## Abstract

We study a class of due-window assignment problems. The objective is to find the job sequence and the window starting time and size, such that the total cost of earliness, tardiness and due-window is minimized. The study assumes unit-time jobs, and considers settings of a single machine and of parallel identical machines. Both the due-window starting time and size are decision variables. For the single machine setting, we study a complete set of problems consisting of all possible combinations of the decision variables and four cost factors (earliness, tardiness, due-window size and due-window starting time). For parallel identical machines, we study a complete set of problems consisting of all possible combinations of the decision variables and three cost factors (earliness, tardiness and due-window size). All the problems are shown to be solvable in no more than O(n^{3}) time, where n is the number of jobs.

Original language | American English |
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Pages (from-to) | 487-495 |

Number of pages | 9 |

Journal | Applied Mathematics and Computation |

Volume | 220 |

DOIs | |

State | Published - 2013 |

### Bibliographical note

Funding Information:This paper was supported in part by The Charles Rosen Chair of Management and the Recanati Fund of The School of Business Administration, The Hebrew University, Jerusalem, Israel.

## Keywords

- Assignment problem
- Due-window
- Earliness-tardiness
- Parallel machines
- Scheduling