### Abstract

In this paper we look at semi-infinite assignment problems. These are situations where a finite set of agents of one type has to be assigned to an infinite set of agents of another type. This has to be done in such a way that the total profit arising from these assignments is as large as possible. An infinite programming problem and its dual arise here, which we tackle with the aid of finite approximations. We prove that there is no duality gap and we show that the core of the corresponding game is nonempty. Finally, the existence of optimal assignments is discussed.

Original language | Undefined |
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Pages (from-to) | 67-78 |

Number of pages | 12 |

Journal | Mathematical methods of operations research |

Volume | 57 |

Issue number | 1 |

DOIs | |

Publication status | Published - Apr 2003 |

### Keywords

- IR-58671
- Infinite programs
- assignment
- Cooperative games
- METIS-212030
- EWI-17804
- Balancedness

## Cite this

Llorca, N., Tijs, S., & Timmer, J. B. (2003). Semi-infintite assignment problems and related games.

*Mathematical methods of operations research*,*57*(1), 67-78. https://doi.org/10.1007/s001860200245