We consider the problem of fairly dividing a two dimensional heterogeneous good among multiple players. Applications include division of land as well as ad space in print and electronic media. Classical cake cutting protocols primarily consider a one-dimensional resource, or allocate each player multiple infinitesimally small “pieces”. In practice, however, the two dimensional shape of the allo...

This work presents a genetic symbiotic algorithm to minimize the number of objects and the setup in a one-dimensional cutting stock problem. The algorithm implemented can generate combinations of ordered lengths of stock (the cutting pattern) and, at the same time, the frequency of the cutting patterns, through a symbiotic process between two distinct populations, solutions and cutting patterns...

When making wood board production, defects on board will influence the machining process automation degree. Therefore, how to fast, accurately remove of wood defects and realize optimal combination cutting stock problem has always been a research hotspot in the field of wood processing. According to the decayed wood board, the paper designed the one dimensional optimization cutting stock combin...

The cutting stock problem it is of great interest in relation with several real world problems. Basically it means that there are some smaller pieces that have to be cut from a greater stock piece, in such a way, that the remaining part of the stock piece should be minimal. The classical solution methods of this problem generally need a great amount of calculation. In order to reduce the comput...

Efficient cutting design is essential to reduce the costs of production in the open die forging industry. This article discusses a slab cutting design problem that occurs when parallel piped items are cut from raw material steel slabs with varying widths and lengths to meet a volume requirement. The problem is modeled as a two-dimensional cutting stock problem or bin packing problem with size-c...

Research addressing two-dimensional irregular shape packing has largely focused on the strip packing variant of the problem. However, it can be argued that this is a simplification. Materials from which pieces are required to be cut will ultimately have a fixed length either due to the physical dimensions of the material or through constraints on the cutting machinery. Hence, in order to cut al...

We present algorithms for the following three-dimensional (3D) guillotine cutting problems: Unbounded Knapsack, Cutting Stock and Strip Packing. We consider the case where the items have fixed orientation and the case where orthogonal rotations around all axes are allowed. For the Unbounded 3D Knapsack problem, we extend the recurrence formula proposed by Beasley for the Rectangular Knapsack Pr...

An Iterated Local Search method for the constrained two-dimensional non-guillotine cutting problem is presented. This problem consists in cutting pieces from a large stock rectangle to maximize the total value of pieces cut. In this problem, we take into account restrictions on the number of pieces of each size required to be cut. It can be classified as 2D-SLOPP (two dimensional single large o...