The article is devoted to mathematical models and practical algorithms for solving the cutting and packing (C&P) problem. We review and further enhance the main tool of our studies – phi-functions. Those are constructed here for 2D and 3D objects (unlike other standard tools, such as no-fit polygons, which are restricted to the 2D geometry). We also demonstrate that in many realistic cases the ...

From 13.03. to 16.03.2007, the Dagstuhl Seminar 07112 Cutting, Packing, Layout and Space Allocation was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of semi...

The paper deals with the purpose of one hybrid approach for solving the constrained two-dimensional cutting (2DC) problem. We study this hybrid approach that combines the genetic algorithm and the Tabu search method. For this problem, we assume a packing of a whole number of rectangular pieces to cut, and that all cuts are of guillotine type in one sheet of a fixed width and an infinite height....

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...

We describe an anytime chart realization algorithm for Combinatory Categorial Grammar (CCG) that essentially interleaves the packing and unpacking stages employed in previous hybrid symbolicstatistical approaches. With this algorithm, it becomes possible to use statistical language models both for improving the quality of the output text and for increasing the speed with which it is produced. I...

Server consolidation of virtual machines is very much essential in a cloud environment for energy conservation and cost cutting . Consolidation can be achieved through live migration of virtual machines. We propose a modified bin packing algorithm for Server Consolidation that avoids unnecessary migrations and minimizes the instantiation of new physical servers. We implement ideas from the Firs...

The bin-packing problem asks for a packing of a list of items of sizes from (0; 1] into the smallest possible number of bins having unit capacity. The k-item bin-packing problem additionally imposes the constraint that at most k items are allowed in one bin. We present two e6cient on-line algorithms for this problem. We show that, for increasing values of k, the bound on the asymptotic worst-ca...

The investigation was conducted on wet and dry seasons of Ethiopia during the year 2012/2013 at Wondo Genet Agricultural Research Center Nursery site. Four levels of cutting size and three levels of cutting positions were arranged in randomized complete block design with three replications. Data on seedling height, branch number/seedling, root number/seedling, root weigh/seedling, root length/s...

Since the cutting tools used in machining process of super alloys are subjected to high cutting forces, accordingly tools life is reduced, therefore improvement in alloys machining and reducing cutting forces to achieve longer tools life is an essential necessity. In this research, the effect of changes in feed rate on cutting forces in machining process of nickel based super alloys is investig...

brass ferrules have been used as packing in a laboratory- scale glass distillation column approaching pilot plant size because of their availability in all sizes and low cost. the available size range is such that these ferrules could also be used in industry and the results of this study could be scaled up. the performance of the new packing has been compared with the performance of glass pack...