We consider two related optimization problems: bin-packing with fragile objects and frequency allocation in cellular networks. The former is a generalization of the classical bin packing problem and is motivated by the latter. The problem is as follows: Each object has two attributes, weight and fragility. The goal is to pack objects into bins such that, for every bin, the sum of weights of obj...

In this paper, we study 1-space bounded multi-dimensional bin packing and hypercube packing. A sequence of items arrive over time, each item is a d-dimensional hyperbox (in bin packing) or hypercube (in hypercube packing), and the length of each side is no more than 1. These items must be packed without overlapping into d-dimensional hypercubes with unit length on each side. In d-dimensional sp...

We consider a variant of the generalized assignment problem (GAP) where the amount of space used in each bin is restricted to be either zero (if the bin is not opened) or above a given lower bound (aminimum quantity). We provide several complexity results for different versions of the problem and give polynomial time exact algorithms and approximation algorithms for restricted cases. For the mo...

The nuclear fuel cycle can be truly closed by supp lementing today’s thermal reactors with fast reactors, which can use as fuel the heavy, fissionable isotopes that accumulate in thermal-reactor fuel. In a fully closed cycle, the waste for disposal consists only of fission products with trace amounts of actinides. Eliminating the transuranics reduces the heat load in the repository, increasing ...

Given a set of numbers, and a set of bins of fixed capacity, the NP-complete problem of bin packing is to find the minimum number of bins needed to contain the numbers, such that the sum of the numbers assigned to each bin does not exceed the bin capacity. We present two improvements to our previous bin-completion algorithm. The first speeds up the constant factor per node generation, and the s...

This paper presents the use of genetic algorithms (GA) for solving the dual bin packing problem using fuzzy objectives. In bin packing problems, a list, L of items is to be packed into a minimum number of bins. In dual bin packing the items are packed into a maximum number of bins, assuring a minimum weight for each bin. We consider a class which we call dynamic dual bin packingg. Similar to th...

We consider the two-dimensional bin packing problem (BPP): given a set of rectangular items, find the minimal number of rectangular bins needed to pack all items. Rotation of the items is not permitted. We show for any integer k ≥ 3 that at most k − 1 bins are needed to pack all items if every item fits into a bin and if the total area of items does not exceed k/4-times the bin area. Moreover, ...