Let us imagine that red candles and blue candles are placed on the top of a cake. We want to cut it with a knife into two pieces in such a way that all the red candles are on one of the two pieces and all the blue candles are on the other piece. A question is when we can cut it successfully. The following Kirchberger’s theorem [5] answers this question in a general setting. Let X be a finite su...

We consider a one-dimensional cutting stock problem (CSP) in which the stock widths are not used to fulfill the order but kept for use in the future for the industrial-use paper production. We present a new model based on the flexible stock allocation and trim loss control to determine the production quantity. We evaluate our approach using a real data and show that we are able to solve industr...

This work presents a hybrid approach based on the use of genetic algorithms to solve efficiently the problem of cutting structural beams arising in a local metalwork company. The problem belongs to the class of onedimensional multiple stock sizes cutting stock problem, namely 1dimensional multiple stock sizes cutting stock problem. The proposed approach handles overproduction and underproductio...

The cutting stock problem is an important problem in the field of combinational optimization. In classic versions of this problem, the aim is to find a solution for cutting some equalwidth mother rolls into smaller parts with given width so that the amount of trim-loss become as small as possible. There are plenty of works which addressed the classic cutting stock problem. However in real world...

Despite its great applicability in several industries, the combined cutting stock and lot-sizing problem has not been sufficiently studied because of its great complexity. This paper analyses the trade-off that arises when we solve the cutting stock problem by taking into account the production planning for various periods. An optimal solution for the combined problem probably contains non-opti...

Selection of feasible cutting patterns in order to minimize the raw material wastage which is known as cutting stock problem has become a key factor of the success in today’s competitive manufacturing industries. In this paper, solving a rectangular shape medium size two-dimensional cutting stock problem is discussed. Our study is restricted to raw materials (main sheets) in a rectangular shape...

Starting from a two-dimensional rectangular Cutting-Stock pattern with gaps, this paper is focuses on the problem of determination if the pattern is with guillotine restrictions or not and proposes an algorithm for solving it. First we present two new graph representations of the cutting pattern, weighted graph of downward adjacency and weighted graph of rightward adjacency. Using these represe...