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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]

This paper proposes a hybrid heuristic that combines Variable Neighborhood Search (VNS) with Ant Colony Optimization (ACO) to solve the scheduling problem of nonrelated parallel machines with sequence dependent setup times in order to minimize the makespan. The Variable Neighborhood Search is proposed to solve the scheduling problem with a descending scheme in a first phase, with an ACO algorithm, which successively reorder the jobs in the machine with the largest makespan in a second phase. An experimental study was performed using test problems from the literature showing that the second phase of the algorithm improves the solution obtained in the first phase. The results obtained are also compared with other methods in the literature proving to be a competitive method. [ABSTRACT FROM AUTHOR]

Using the classification methods for mathematical problems in textbooks (Fan & Zhu, 2000) and strategies used to solve problems (Fan & Zhu, 2007), this paper reports the results of an analysis and classification of the type of mathematical problems and problem-solving strategies in a sample made up of the five most widely-used mathematics textbooks for the first year of junior high school in the 2013- 2014 school year in Mexico. It is concluded that the textbooks focus on providing a comprehensive range of problems that, for the most part, do not allow multiple problem-solving strategies, whereas others can be solved using an algorithm or direct procedure. [ABSTRACT FROM AUTHOR]