## Abstract

We study the problem of minimizing the total weighted tardiness when scheduling unti-length jobs on a single machine, in the presence of large sets of identical jobs. Previously known algorithms, which do not exploit the set structure, are at best pseudo-polynomial, and may be prohibitively inefficient when the set sizes are large. We give a polynomial algorithm for the problem, whose number of operations is independent of the set sizes. The problem is reformulated as an integer program with a quadratic, non-separable objective and transportation constraints. Employing methods of real analysis, we prove a tight proximity result between the integer solution to that problem and a fractional solution of a related problem. The related problem is shown to be polynomially solvable, and a rounding algorithm applied to its solution gives the optimal integer solution to the original problem.

Original language | English |
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Pages (from-to) | 359-371 |

Number of pages | 13 |

Journal | Mathematical Programming |

Volume | 55 |

Issue number | 1-3 |

DOIs | |

State | Published - Apr 1992 |

## Keywords

- Integer programming
- proximity
- quadratic non-separable programming
- scheduling
- transportation