### Abstract

The paper is concerned with constructing general integer programming problems (GIP) with well-determined duality gaps. That is, given an integer solution vector, X*, our problem is to develop a set of integer linear inequalities AX ≤ b and an objective function c such that X* lies within some known objective function distance of the optimal solution of the relaxed linear-programming problem. By well-determined, we mean that on completion an upper bound on the problem duality gap and an integer solution (optimal or best known) are available to the problem developer. Such a procedure can, therefore, be used to develop test problems to support the research effort in the area of general IP.

Original language | English (US) |
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Pages (from-to) | 81-94 |

Number of pages | 14 |

Journal | European Journal of Operational Research |

Volume | 136 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2002 |

### Keywords

- Duality gap
- General integer programming
- Linear programming
- Test problem generation

### ASJC Scopus subject areas

- Computer Science(all)
- Modeling and Simulation
- Management Science and Operations Research
- Information Systems and Management