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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
Vol. 46, No. 3 (May - Jun., 1998), pp. 316-329
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/222825
Page Count: 14
You can always find the topics here!Topics: Integers, Algorithms, Linear programming, Pricing, Scheduling, Convexity, Integer programming, Mathematical problems, Lagrangian function, Approximation
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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.
Operations Research © 1998 INFORMS