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This document presents in detail the mathematical formulation of the second renewable energy auction in Colombia, used for the allocation of long-term energy contracts, which was carried out through a double-sided auction, defined in Resolutions 4-0590 and 4-0591 of 2019 from the UPME. The mixed integer linear programming model developed in this paper solves an optimization problem that seeks the combination of offers that maximizes the benefit of the consumer, subject to operational and economic constraints proposed by regulatory mechanisms. The effectiveness of the algorithm developed in Python was tested by validating it with real data, obtaining the same results published by UPME. [ABSTRACT FROM AUTHOR]

In this paper we propose to use the principle of available data derived from the NIPALS (Nonlinear estimation by Iterative Partial Least Square) algorithm to work on the Principal Components Analysis (PCA) in the presence of missing data. This proposal is important since it does not perform data imputation, nor are individuals discarded from the database; the proposed method works with the available pairs to form the quasicorrelation matrices in 𝑹𝒑 and in 𝑹𝒏; the spectral decomposition of these matrices allows through the transition relations to realize a conventional PCA. From the simulation study carried out, it was found that as the percentage of missing data increases, the inertia explained in the first factorial plane decreases. The solution algorithm was developed under the R programming environment and the code is appended for free use. [ABSTRACT FROM AUTHOR]

The quadratic eigenvalue problem has attracted the interest of many researchers due to its numerous applications in areas such as fluid mechanics, acoustics and engineering, among others. In this paper we present a hybrid algorithm to solve this problem, which combines an algorithm for the calculation of solutions of the matrix quadratic equation with a traditional one for the calculation of eigenvalues. Twelve application problems were selected, in different areas, to make a comparative analysis of the performance of the proposed algorithm with the traditional Newton method. In conclusion, it was determined that the algorithmic proposal is competitive with Newton's method and more efficient. [ABSTRACT FROM AUTHOR]

This paper presents the design of a charge regulator operating in an isolated micro grid with photovoltaic generation. The converter selected for this application is a SEPIC with a MPPT algorithm for the cases in which the energy demand is greater than the energy available. The algorithm is able to modify its point of maximum power, in order to perform the recharging and supply of power to the battery bank of the system (isolated microgrid) and a group of charges set at a level of determined of voltage. Finally, the results of the tests carried out are presented and the conclusions are given. [ABSTRACT FROM AUTHOR]

This paper is about the application of heuristics to solve a programming problem sequential multiple jobs to multiple machines in parallel, in a production by order, which applies in organizations where each customer order is unique and has its own parameters and conditions. A brief introduction of sequential programming concepts, it's constituent elements, performance measures relationship and is complemented by a case study presentation, with it's statement, the organization of information, the technological sequence, routes each task, the graph that represents the production system, the precedence list, the feasible implementation program, the decision criteria for programming operations and the application of Matlab to solve the problem. In the end, relate valuable conclusions that can be taken as a result of this important heuristic, which may serve to improve the control of any enterprise production and it's application in a specific case of the production orders. [ABSTRACT FROM AUTHOR]

This paper is about the application of heuristics to solve a programming problem sequential multiple jobs to multiple machines in parallel, in a production by order, which applies in organizations where each customer order is unique and has its own parameters and conditions. A brief introduction of sequential programming concepts, it's constituent elements, performance measures relationship and is complemented by a case study presentation, with it's statement, the organization of information, the technological sequence, routes each task, the graph that represents the production system, the precedence list, the feasible implementation program, the decision criteria for programming operations and the application of Matlab to solve the problem. In the end, relate valuable conclusions that can be taken as a result of this important heuristic, which may serve to improve the control of any enterprise production and it's application in a specific case of the production orders. [ABSTRACT FROM AUTHOR]