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In this work the problem of determination of the optimal catheter position and source loading in HDR prostate brachytherapy is modeled as a Mixed Integer Linear Programming (MILP) problem and solved by ILOG CPLEX. The results are compared to those of HIPO, a state of the art inverse treatment plan optimization algorithm. Given that MILP is guaranteed to find the global optimum, it provides the baseline for the evaluation of HIPO solutions. The quality of 12 clinical HDR brachytherapy implants for prostate utilizing HIPO, for dwell time optimization only, has been compared to alternative plans with Linear Programming (LP). All common dose-volume indices for the prostate and the organs at risk have been considered. Our results demonstrate that in the case of dwell time optimization, HIPO delivers high quality plans and the differences to the LP solutions are statistically insignificant (p > 0.05) for all indices examined. In the case of combined catheter position and dwell time optimization, the results for 3 clinical cases have been compared. MILP was able to deliver the optimal solution only for one simple case and upper- lower bounds for the rest. The plans produced by HIPO were clinically acceptable, close and clinically equivalent to the global optimum or the upper bounds delivered by MILP for all 3 cases. [ABSTRACT FROM AUTHOR]

Mixed Integer Programs are a class of optimization problems which have a vast range of applications in engineering, business, science, health care, and other areas. For many applications, however, problems of realistic size can take a an impractical amount of time to solve on a single workstation. However, using parallel computing resources to solve MIP is difficult, as parallelizing the standard branch-and-bound framework presents an array of challenges. In this paper we present a novel framework called a Parallel Macro Partitioning (PMaP) framework for solving mixed integer programs in parallel. The framework exploit ideas from modern MIP heuristics to partition the problem at a high-level into MIP subproblems, each of which can be solved on a separate processor by an MIP algorithm. Initial computational resources suggest that PMaP has significant promise as a framework capable of bringing many processors to bear effectively on difficult problems. [ABSTRACT FROM AUTHOR]

We present an overview of mathematical optimization models and solution algorithms related to optimal network design and dimensioning in telecommunications. All the models discussed are expressed in terras of minimum cost multicommodity network flows with appropriate choice of link (or node) cost functions. Various special cases related to practical applications are examined, including the linear case, the linear with fixed cost case, and the case of general discontinuous nondecreasing cost functions. It is also shown how the generic models presented can accommodate a variety of constraints frequently encountered in applications, such as, among others, constraints on the choice of routes, robustness and survivability constraints. Finally we provide an overview of recent developments in solution algorithms, emphasizing those approaches capable of finding provably exact solutions, which are essentially based on general mixed integer programming techniques, relaxation, cutting-plane generation techniques and branch & cut. [ABSTRACT FROM AUTHOR]

The article discusses the importance of advanced information technologies and expanded logistics infrastructure in the improvement of global business environment. Buyers and sellers are able to share information and exchange decisions in real time while products can be moved from place to place globally.