### 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) |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Modeling and Simulation
- Management Science and Operations Research
- Information Systems and Management

### Cite this

**A framework for constructing general integer problems with well-determined duality gaps.** / Joseph, Anito; Gass, S. I.

Research output: Contribution to journal › Article

*European Journal of Operational Research*, vol. 136, no. 1, pp. 81-94. https://doi.org/10.1016/S0377-2217(01)00035-2

}

TY - JOUR

T1 - A framework for constructing general integer problems with well-determined duality gaps

AU - Joseph, Anito

AU - Gass, S. I.

PY - 2002/1/1

Y1 - 2002/1/1

N2 - 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.

AB - 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.

KW - Duality gap

KW - General integer programming

KW - Linear programming

KW - Test problem generation

UR - http://www.scopus.com/inward/record.url?scp=0036027417&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036027417&partnerID=8YFLogxK

U2 - 10.1016/S0377-2217(01)00035-2

DO - 10.1016/S0377-2217(01)00035-2

M3 - Article

AN - SCOPUS:0036027417

VL - 136

SP - 81

EP - 94

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 1

ER -