Abstract
We consider two semi-online scheduling problems on a single batch (processing) machine with jobs’ nondecreasing processing times and jobs’ nonincreasing processing times, respectively. Our objective is to minimize the makespan. A batch processing machine can handle up to B jobs simultaneously. We study an unbounded model where B = ∞. The jobs that are processed together construct a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. Jobs arrive over time. Let p j denote the processing time of job J j . Given job J j and its following job J j + 1, we assume that p j + 1 ≥ αp j , where α ≥ 1 is a constant number, for the first problem with jobs’ nondecreasing processing times. For the second problem, we assume that p j + 1 ≤ αp j , where 0 < α< 1 is a constant number. We propose an optimal algorithm for both problems with a competitive ratio \(\frac{\sqrt{\alpha^2+4}-\alpha}{2}+1\) for the first problem and \(\frac{\sqrt{4\alpha+1}+1}{2}\) for the second problem.
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References
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)
Deng, X., Poon, C.K., Zhang, Y.: Approximation Algorithms in Batch Processing. Journal of Combinatorial Optimization 7, 247–257 (2003)
Fu, R., Tian, J., Yuan, J., He, C.: On-Line Scheduling on a Batch Machine to Minimize Makespan with Limited Restarts. Operational Research Letters 36, 255–258 (2008)
Fu, R., Tian, J., Yuan, J., Lin, Y.: On-Line Scheduling in a Parallel Batch Processing System to Minimize Makespan Using Restarts. Theoretical Computer Science 374, 196–202 (2007)
Pruhs, K., Sgall, J., Torng, E.: Online Scheduling. In: Leung, J.Y.-T. (ed.) Handbook of Scheduling: Algorithms, Models, and Performance Analysis (2004)
Lee, C.Y., Uzsoy, R.: Minimizing Makespan on a Single Batch Processing Machine with Dynamic Job Arrivals. International Journal of Production Research 37, 219–236 (1999)
Lee, C.Y., Uzsoy, R., Martin-Vega, L.A.: Efficient Algorithms for Scheduling Semiconductor Burn-in Operations. Operations Research 40, 764–775 (1992)
Nong, Q., Yuan, J., Fu, R., Lin, L., Tian, J.: The Single-Machine Parallel-Batching On-Line Scheduling Problem with Family Jobs to Minimize Makespan. International Journal of Production Economics 111, 435–440 (2008)
Poon, C.K., Yu, W.: Online Scheduling Algorithms for a Batch Machine with Finite Capacity. Journal of Combinatorial Optimization 9, 167–186 (2005)
Zhang, G., Cai, X., Wong, C.: On-Line Algorithms for Minimizing Makespan on Batch Processing Machines. Naval Research Logistics 48, 241–258 (2001)
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Liu, M., Xu, Y., Chu, C., Wang, L. (2009). Optimal Semi-online Algorithm for Scheduling on a Batch Processing Machine. In: Du, DZ., Hu, X., Pardalos, P.M. (eds) Combinatorial Optimization and Applications. COCOA 2009. Lecture Notes in Computer Science, vol 5573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02026-1_32
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DOI: https://doi.org/10.1007/978-3-642-02026-1_32
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