# Scheduling jobs with time-resource tradeoff via nonlinear programming

Grigoriev, Alexander and Uetz, Marc (2009) *Scheduling jobs with time-resource tradeoff via nonlinear programming.* Discrete Optimization, 6 (4). pp. 414-419. ISSN 1572-5286

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Abstract: | We consider a scheduling problem where the processing time of any job is dependent on the usage of a discrete renewable resource, e.g. personnel. An amount of units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its processing time. The objective is to find a resource allocation and a schedule that minimizes the makespan. We explicitly allow for succinctly encodable time-resource tradeoff functions, which calls for mathematical programming techniques other than those that have been used before. Utilizing a (nonlinear) integer mathematical program, we obtain the first polynomial time approximation algorithm for the scheduling problem, with performance bound for any . Our approach relies on a fully polynomial time approximation scheme to solve the nonlinear mathematical programming relaxation. We also derive lower bounds for the approximation. |

Item Type: | Article |

Copyright: | © 2009 Elsevier |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/67838 |

Official URL: | http://dx.doi.org/10.1016/j.disopt.2009.05.002 |

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