In this paper the solution of two-stage guillotine cutting stock problems is considered. Especially such problems are under investigation where the sizes of the order demands diier in a large range. We propose a new approach dealing with such situations and compare it with the classical Gilmore/Gomory approach. We report results of extensive numerical experiments which show the advantages of th...

We characterize separable multidimensional permutations in terms of forbidden patterns and enumerate them by means of generating function, recursive formula, and explicit formula. We find a connection between multidimensional permutations and guillotine partitions of a box. In particular, a bijection between separable d-dimensional permutations and guillotine partitions of a 2d−1-dimensional bo...

We consider two-dimensional rectangular strip packing without rotation of items and without the guillotine cutting constraint. We propose a single-pass heuristic which fills every free space in a onedimensional knapsack fashion, i.e. considering only item widths. It appears especially important to assign suitable heuristic “pseudo-values” as profits in this knapsack problem. This simple heurist...

In this paper, two-dimensional cutting stock problem with demand has been studied.In this problem, cutting of large rectangular sheets into specific small pieces should be carried out hence, the waste will be minimized. Solving this problem is important to decrease waste materials in any industry that requires cutting of sheets. In most previus studies, the demand of pieces has not been usually...

In this paper, two-dimensional cutting stock problem with demand has been studied.In this problem, cutting of large rectangular sheets into specific small pieces should be carried out hence, the waste will be minimized. Solving this problem is important to decrease waste materials in any industry that requires cutting of sheets. In most previus studies, the demand of pieces has not been usually...

Given a set of rectangular pieces and a rectangular container, the two-dimensional knapsack problem (2D-KP) consists of orthogonally packing a subset of the pieces within the container such that the sum of the values of the packed pieces is maximized. If the value of a piece is given by its area the objective is to maximize the covered area of the container. A genetic algorithm (GA) is proposed...

We investigate several two-dimensional guillotine cutting stock problems and their variants in which orthogonal rotations are allowed. We first present two dynamic programming based algorithms for the Rectangular Knapsack (RK) problem and its variants in which the patterns must be staged. The first algorithm solves the recurrence formula proposed by Beasley; the second algorithm —for staged pat...

In this paper, genetic algorithm (GA) and simulated annealing (SA) with improved bottom left (BL) algorithm were applied to twodimensional non-guillotine rectangular packing problems. The performance and efficiency of these algorithms on several test problems [Hopper, E., Turton, B.C.H., 2000. An empirical investigation of meta-heuristic and heuristic algorithms for two-dimensional packing prob...

We investigate the two-stage guillotine two-dimensional cutting stock problem. This problem commonly arises in the industry when small rectangular items need to be cut out of large stock sheets. We propose an integer programming formulation that extends the well-known Gilmore and Gomory model by explicitly considering solutions that are obtained by both slitting some stock sheets down their wid...