We consider the two-dimensional bin packing and strip packing problem, where a list of rectangles has to be packed into a minimal number of rectangular bins or a strip of minimal height, respectively. All packings have to be non-overlapping and orthogonal, i.e., axisparallel. Our algorithm for strip packing has an absolute approximation ratio of 1.9396 and is the first algorithm to break the ap...

The cumulative resource constraints of the resource-constrained project scheduling problem (RCPSP) do not treat the resource demands as geometric rectangles, that is, activities are not necessarily assigned to the same resource units over their processing times. In spite of this fact, most papers on resource-constrained project scheduling mainly in the motivation phase use a strip packing of re...

We consider the problem of finding all enclosing rectangles of minimum area that can contain a given set of rectangles without overlap. Our rectangle packer chooses the xcoordinates of all the rectangles before any of the y-coordinates. We then transform the problem into a perfect-packing problem with no empty space by adding additional rectangles. To determine the y-coordinates, we branch on t...

One advantage of smart grids is that they can reduce the peak load by distributing electricity-demands over multiple short intervals. Finding a schedule that minimizes the peak load corresponds to a variant of a strip packing problem. Normally, for strip packing problems, a given set of axis-aligned rectangles must be packed into a fixed-width strip, and the goal is to minimize the height of th...

One advantage of smart grids is that they can reduce the peak load by distributing electricity-demands over multiple short intervals. Finding a schedule that minimizes the peak load corresponds to a variant of a strip packing problem. Normally, for strip packing problems, a given set of axis-aligned rectangles must be packed into a fixed-width strip, and the goal is to minimize the height of th...

We examine various strategies for exact approaches to the 2dimensional strip packing problem (2SP) with and without rotations of 90 degrees. We first develop a branch-and-bound algorithm based on the sequence pair representation. Next, we focus on the perfect packing problem (PP), which is a special case of 2SP where all given rectangles are required to be packed without wasted space, and desig...

Good algorithms exist for solving the 2D rectangular strip packing problem when the objective is to minimize the amount of wasted material. However, in some applications other criteria are also important. We describe new heuristics for strip packing that optimize not only for wastage, but also for the efficient use of the cutting equipment, by minimizing the number of independent cuts required ...

Given a set of rectangles and a rectangular container with a fixed width, called a strip, the twodimensional strip packing problem (2SP) requires all the given rectangles to be placed orthogonally without overlap within the strip so as to minimize the height of the strip. 2SP and its variants have many applications in steel and textile industries, and it has indirect application in scheduling p...