Given a container of fixed width, infinite height and a set of rectangular block, the 2D-strip packing problem consists of orthogonally placing all the rectangles such that the height is minimized. The position is subject to confinement of no overlapping of blocks. The problem is a complex NP-hard combinatorial optimization, thus a heuristic based on genetic algorithm is proposed to solve it. I...

Given a finite set of spheres of different sizes we study the three-dimensional Strip Packing Problem (3D-SPP) as well as the three-dimensional Knapsack Problem (3D-KP). The 3D-SPP asks for a placement of all spheres within a cuboidal strip of fixed width and height so that the variable length of the cuboidal strip is minimized. The 3D-KP requires packing of a subset of the spheres in a given c...

In this paper, we show how the introduction of a new primitive constraint over finite domains in the constraint logic programming system CHIP allows us to find very good solutions for a large class of very difficult scheduling and placement problems. Examples on the cumulative scheduling problem, the 10 jobs x 10 machines problem, the perfect square problem, the strip packing problem and the in...

Two-Dimensional Irregular Strip Packing Problem is a classical cutting/packing problem. The problem is to assign, a set of 2-D irregular-shaped items to a rectangular sheet. The width of the sheet is fixed, while its length is extendable and has to be minimized. A sequence-based approach is developed and tested. The approach involves two phases; optimization phase and placement phase. The optim...

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...

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 paper we establish a general algorithmic framework between bin packing and strip packing, with which we achieve the same asymptotic bounds by applying bin packing algorithms to strip packing. More precisely we obtain the following results: (1) Any offline bin packing algorithm can be applied to strip packing maintaining the same asymptotic worst-case ratio. Thus using FFD (MFFD) as a su...

In this paper we consider a two dimensional strip packing problem. The problem consists of packing a set of rectangular items in one strip of width W and infinite height. They must be packed without overlapping, parallel to the edge of the strip and we assume that the items are oriented, i.e. they cannot be rotated. To solve this problem, we use three exact methods: a branch and bound method, a...

We present an asymptotic fully polynomial approximation scheme for strip-packing, or packing rectangles into a rectangle of xed width and minimum height, a classical NP-hard cutting-stock problem. The algorithm nds a packing of n rectangles whose total height is within a factor of (1 +) of optimal (up to an additive term), and has running time polynomial both in n and in 1==. It is based on a r...