### Abstract

We examine bilevel mixed-integer programs whose constraints and objective functions depend on both upper- and lower-level variables. The class of problems we consider allows for nonlinear terms to appear in both the constraints and the objective functions, requires all upper-level variables to be integer, and allows a subset of the lowerlevel variables to be integer. This class of bilevel problems is difficult to solve because the upper-level feasible region is defined in part by optimality conditions governing the lower-level variables, which are difficult to characterize because of the nonconvexity of the follower problem. We propose an exact finite algorithm for these problems based on an optimal-value-function reformulation. We demonstrate how this algorithm can be tailored to accommodate either optimistic or pessimistic assumptions on the follower behavior. Computational experiments demonstrate that our approach outperforms a state-of-the-art algorithm for solving bilevel mixed-integer linear programs.

Original language | English (US) |
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Pages (from-to) | 768-786 |

Number of pages | 19 |

Journal | Operations Research |

Volume | 65 |

Issue number | 3 |

DOIs | |

State | Published - May 1 2017 |

Externally published | Yes |

### Keywords

- Bilevel optimization
- Integer programming
- Nonlinear programming
- Scheduling

### ASJC Scopus subject areas

- Computer Science Applications
- Management Science and Operations Research