## Abstract

A relatively new class of scheduling problems consists of multiple agents who compete on the use of a common processor. We focus in this paper on a two-agent setting. Each of the agents has a set of jobs to be processed on the same processor, and each of the agents wants to minimize a measure which depends on the completion times of its own jobs. The goal is to schedule the jobs such that the combined schedule performs well with respect to the measures of both agents. We consider measures of minmax and minsum earliness. Specifically, we focus on minimizing maximum earliness cost or total (weighted) earliness cost of one agent, subject to an upper bound on the maximum earliness cost of the other agent. We introduce a polynomial-time solution for the minmax problem, and prove NP-hardness for the weighted minsum case. The unweighted minsum problem is shown to have a polynomial-time solution.

Original language | American English |
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Pages (from-to) | 540-546 |

Number of pages | 7 |

Journal | European Journal of Operational Research |

Volume | 206 |

Issue number | 3 |

DOIs | |

State | Published - 1 Nov 2010 |

### Bibliographical note

Funding Information:We thank P. Sreekumar for assistance in processing EGRET data and D. Bertsch, D. Helfand, and D. J. Thompson for discussions and comments. Research supported by the NASA CGRO Guest Investigator Program (grant NAG 5-2729), the NASA Cooperative Agreement NCC 5-93, NASA contract NAS-5-32484, NASA LTSA grant NAG 5-3384, and DGICYT grant PB94-0904.

## Keywords

- Earliness
- Multi-agent scheduling
- Single machine