Abstract
We consider the problem of minimizing the weighted number of tardy jobs (\(\sum_{j=1}^{n}w_jU_j\)) on an unbounded batch processing machine. The batch processing machine can process up to B (B ≥ n) jobs simultaneously. The jobs that are processed together form a batch, and all jobs in a batch start and complete at the same time. For a batch of jobs, the processing time of the batch is equal to the largest processing time among the jobs in this batch. In this paper, we design a fully polynomial time approximation scheme (FPTAS) to solve the unbounded batch scheduling problem \(1|B\geq n|\sum_{j=1}^{n}w_jU_j.\) This is the strongest possible polynomial time approximation result that we can derive for an NP-hard problem (unless P = NP holds).
Supported by the National Natural Science Foundation (Grant Number 10671108) and the Natural Science Foundation of Shandong Province (Grant Number Y2005A04).
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Ren, J., Zhang, Y., Zhang, X., Sun, G. (2009). Approximation Algorithm for Minimizing the Weighted Number of Tardy Jobs on a Batch 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_38
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DOI: https://doi.org/10.1007/978-3-642-02026-1_38
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