منابع مشابه
A branch-and-cut-and-price algorithm for one-dimensional stock cutting and two-dimensional two-stage cutting
The one-dimensional cutting stock problem (1D-CSP) and the twodimensional two-stage guillotine constrained cutting problem (2D-2CP) are considered in this paper. The Gilmore-Gomory model of these problems has a very strong continuous relaxation which provides a good bound in an LP-based solution approach. In recent years, there have been several efforts to attack the one-dimensional problem by ...
متن کاملA Cut and Branch Approach for the Capacitated p-Median Problem Based on Fenchel Cutting Planes
The capacitated p-median problem (CPMP) consists of finding p nodes (the median nodes) minimizing the total distance to the other nodes of the graph, with the constraint that the total demand of the nodes assigned to each median does not exceed its given capacity. In this paper we propose a cutting plane algorithm, based on Fenchel cuts, which allows us to considerably reduce the integrality ga...
متن کاملA Branch&bound Algorithm for Solving One-dimensional Cutting Stock Problems Exactly
Many numerical computations reported in the literature show an only small diierence between the optimal value of the one-dimensional cutting stock problem (1CSP) and that of its corresponding linear programming relaxation. Moreover, theoretical investigations have proven that this difference is smaller than 2 for a wide range of subproblems of the general 1CSP. In this paper we give a branch&bo...
متن کاملSeparation of Generic Cutting Planes in Branch-and-Price Using a Basis
Dantzig-Wolfe reformulation of a mixed integer program partially convexifies a subset of the constraints, i.e., it implicitly adds all valid inequalities for the associated integer hull. Projecting an optimal basic solution of the reformulation’s LP relaxation to the original space does is in general not yield a basic solution of the original LP relaxation. Cutting planes in the original proble...
متن کاملA branch-and-price algorithm for the two-stage guillotine cutting stock problem
We investigate the two-stage guillotine two-dimensional cutting stock problem. This problem commonly arises in the industry when small rectangular items need to be cut out of large stock sheets. We propose an integer programming formulation that extends the well-known Gilmore and Gomory model by explicitly considering solutions that are obtained by both slitting some stock sheets down their wid...
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ژورنال
عنوان ژورنال: Nature
سال: 1880
ISSN: 0028-0836,1476-4687
DOI: 10.1038/022533b0