A number of optimisation problems involve the optimal grouping of a finite set of items into a number of categories subject to one or more constraints. Such problems raise interesting issues in mapping solutions in genetic algorithms. These problems range from the knapsack problem to bin packing and cutting stock problems. This paper describes research involving cutting stock problems. Results ...

We report on a user-friendly decision support system (DSS) for solving specific cutting stock problem from a smaller wood-processing company. A prototype DSS is developed for use in veneers production and is designed to aid mangers in create or improving existing tailoring of logs using their experience and preference s. The results of testing a typical cutting-stock problem are shown to point ...

We present an asymptotic fully polynomial approximation scheme for strip-packing, or packing rectangles into a rectangle of xed width and minimum height, a classical N P-hard cutting-stock problem. The algorithm nds a packing of n rectangles whose total height is within a factor of (1 +) of optimal (up to an additive term), and has running time polynomial both in n and in 1==. It is based on a ...

This work focuses on the K-staged two-dimensional cutting stock problem with variable sheet size. High-quality solutions are computed by an efficient beam-search algorithm that exploits the congruency of subpatterns and takes informed decisions on which of the available sheet types to use for the solutions. We extend this algorithm by embedding it in a sequential value-correction framework that...

This study focuses on developing fully functional cutting stock software by utilizing an improved multi-phase heuristic algorithm to find the optimal solution for the cutting material. Issues which commonly appear in real-world cutting stock applications are also discussed

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-...

In this paper we present a new parallelization of an efficient best-first branch-and-bound algorithm to solve the constrained two-dimensional single stock guillotine cutting stock problem (CSP) to optimality. The underlying sequential branch-and-bound algorithm is based on an exact version of Wang's heuristic suggested by Viswanathan and Bagchi. In our algorithm we improve the upper bound and i...