. Download preview PDF.
- 3.Dacre, M., Glazebrook, K.D., Niño-Mora, J.: The achievable region approach to the optimal control of stochastic systems. Journal of the Royal Statistical Society (to appear)Google Scholar
- 5.K. D. Glazebrook, Personal communication (January 1999) Google Scholar
- 9.Hall, W.J., Wellner, J.A.: Mean residual life. In: Csörgöo, M., Dawson, D.A., Rao, J.N.K., Saleh, A.K.Md.E. (eds.) Statistics and Related Topics, Proceedings of the International Symposium on Statistics and Related Topics, pp. 169–184. North-Holland, Amsterdam (1981)Google Scholar
- 15.Möhring, R.H., Schulz, A.S., Uetz, M.: Approximation in stochastic scheduling: The power of LP-based priority policies, Tech. Rep. 595/1998, Department of Mathematics, Technical University of Berlin (1998)Google Scholar
- 16.Phillips, C.A., Stein, C., Wein, J.: Minimizing average completion time in the presence of release dates. WADS 1995 82, 199–223 (1998); A preliminary version of this paper (Scheduling jobs that arrive over time). In: Mathamaticial Programming. LNCS, vol. 955, pp. 86–97. Springer, Heidelberg (1995)Google Scholar
- 18.Schulz, A.S.: Scheduling to minimize total weighted completion time: Performance guarantees of LP-based heuristics and lower bounds, in Integer Programming and Combinatorial Optimization. In: Cunningham, W.H., Queyranne, M., McCormick, S.T. (eds.) IPCO 1996. LNCS, vol. 1084, pp. 301–315. Springer, Heidelberg (1996)Google Scholar
- 19.Sgall, J.: On-line scheduling, in Online Algorithms: The State of the Art. In: Fiat, A. (ed.) Dagstuhl Seminar 1996. LNCS, vol. 1442, pp. 196–231. Springer, Heidelberg (1998)Google Scholar
- 25.Weiss, G.: Personal communication (January 1999)Google Scholar