One of the main issues in addressing three-dimensional packing problems is finding an efficient and accurate definition of the points where to place the items inside the bins. The performance of exact and heuristic methods is actually strongly influenced by the choice of a placement rule. We introduce the Extreme Point concept and present a new Extreme Point-based rule for packing items inside ...

The exponential growth of computational power of the extreme scale machines over the past few decades has led to a corresponding decrease in reliability and a sharp increase of the frequency of hardware faults. Our research focuses on the mathematical challenges presented by the silent hardware faults. i.e., faults that can perturb the result of computations in an inconspicuous way. Using the a...

We present a Simplex-type algorithm, that is, an algorithm that moves from one extreme point of the infinite-dimensional feasible region to another not necessarily adjacent extreme point, for solving a class of linear programs with countably infinite variables and constraints. Each iteration of this method can be implemented in finite time, while the solution values converge to the optimal valu...