TY - JOUR

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

AU - Joseph, A.

AU - Gass, S. I.

N1 - Funding Information:
We thank the referees for their comments which have helped improve the quality of the paper. The work of A. Joseph was supported in part by NSF grant DMI9622104, and a James McLamore Award from the University of Miami.
Copyright:
Copyright 2007 Elsevier B.V., All rights reserved.

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

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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 -