MPI parallel programming of mixed integer optimization problems using CPLEX with COIN-OR

The aim of this technical report is to present some detailed explanations in order to help to understand and use the Message Passing Interface (MPI) parallel programming for solving several mixed integer optimization problems. We have developed a C++ experimental code that uses the IBM ILOG CPLEX optimizer within the COmputational INfrastructure for Operations Research (COIN-OR) and MPI parallel computing for solving the optimization models under UNIX-like systems. The computational experience illustrates how can we solve 44 optimization problems which are asymmetric with respect to the number of integer and continuous variables and the number of constraints. We also report a comparative with the speedup and efficiency of several strategies implemented for some available number of threads.

Distribution of Healthcare resources II.Study and Comparison of a Linear Programming Problem and its Dual. Resolution and Evaluation of a Practical Case and its Programming using Excel and Win QSB.

[EN]This research had as primary objective to model different types of problems using linear programming and apply different methods so as to find an adequate solution to them. To achieve this objective, a linear programming problem and its dual were studied and compared. For that, linear programming techniques were provided and an introduction of the duality theory was given, analyzing the dual problem and the duality theorems. Then, a general economic interpretation was given and different optimal dual variables like shadow prices were studied through the next practical case: An aesthetic surgery hospital wanted to organize its monthly waiting list of four types of surgeries to maximize its daily income. To solve this practical case, we modelled the linear programming problem following the relationships between the primal problem and its dual. Additionally, we solved the dual problem graphically, and then we found the optimal solution of the practical case posed through its dual, following the different theorems of the duality theory. Moreover, how Complementary Slackness can help to solve linear programming problems was studied. To facilitate the solution Solver application of Excel and Win QSB programme were used.

Do Nutritional Supplements Have a Role in Age Macular Degeneration Prevention?

Purpose. To review the proposed pathogenic mechanisms of age macular degeneration (AMD), as well as the role of antioxidants (AOX) and omega-3 fatty acids (omega-3) supplements in AMD prevention. Materials and Methods. Current knowledge on the cellular/molecular mechanisms of AMD and the epidemiologic/experimental studies on the effects of AOX and omega-3 were addressed all together with the scientific evidence and the personal opinion of professionals involved in the Retina Group of the OFTARED (Spain). Results. High dietary intakes of omega-3 and macular pigments lutein/zeaxanthin are associated with lower risk of prevalence and incidence in AMD. The Age-Related Eye Disease study (AREDS) showed a beneficial effect of high doses of vitamins C, E, beta-carotene, and zinc/copper in reducing the rate of progression to advanced AMD in patients with intermediate AMD or with one-sided late AMD. The AREDS-2 study has shown that lutein and zeaxanthin may substitute beta-carotene because of its potential relationship with increased lung cancer incidence. Conclusion. Research has proved that elder people with poor diets, especially with low AOX and omega-3 micronutrients intake and subsequently having low plasmatic levels, are more prone to developing AMD. Micronutrient supplementation enhances antioxidant defense and healthy eyes and might prevent/retard/modify AMD.