Branch-and-Price Algorithms for the One-Dimensional Cutting Stock Problem

Authors:
Pamela H. Vance
Affiliations:
Department of Industrial and Systems Engineering Auburn University Auburn, Alabama 36849-5346. E-mail: pvance@eng.auburn.edu
Venue:
Computational Optimization and Applications
Year:
1998

Citing 5
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Abstract

We compare two branch-and-price approaches for the cutting stock problem. Each algorithm is based on a different integer programming formulation of the column generation master problem. One formulation results in a master problem with 0–1 integer variables while the other has general integer variables. Both algorithms employ column generation for solving LP relaxations at each node of a branch-and-bound tree to obtain optimal integer solutions. These different formulations yield the same column generation subproblem, but require different branch-and-bound approaches. Computational results for both real and randomly generated test problems are presented.