On Some Aspects of the Examination in Econometrics

Teaching econometrics has been studied by a number of researchers, however, there is little information available on the quality of examination and on simplification of tests for demonstration the high-quality knowledge by students in concrete topics of econometrics or mathematical economics.One can note the following main goals of studying the basics of mathematical economics or econometrics by students: forming the notions of mathematical model and of modeling economic processes and phenomena; understanding a role of using mathematical models for economics research and obtaining scientific results; formatting skills for constructing mathematical models in economics, for solving economics problems by mathematical modeling.The main goal of this paper is to simplify test tasks, is to help to students to demonstrate the high-quality knowledge in certain areas of mathematical economics, and also is to construct a system of testing tasks, in which the emphasis was placed on the knowledge and understanding of an algorithm of solving the problem.In the present paper, to quality examine the student knowledge in the basics of mathematical economics, a certain system of tests was constructed and is considered. The main attention is also given to algorithms and techniques of solving some tasks (problems) of mathematical economics. The following topics of mathematical economics are viewed: constructing mathematical models of linear programming, the input-output model, the Monge-Kantorovich transportation problem, the simplex method of linear programming, the graphic method of linear and nonlinear programming, the method of Lagrange multipliers in mathematical optimization. Some primary basic results of studying linear programming, nonlinear programming, and the input-output model are noted.A new system of tests that satisfies the aim of this paper is modeled. The described tests require less time for solving than usual tasks. Here we do not focus on the repetition of auxiliary mathematical knowledge and arithmetic skills. These tests are simplified versions of standard tasks and help students to demonstrate knowledge in the mentioned topics of mathematical economics. The tasks are focused only on the knowledge of basic formulas, techniques, and connections between mathematical objects, economic systems, and their elements.

A Review on the Complementarity Modelling in Competitive Electricity Markets

In recent years, the ever-increasing research interest in various aspects of the electricity pool-based markets has generated a plethora of complementarity-based approaches to determine participating agents’ optimal offering/bidding strategies and model players’ interactions. In particular, the integration of multiple and diversified market agents, such as conventional generation companies, renewable energy sources, electricity storage facilities and agents with a mixed generation portfolio has instigated significant competition, as each player attempts to establish their market dominance and realize substantial financial benefits. The employment of complementarity modelling approaches can also prove beneficial for the optimal coordination of the electricity and natural gas market coupling. Linear and nonlinear programming as well as complementarity modelling, mainly in the form of mathematical programs with equilibrium constraints (MPECs), equilibrium programs with equilibrium constraints (EPECs) and conjectural variations models (CV) have been widely employed to provide effective market clearing mechanisms, enhance agents’ decision-making process and allow them to exert market power, under perfect and imperfect competition and various market settlements. This work first introduces the theoretical concepts that regulate the majority of contemporary competitive electricity markets. It then presents a comprehensive review of recent advances related to complementarity-based modelling methodologies and their implementation in current competitive electricity pool-based markets applications.

Reverse logistics models for the collection of plastic waste: A literature review

To support the understanding of recycling models applied to plastics, the main objective of this work is to offer a literature review of the different reverse logistics (RL) models for collecting plastic waste (PW). The methodology used for processing the scientific literature was content analysis, using the google scholar search engine. The main keywords used were RL and PW. This article is divided into two parts: the first part discusses the development of circular economy models and RL networks and raises the conceptual framework of the research, and the second part presents mathematical models and exploratory studies, proposed as a solution for RL problems of PW. Articles published between years 2014 and 2019 were reviewed. In total, 102 references were used, 70 of them are part of the literature review. According to our findings, we can state that the most widely used solution method for mathematical modeling is mixed-integer linear programming, and for exploratory studies, it was evaluations. About 93% of studies evaluated raw materials related to PW; only 13% of studies had models with stochastic processes; and 88% of the investigations used continuous variables, being the multiobjective functions one of the most used to provide solutions to RL problems. Regarding the mathematical models, 49% were evaluations, 9% corresponded to multicriteria analysis, 29% to linear and nonlinear programming, and 4% to another type of evaluation or model.

Neutrosophic Number Optimization Models and Their Application in the Practical Production Process

In order to simplify the complex calculation and solve the difficult solution problems of neutrosophic number optimization models (NNOMs) in the practical production process, this paper presents two methods to solve NNOMs, where Matlab built-in function “fmincon()” and neutrosophic number operations (NNOs) are used in indeterminate environments. Next, the two methods are applied to linear and nonlinear programming problems with neutrosophic number information to obtain the optimal solution of the maximum/minimum objective function under the constrained conditions of practical productions by neutrosophic number optimization programming (NNOP) examples. Finally, under indeterminate environments, the fit optimal solutions of the examples can also be achieved by using some specified indeterminate scales to fulfill some specified actual requirements. The NNOP methods can obtain the feasible and flexible optimal solutions and indicate the advantage of simple calculations in practical applications.

Modeling the Activities of the Operating Personnel in the Process of Managing Production Facilities of the Fuel and Energy Complex

Most of the enterprises of the fuel and energy complex are controlled using the automated system that identifies information about the state of the control object, transforms it, makes a control decision and transfers it to the control object. The model of such a system was developed — it consists of 13 blocks. Systematic approach to its building based on the use of linear and nonlinear programming methods is proposed. In some cases, in the event of emergency situations, it becomes difficult for the automated system to make management decisions, and it grants this right to the human operator. The algorithm for solving the problem by the operator was created. For the convenience of its formalization, it was simplified to four basic operations. In the first operation, the information is identified and presented in the formalized form. At the second stage, the information is decoded. Further, the information is analyzed. At the fourth stage, automatic systems turn off and switch to a backup (manual) information control algorithm. The control model is formed based on the mismatch of the current and set values of the object parameters. This is followed by the processing of information, after which the output signal is generated. There are two possible control options — discrete and continuous parameters. The output signal is generated based on the input signal. The analysis of the process of information perception includes two aspects: determining the time of arrival of information and obtaining the necessary data for establishing the algorithm for working actions. The staff forms the required base and conditions for the implementation of these aspects. The output signal control function is built. The expression is obtained for determining the condition, after which the person starts to control. With the developed form of control, the mismatch of the parameters at some point in time tends to zero. Thus, the mechanism for the implementation of human actions in an automated control system was investigated from the moment the «alarm» signal arrives to the formation of tasks by the manager.

Nonlinear problems of structural mechanics. Methods of optimal design of structures

The textbook discusses methods of optimal design of structures, including methods for minimizing the functions of one and several variables; methods for solving linear and nonlinear programming problems; examples of optimal design of flat steel frames with elements made of rolled and composite I-beams. It is intended for students studying in the specialty 08.05.01 "Construction of unique buildings and structures", undergraduates studying in the training program 08.04.01.24 "Modern technologies of design and construction of buildings and structures", studying the discipline "Nonlinear problems of structural mechanics", as well as for postgraduates of the direction 08.06.01 " Engineering and construction technologies. Construction of buildings and structures", studying the discipline "Construction Mechanics".