The single machine serial batch scheduling problems with rejection
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We consider several serial batch scheduling problems with rejection. Each job is either processed on a single serial batching machine or rejected by paying a penalty. We analyze two models with rejection. The first model is to minimize the sum of the scheduling cost of the accepted jobs and the total penalty of the rejected jobs, where the scheduling costs are the total completion time, the makespan, the maximum lateness and the weighted number of tardy jobs, respectively. For the former two problems, we propose two polynomial time algorithms to solve them. For the last two problems, we derive efficient dynamic programming algorithms. The second model is to minimize the makespan, given an upper bound on the total rejection cost, we present a fully polynomial time approximation scheme.
KeywordsScheduling Serial batching Rejection Dynamic programming
The authors thank the anonymous reviewers for their helpful and detailed comments on an earlier version of our paper. This paper is supported by the National Natural Science Foundation of China (11201259) and the Doctoral Fund of the Ministry of Education (20123705120001 & 20123705110003).
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