Setup and Open-Stacks Minimization in One-Dimensional Stock Cutting
INFORMS Journal on Computing
The Co-Printing Problem: A Packing Problem with a Color Constraint
Operations Research
Production design for plate products in the steel industry
IBM Journal of Research and Development - Business optimization
An Inexact Bundle Approach to Cutting-Stock Problems
INFORMS Journal on Computing
Mass customization in cutting stock process
ACOS'06 Proceedings of the 5th WSEAS international conference on Applied computer science
On the one-dimensional stock cutting problem in the paper tube industry
Journal of Scheduling
New Stabilization Procedures for the Cutting Stock Problem
INFORMS Journal on Computing
Using the primal-dual interior point algorithm within the branch-price-and-cut method
Computers and Operations Research
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In this paper we present a state-of-the-art version of the branch-and-price procedure of Degraeve and Schrage (1999) for the exact solution of the cutting-stock problem. The average solution time is reduced by a factor of more than 300. This allows us to solve problems twice as large as the largest problems solved in the literature today. The two most important improvements are (1) a hybrid simplex method/subgradient-optimization procedure to find the LP relaxation, and (2) a branching scheme that first focuses on the residual problem throughout the enumeration tree. In addition, the strength of our algorithm is the integration of different components into one comprehensive procedure. The other components are using heuristics intensively, a pruning rule, and the use of a dominance rule. We validate our methodology with both industrial and generated data sets. The performance of our algorithm is compared extensively with other implementations and various heuristics for the problem. The proposed algorithm is very efficient for solving the bin-packing problem as well. The major implication of our methodology is that we solve industrial sizes of an NP-hard problem practically in a time to solve its LP relaxation.