Branch-and-Price: Column Generation for Solving Huge Integer Programs

Cynthia Barnhart, Ellis L. Johnson, George L. Nemhauser, Martin W. P. Savelsbergh and Pamela H. Vance
Additional contact information
Cynthia Barnhart: Georgia Institute of Technology, Atlanta, Georgia
Ellis L. Johnson: Georgia Institute of Technology, Atlanta, Georgia
George L. Nemhauser: Georgia Institute of Technology, Atlanta, Georgia
Martin W. P. Savelsbergh: Georgia Institute of Technology, Atlanta, Georgia
Pamela H. Vance: Georgia Institute of Technology, Atlanta, Georgia

Operations Research, 1998, vol. 46, issue 3, 316-329

Abstract: We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branch-and-bound tree. We present classes of models for which this approach decomposes the problem, provides tighter LP relaxations, and eliminates symmetry. We then discuss computational issues and implementation of column generation, branch-and-bound algorithms, including special branching rules and efficient ways to solve the LP relaxation. We also discuss the relationship with Lagrangian duality.

Keywords: Integer programming; Branch-and-bound; Decomposition algorithms (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (468)

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