## Abstract

A single machine scheduling and due-window assignment problem is studied. The objective function is of a minmax type, i.e., the goal is to minimize the maximum cost among all processed jobs. In the classical setting of due-window assignment problems, there are four cost components: for job-earliness, job-tardiness, due-window starting-time and due-window size. We consider in this note a general cost structure which contains in addition to the standard linear earliness and tardiness cost components, a fixed penalty. Thus, early and tardy jobs are penalized also by a fixed cost which is independent of their actual earliness and tardiness values. We show that there are six candi-dates for the optimal starting time and size of the due-window. Consequently, an efficient, polynomial-time solution algorithm is introduced.

Original language | English |
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Pages (from-to) | 3552-3561 |

Number of pages | 10 |

Journal | Journal of Industrial and Management Optimization |

Volume | 20 |

Issue number | 11 |

DOIs | |

State | Published - Nov 2024 |

### Bibliographical note

Publisher Copyright:© (2024) American Institute of Mathematical Sciences. All rights reserved.

## Keywords

- Due-window assignment
- Fixed-plus-linear cost
- polynomial time solution
- Scheduling
- Single-machine