Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators

In this paper, we establish Fritz John stationary conditions for nonsmooth, nonlinear, semidefinite, multiobjective programs with vanishing constraints in terms of convexificator and introduce generalized Cottle type and generalized Guignard type constraints qualification to achieve strong S—stationary conditions from Fritz John stationary conditions. Further, we establish strong S—stationary necessary and sufficient conditions, independently from Fritz John conditions. The optimality results for multiobjective semidefinite optimization problem in this paper is related to two recent articles by Treanta in 2021. Treanta in 2021 discussed duality theorems for special class of quasiinvex multiobjective optimization problems for interval-valued components. The study in our article can also be seen and extended for the interval-valued optimization motivated by Treanta (2021). Some examples are provided to validate our established results.

Algorithms for Picking and Distribution of Online Orders in New Retail Enterprises

This paper studies joint algorithms of order picking and distribution in new retail enterprises. The problem will consider many factors, such as the type of goods, picking time, batch capacity of distribution, distribution time, and distribution cost. First of all, the research problems are summarized as mathematical programming problems. Then, a genetic algorithm and comparison algorithms are proposed. Finally, the rationality of the model and the effectiveness of the algorithms are verified by computational experiments, and management enlightenments are revealed.

Multi-criteria analysis of road bitumen production processes by oxidation of refined petroleum products

Based on the DEA method, an approach has been developed for the multivariate analysis of the road bitumen production processes, allowing obtaining integral comparative assessments that ensure the ranking of processes according to various heterogeneous criteria. The main quantitative characteristics, qualitative indicators, and technological parameters of the oxidation processes are selected to form target functions when solving mathematical programming problems. Based on the CCR and Super Efficiency models of the DEA method, the problems of multivariate analysis of the efficiency of road bitumen production processes for the actual values ​​of the characteristics of raw materials and parameters of technological processes were formulated and solved, a comparative analysis of the estimates obtained for 64 bitumen samples was carried out. The results of the studies carried out make it possible to significantly expand the scope of the DEA method application and create on its basis a software package for multivariate analysis and optimization of bitumen production processes by improving the quality of the final product, reducing the resources for its production and reducing the negative impact on the environment.

Multi-factor analysis and operation optimization for the imple-mentation of foreign economic activity AT an industrial enterprise

The paper is devoted to the urgent problem of increasing the efficiency of foreign economic activity of enterprises of the metallurgical and machine-building industries. To increase the economic efficiency of industrial enterprises functioning in the process of implementing foreign economic activity, the paper proposes an algorithm for multivariate analysis, including the procedure for optimizing the system of interaction between an enterprise and customs authorities. When developing and testing the algorithm, customs operations are considered as critical links that determine the increase of the enterprise foreign economic activity efficiency. The mathematical programming problems are formulated on the basis of the CCR model of the DEA (Data envelopment Analysis) method to carry out a multivariate analysis of the comparative efficiency of import and/or export customs operations. The relative efficiency estimates obtained from solving mathematical programming problems make it possible to identify ineffective or least effective export and import customs operations. Based on directed weighted graphs, the special procedures have been developed to optimize the following parameters of customs operations: time of customs operations, labor costs of the enterprise, financial costs associated with compliance with the established prohibitions and restrictions of foreign trade. The algorithm was tested on the example of an industrial enterprise in the metallurgical industry Arkonik SMZ, which carries out export operations for the sale of lid tape of its own production, as well as import operations for the supply of varnish, which is a necessary technological material to ensure the production process of the tape. The administrative and operational decisions made on the basis of comparative evaluations of the obtained optimization results make it possible to exclude ineffective customs operations of foreign economic activity of an industrial enterprise.

Development and application of optimization models in the production capacity management strategy

Subject. The article addresses elaboration of methods for strategic management of production capacities to bring them to practical use at the level of individual industrial enterprises. Objectives. The purpose of the study is to develop optimization models to manage production capacities of industrial enterprises at the strategic level. The models are focused on bringing enterprise structure to the optimal condition in terms of output of products that are in demand in the market. Methods. The study employs methods of analysis and synthesis, principles of consistency and complexity, theory of graphs, matrix calculus. Results. To develop existing approaches to the strategic management of production capacities, I offer a multicriteria optimization model, structurally consisting of several mathematical programming problems. Conclusions. If used, the optimization models for the development of a production capacity management strategy will enable modern Russian enterprises to significantly increase their competitiveness and operational efficiency, since the level of production capacity affects the positioning of an enterprise in the market, its cost structure, etc.

