## Abstract

This research basically extends the boundaries of the minimization of the number of tardy jobs (N_{T}) problem to where processing times are controllable by allocating a common, continuous, and nonrenewable resource. Most of the research on scheduling with controllable resource-dependent processing times assumed either a linear resource consumption function, that does not obey the law of diminishing returns or a specific convex consumption function, that applies only to a limited number of problems. We, on the other hand, assume a general consumption function, which guarantees a very robust solution that can be applied for a very wide range of problems and is appropriate for real life situations. We established the computational complexity for the N_{T} problem with controllable resource dependent processing times, proving it to be NP-hard. We present a polynomial algorithm to solve a special case of that problem, where all jobs are identical. We also suggest and compare four different heuristic algorithms to solve this problem.

Original language | English |
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State | Published - 1 Dec 2006 |

Event | 2006 IIE Annual Conference and Exposition - Orlando, FL, United States Duration: 20 May 2006 → 24 May 2006 |

### Conference

Conference | 2006 IIE Annual Conference and Exposition |
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Country/Territory | United States |

City | Orlando, FL |

Period | 20/05/06 → 24/05/06 |

## Keywords

- Controllable processing times
- N problem
- NP-hard
- Resource allocation
- Scheduling