On the choice of explicit stabilizing terms in column generation
Discrete Applied Mathematics
An Inexact Bundle Approach to Cutting-Stock Problems
INFORMS Journal on Computing
Branch and Price for Large-Scale Capacitated Hub Location Problems with Single Assignment
INFORMS Journal on Computing
Chebyshev center based column generation
Discrete Applied Mathematics
A Column-Generation Based Tactical Planning Method for Inventory Routing
Operations Research
Using the primal-dual interior point algorithm within the branch-price-and-cut method
Computers and Operations Research
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When a column generation approach is applied to decomposable mixed integer programming problems, it is standard to formulate and solve the master problem as a linear program. Seen in the dual space, this results in the algorithm known in the nonlinear programming community as the cutting-plane algorithm of Kelley and Cheney-Goldstein. However, more stable methods with better theoretical convergence rates are known and have been used as alternatives to this standard. One of them is the bundle method; our aim is to illustrate its differences with Kelley’s method. In the process we review alternative stabilization techniques used in column generation, comparing them from both primal and dual points of view. Numerical comparisons are presented for five applications: cutting stock (which includes bin packing), vertex coloring, capacitated vehicle routing, multi-item lot sizing, and traveling salesman. We also give a sketchy comparison with the volume algorithm.