Optimization has become an important tool in treatment planning for cancer radiation therapy. It may be used to determine beam weights, beam directions, and appropriate use of beam modifiers such as wedges and blocks, with the aim of delivering a required dose to the tumor, while sparing nearby critical structures and normal tissue. Linear programing formulations are a core computation in many ...

Graphics Processing Units (GPUs) with high computational capabilities used as modern parallel platforms to deal with complex computational problems. We use this platform to solve large-scale linear programing problems by revised simplex algorithm. To implement this algorithm, we propose some new memory management strategies. In addition, to avoid cycling because of degeneracy conditions, we use...

Presents article is deal with optimization of the fixture for end milling process, the most important objective being the minimization of work piece deformation by changing the layout of fixture elements and the clamping forces. The main objective of this work has been the optimization of the fixtures Work piece deformation subjected to clamping forces for End milling operation. The present ana...

The Roman domination problem is considered. An improvement of two existing Integer Linear Programing (ILP) formulations is proposed and a comparison between the old and new ones is given. Correctness proofs show that improved linear programing formulations are equivalent to the existing ones regardless of the variables relaxation and usage of lesser number of constraints.

This paper deals with the average-case-analysis of the number of pivot steps required by the simplex method. It generalizes results of Borgwardt (who worked under the assumpution of the rotation-symmetry-model) for the shadow-vertex-algorithm to so-called cylindric distributions. Simultaneously it allows to analyze an extended dimension-by-dimension-algorithm, which solves linear programing pro...

there are two interesting methods, in the literature, for solving fuzzy linear programming problems in which the elements of coefficient matrix of the constraints are represented by real numbers and rest of the parameters are represented by symmetric trapezoidal fuzzy numbers. the first method, named as fuzzy primal simplex method, assumes an initial primal basic feasible solution is at hand. t...