This paper presents an approach for solving a new real problem in Cutting and Packing. At its core is an innovative mixed integer programme model that places irregular pieces and defines guillotine cuts. The two-dimensional irregular shape bin packing problem with guillotine constraints arises in the glass cutting industry, for example, the cutting of glass for conservatories. Almost all cuttin...

We study pseudo-polynomial Strip Packing. Given a set of rectangular axis parallel items and a strip with bounded width and infinite height the objective is to find a packing of the items into the strip which minimizes the packing height. We speak of pseudo-polynomial Strip Packing if we consider algorithms with pseudo-polynomial running time with respect to the width of the strip. It is known ...

Poorly drained claypan soils can increase the importance of tillage and N management for corn (Zea mays L.) production. Field research in 2008, 2009 and 2010 (high rainfall years) near Novelty, MO (40° 1' N, 92° 11' W) sought to determine the effect of polymer-coated urea (PCU) placement [strip-tillage (ST) deep banded and no-till (NT) broadcast] and application timing (fall, early preplant...

The two-dimensional level strip packing problem (2LSPP) consists in packing rectangular items of given size into a strip of given width divided into levels. Items packed into the same level cannot be put on top of one another and their overall width cannot exceed the width of the strip. The objective is to accommodate all the items while minimizing the overall height of the strip. The problem i...

It is shown that for any positive E the strip-packing problem, i.e. the problem of packing a given list of rectangles into a strip of width 1 and minimum height. can be solled within I c 2: times the optimal height, in linear time, if the heights and widths of these rectangles are all bounded below by an absolute constant 2 >O. @ 1998 Elsevicr Science B.V. All rights reserved. K~YIYJY~/S: Strip...

In this paper we introduce a hyperheuristic to solve hard strip packing problems. The hyperheuristic manages a sequence of greedy low-level heuristics, each element of the sequence placing a given number of objects. A low-level solution is built by placing the objects following the sequence of low-level heuristics. The hyperheuristic performs a hill-climbing algorithm on this sequence by testin...

We study strip packing, which is one of the most classical two-dimensional packing problems: given a collection of rectangles, the problem is to find a feasible orthogonal packing without rotations into a strip of width 1 and minimum height. In this paper we present an approximation algorithm for the strip packing problem with absolute approximation ratio of 5/3 + ε for any ε > 0. This result s...