Parametric formulation of the general integer linear programming problem

A parametric approach to the general integer programming problem is explored. If a solution to the general integer linear programming problem exists, it can be expressed as a convex combination of the extreme points of the convex polytope of the associated linear programming relaxation. The combinat...

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Bibliographic Details
Published inComputers & operations research Vol. 22; no. 9; pp. 883 - 892
Main Author Joseph, Anito
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 01.11.1995
Elsevier Science
Pergamon Press Inc
Subjects
Applied sciences
Exact sciences and technology
Mathematical programming
Operational research and scientific management
Operational research. Management science
Parametric method
Integer programming
Convex set
Formulation
Optimal solution
Heuristic method
Problem solving
Linear programming
Objective function
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Summary:A parametric approach to the general integer programming problem is explored. If a solution to the general integer linear programming problem exists, it can be expressed as a convex combination of the extreme points of the convex polytope of the associated linear programming relaxation. The combination may or may not be unique for the convex polytope and will depend on the extreme points used in the determination. Therefore, a heuristic approach to solving the general integer programming problem can be taken by generating extreme points of the convex polytope and reformulating a mixed integer linear programming problem over these extreme points. This approach guarantees a feasible solution in a reasonable time frame. Further, such a technique can be used to provide quick lower bound information for an optimal search procedure.
ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/0305-0548(94)00077-L