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

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.