In a non-guillotinable rectangular strip packing problem (RF-SPP), the best orthogonal placement of given rectangular pieces on a strip of stock sheet having fixed width and infinite height are searched. The aim is to minimize the height of the strip while including all the pieces in appropriate orientations. In this study, a novel bidirectional best-fit heuristic (BBF) is introduced for solvin...

In this thesis we consider solution methods for packing problems. Packing problems occur in manydifferent situations both directly in the industry and as sub-problems of other problems. High-qualitysolutions for problems in the industrial sector may be able to reduce transportation and productioncosts significantly. For packing problems in general are given a set of items and one of...

We propose two mixed-integer linear programming based approaches for the 2-D orthogonal strip packing problem. Using knowledge from the alternative forms of time representation in scheduling formulations, we show how to efficiently combine three different concepts into the xand ydimensions. One model features a discrete representation on the x-axis (strip width) and a continuous representation ...

Processing Time first algorithm always finds a schedule having makespan within 43 1. Key words, bin packing, multiprocessor scheduling, approximation.Single capacity bin-packing algorithms were applied to solve this problem. Available system resources, the scheduling algorithm must be able to maintain a job working set. Bounds for multiprocessor scheduling with resource.We consider a natural ge...

This note presents a lower bound of 3/2+ √ 33/6 ≈ 2.457 on the competitive ratio for online strip packing. The instance construction we use to obtain the lower bound was first coined by Brown, Baker and Katseff [2]. Recently this instance construction is used to improve the lower bound in computer aided proofs. We derive the best possible lower bound that can be obtained with this instance cons...

In this paper, the two-dimensional strip packing problem with 3-stage level patterns is tackled using genetic algorithms (GAs). We evaluate the usefulness of a knowledge-based greedy seeding procedure used for creating the initial population. This is motivated by the expectation that the seeding will speed up the GA by starting the search in promising regions of the search space. An analysis of...

The computing resources available on dynamically partially reconfigurable devices increase every year enormously. In the near future, we expect that many applications run on a single reconfigurable device. In this paper, we present a concept for multitasking on dynamically partially reconfigurable systems called virtual area management. We explain its advantages, show its challenges, and discus...

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...

We study the strip packing problem, in which a set of two-dimensional rectangular items has to be packed in a rectangular strip of fixed width and infinite height, with the aim of minimizing the height used. The problem is important because it models a large number of real-world applications, including cutting operations where stocks of materials such as paper or wood come in large rolls and ha...