In this paper we deal with a variant of the Multiple Stock Size Cutting Stock Problem (MSSCSP) arising from population harvesting, in which some sets of large pieces of raw material (of different shapes) must be cut following certain patterns to meet customer demands of certain product types. The main extra difficulty of this variant of the MSSCSP lies in the fact that the available patterns ar...

Branch-and-price is a well established technique for solving large scale integer programming problems. This method combines the standard branch-and-bound framework of solving integer programming problems with Column Generation. In each node of the branch-and-bound tree, the bound is calculated by solving the LP relaxation. The LP relaxation is solved using Column Generation. In this report, we ...

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 NP-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 r...

The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimisation problems. Exact solution methods can only be used for very small instances, so for real-world problems we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary ...

There appear to be two versions of the Dual Bin Packing problem in the literature. In addition, one of the versions has a counterpart in the cutting stock literature, known as the Skiving Stock Problem. This paper outlines branch-andprice algorithms for both. We introduce combinatorial upper bounds and well-performing heuristics from the literature in the branch-and-price framework. Extensive c...

This paper explores the use of Simulated Annealing as an optimization technique for the problem Composite Material Stock Cutting. The shapes are not constrained to be convex polygons or even regular shapes. However, due to the composite nature of the material, the orientation of the shapes on the stock is restricted. For placements of various shapes, we show how to determine a cost function, an...

Fair allocation of goods or resources among various agents is a central task in multiagent systems and other fields. The specific setting where just one divisible resource is to be divided fairly is commonly referred to as cake cutting, and agents are called players in this setting. Cake-cutting protocols aim at dividing a cake and assigning the resulting portions to several players in a way th...