Operations Research Proceedings 2018 pp 475-480 | Cite as

# Complexity and Approximation Results for Setup-Minimal Batch Scheduling with Deadlines on a Single Processor

## Abstract

We address the problem of sequencing *n* jobs that are partitioned into *F* families on a single processor. A setup operation is needed at the beginning of the schedule and whenever a job of one family is succeeded by a job of another family. These setup operations are assumed to not require time but are associated with a fixed setup cost which is identical for all setup operations. Jobs must be completed no later than by a given deadline. The objective is to schedule all jobs such that the total setup cost is minimized. This objective is identical to minimizing the number of setup operations. We provide a sketch of the proof of the problem’s strong NP-hardness as well as some properties of optimal solutions and an \(O(n \log n + nF)\) algorithm that approximates the cost of an optimal schedule by a factor of *F*. For details, we refer to our full paper.

## Keywords

Batch scheduling Setup cost Approximation algorithm## References

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