Approximation Algorithms in Batch Processing
We study the scheduling of a set of jobs, each characterised by a release (arrival) time and a processing time, for a batch processing machine capable of running (at most) a fixed number of jobs at a time. When the job release times and processing times are known a-priori and the inputs are integers, we obtained an algorithm for finding a schedule with the minimum makespan. The running time is pseudo-polynomial when the number of distinct job release times is constant. We also ob- tained a fully polynomial time approximation scheme when the number of distinct job release times is constant, and a polynomial time approxi- mation scheme when that number is arbitrary. When nothing is known about a job until it arrives, i.e., the on-line setting, we proved a lower bound of \( (\sqrt 5 + 1)/2 \) on the competitive ratio of any approximation al- gorithm. This bound is tight when the machine capacity is unbounded.
Unable to display preview. Download preview PDF.
- 2.J.J. Bartholdi. unpublished manuscript, 1988.Google Scholar
- 6.G. Dobson and R.S. Nambinadom. The batch loading scheduling problem. Technical report, Simon Graduate School of Business Administration, University of Rochester, 1992.Google Scholar
- 7.C.R. Glassey and W.W. Weng. Dynamic batching heuristics for simultaneous processing. IEEE Transactions on Semiconductor Manufacturing, pages 77–82, 1991.Google Scholar
- 10.C.Y. Lee and R. Uzsoy. Minimizing makespan on a single batch processing machine with dynamic job arrivals. Technical report, Department of Industrial and System Engineering, University of Florida, January 1996.Google Scholar
- 13.R. Uzsoy. Scheduling batch processing machines with incompatible job families. International Journal of Production Research, pages 2605–2708, 1995.Google Scholar