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...

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...

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 ...

An instance of the two-dimensional strip packing problem is specified by n rectangular items, each having a width, 0 < wn ≤ 1, and height, 0 < hn ≤ 1. The objective is to place these items into a strip of width 1, without rotations, such that they are nonoverlapping and the total height of the resulting packing is minimized. In this thesis, we consider the version of the twodimensional strip pa...

In the strip packing problem, a given set of axis-aligned rectangles must be packed into a fixed-width strip, and the goal is to minimize the height of the strip. In this paper, we examine a variant in which each rectangle may be cut vertically into multiple slices and the slices may be packed into the strip as individual pieces. Our results are: (1) analysis of the approximation ratio of sever...

Orthogonal packing problems are natural multidimensional generalizations of the classical bin packing problem and knapsack problem and occur in many different settings. The input consists of a set I = {r1, . . . , rn} of d-dimensional rectangular items ri = (ai,1, . . . , ai,d) and a space Q. The task is to pack the items in an orthogonal and non-overlapping manner without using rotations into ...

We study the well-known two-dimensional strip packing problem. Given is a set of rectangular axis-parallel items and a strip of width W with infinite height. The objective is to find a packing of these items into the strip, which minimizes the packing height. Lately, it has been shown that the lower bound of 3/2 of the absolute approximation ratio can be beaten when we allow a pseudo-polynomial...

We study certain adversary sequences for online strip packing which were first designed and investigated by Brown, Baker and Katseff (Acta Inform. 18:207– 225) and determine the optimal competitive ratio for packing such Brown-BakerKatseff sequences online. As a byproduct of our result, we get a new lower bound of ρ ≥ 3/2 +√33/6 ≈ 2.457 for the competitive ratio of online strip packing.

We study the strip packing problem, a classical packing problem which generalizes both bin packing and makespan minimization. Here we are given a set of axis-parallel rectangles in the two-dimensional plane and the goal is to pack them in a vertical strip of fixed width such that the height of the obtained packing is minimized. The packing must be non-overlapping and the rectangles cannot be ro...