## Abstract

We study a batch scheduling problem on a two-machine flowshop. Unlike most relevant research papers focusing on batching with identical job processing times, we assume machine-dependent processing times. The objective function is minimum makespan. For the relaxed version of the problem, where integer batch sizes are not required, we introduce a constant time solution. It consists of: (i) a closed-form expression for the optimal number of batches; and (ii) a geometric sequence of the batch sizes. This optimal non-integer solution is converted into an integer solution by the application of a simple rounding procedure, which runs in O(nlogn) time (where n is the number of jobs).

Original language | American English |
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Pages (from-to) | 457-469 |

Number of pages | 13 |

Journal | 4OR |

Volume | 21 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2023 |

### Bibliographical note

Publisher Copyright:© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

## Keywords

- Batch availability
- Batching
- Flow-shop
- Machine-dependent processing times
- Makespan
- Scheduling