The bin packing problem is a well-studied combinatorial NP-hard problem. In the bin packing problem, a sequence of items are packed into bins, the packed items in a bin do not overlap. The objective is to minimize the number of used bins. The size of each item should be no more than the size of a bin. (Zhang, 2011) The algorithms can be divided into two categories: offline algorithm, requiring ...

Two-dimensional bin packing problems are highly relevant combinatorial optimization problems. They find a large number of applications, for example, in the context of transportation or warehousing, and for the cutting of different materials such as glass, wood or metal. In this work we deal with the oriented two-dimensional bin packing problem under free guillotine cutting. In this specific pro...

In this study we are concerned with the non-exact two-stage two-dimensional guillotine cutting problem considering usable leftovers, in which stock plates remainders of the cutting patterns (non-used material or trim loss) can be used in the future, if they are large enough to fulfill future demands of items (ordered smaller plates). This cutting problem can be characterized as a residual bin-p...

We study a bin-packing problem which is one-dimensional and is constrained in the manner items are placed into bins. The problem is motivated by a practical realtime scheduling problem, where redundant periodic tasks need to be assigned to a multiprocessor system. The problem is stated in the traditional light: to use as few bins as possible to pack a given list of items, and it is a generaliza...

Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in multi-agent systems and distributed systems, and can also be found as subproblems of scheduling problems. We propose bin completion, a branch-and-bound stra...

We present approximation algorithms for the three-dimensional strip packing problem, and the three-dimensional bin packing problem. We consider orthogonal packings where ninety-degree rotations are allowed. The algorithms we show for these problems have asymptotic performance bounds 2.64, and 4.89, respectively. These algorithms are for the more general case in which the bounded dimensions of t...

Several combinatorial optimization problems can be formulated as large size SetCovering Problems. In this work, we use the Set-Covering formulation to obtain a general heuristic algorithm for this type of problems, and describe our implementation of the algorithm for solving two variants of the well-known (One-Dimensional) Bin Packing Problem: the Two-Constraint Bin Packing Problem and the basi...