Cutting Stock with Binary Patterns: Arc-flow Formulation
نویسندگان
چکیده
The cutting stock problem with binary patterns (0-1 CSP) is a variant of CSP that usually appears as a relaxation of 2D and 3D packing problems. We present an exact method, based on an arc-flow formulation with side constraints, for solving 0-1 CSP by simply representing all the patterns in a very compact graph. Gilmore-Gomory’s column generation approach is usually used to compute strong lower bounds for 0-1 CSP. We report a computational comparison between the arc-flow approach and the GilmoreGomory’s approach.
منابع مشابه
Cutting Stock with Binary Patterns: Arc-flow Formulation with Graph Compression
The cutting stock problem with binary patterns (0-1 CSP) is a variant of CSP that usually appears as a relaxation of 2D and 3D packing problems. We present an exact method, based on an arc-flow formulation with side constraints, for solving 0-1 CSP by simply representing all the patterns in a very compact graph. Gilmore-Gomory’s column generation approach is usually used to compute strong lower...
متن کاملGeneral Arc-flow Formulation with Graph Compression
We present an exact method, based on an arc-flow formulation with side constraints, for solving bin packing and cutting stock problems — including multi-constraint variants — by simply representing all the patterns in a very compact graph. Our method includes a graph compression algorithm that usually reduces the size of the underlying graph substantially without weakening the model. Our formul...
متن کاملGomory Cuts from a Position-Indexed Formulation of 1D Stock Cutting
Most integer programming problems can be formulated in several ways. Some formulations are better suited for solution by exact methods, because they have either (i) a strong LP relaxation, (ii) few symmetries in the solution space, or both. However, solving one formulation, we can often branch and/or add cutting planes which are implicitly based on variables of other formulations, working in fa...
متن کاملRektor Gomory Cuts from a Position - Indexed Formulation of 1 D Stock Cutting
Most integer programming problems can be formulated in several ways. Some formulations are better suited for solution by exact methods, because they have either (i) a strong LP relaxation, (ii) few symmetries in the solution space, or both. However, solving one formulation, we can often branch and/or add cutting planes which are implicitly based on variables of other formulations, working in fa...
متن کاملArc-Flow Model for the Two-Dimensional Cutting Stock Problem
We describe an exact model for the two-dimensional Cutting Stock Problem with two stages and the guillotine constraint. It is a linear programming arc-flow model, formulated as a minimum flow problem, which is an extension of a model proposed by Valério de Carvalho for the one dimensional case. In this paper, we explore how this model behaves when it is solved with a commercial software, explic...
متن کامل