Pre-Emptive and Non-Pre-Emptive Goal Programming Problems for Optimal Menu Planning in Diet Management of Indian Diabetes Mellitus Patients

Diet management or caloric restriction for diabetes mellitus patients is essential in order to reduce the disease’s burden. Mathematical programming problems can help in this regard; they have a central role in optimal diet management and in the nutritional balance of food recipes. The present study employed linear optimization models such as linear, pre-emptive, and non-pre-emptive goal programming problems (LPP, PGP and NPGP) to minimize the deviations of over and under achievements of specific nutrients for optimal selection of food menus with various energy (calories) levels. Sixty-two food recipes are considered, all selected because of being commonly available for the Indian population and developed dietary intake for meal planning through optimization models. The results suggest that a variety of Indian food recipes with low glycemic values can be chosen to assist the varying glucose levels (>200 mg/dL) of Indian diabetes patients.

Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers

Single-valued neutrosophic set (SVNS) is considered as generalization and extension of fuzzy set, intuitionistic fuzzy set (IFS), and crisp set for expressing the imprecise, incomplete, and indeterminate information about real-life decision-oriented models. The theme of this research is to develop a solution approach to solve constrained bimatrix games with payoffs of single-valued trapezoidal neutrosophic numbers (SVTNNs). In this approach, the concepts and suitable ranking function of SVTNNs are defined. Hereby, the equilibrium optimal strategies and equilibrium values for both players can be determined by solving the parameterized mathematical programming problems, which are obtained from two novel auxiliary SVTNNs programming problems based on the proposed ranking approach of SVTNNs. Moreover, an application example is examined to verify the effectiveness and superiority of the developed algorithm. Finally, a comparison analysis between the proposed and the existing approaches is conducted to expose the advantages of our work.

Correction to: A sequential homotopy method for mathematical programming problems

A correction to this paper has been published: https://doi.org/10.1007/s10107-021-01668-5

Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers

Optimization problems in the fuzzy environment are widely studied in the literature. We restrict our attention to mathematical programming problems with coefficients and/or decision variables expressed by fuzzy numbers. Since the review of the recent literature on mathematical programming in the fuzzy environment shows that the extension principle is widely present through the fuzzy arithmetic but much less involved in the foundations of the solution concepts, we believe that efforts to rehabilitate the idea of following the extension principle when deriving relevant fuzzy descriptions to optimal solutions are highly needed. This paper identifies the current position and role of the extension principle in solving mathematical programming problems that involve fuzzy numbers in their models, highlighting the indispensability of the extension principle in approaching this class of problems. After presenting the basic ideas in fuzzy optimization, underlying the advantages and disadvantages of different solution approaches, we review the main methodologies yielding solutions that elude the extension principle, and then compare them to those that follow it. We also suggest research directions focusing on using the extension principle in all stages of the optimization process.

Ship optimization using the preferences of the designer

В статье рассматривается подход к решению задачи оптимизации характеристик корабля на ранних стадиях проектирования. Задача оптимизационного проектирования формулируется как многокритериальная. Дается краткий обзор подходов к решению задач математического программирования такого класса. Рассматривается такой метод многокритериальной оптимизации, широко используемый в экономических задачах, как оптимизация по Парето. Для решения задач, связанных с созданием технических систем, характерно большое количество частных критериев эффективности, выраженных, как правило, нелинейными функциями, а иногда описанными алгоритмическими процедурами. Следовательно, поверхность эффективных точек Парето, на которой ищется наилучший вариант проекта, представляет собой сложный геометрический объект в n- мерном пространстве частных критериев. Выбор наилучшего решения предлагается путем использования предпочтения проектанта, сформулированными в виде функции ценности. Функция ценности также является сложной поверхностью в n-мерном критериальном пространстве. Аналитическое решение, дающее координаты точек касания этих поверхностей, представляет сложную математическую проблему. В статье предлагается численный метод решения задачи оптимизации по Парето для сложной технической системы, каковой является корабль. The article considers an approach to solving the problem of optimizing the ship's characteristics at the early stages of design. The optimization design problem is formulated as a multi-criteria one. A brief overview of approaches to solving mathematical programming problems of this class is given. We consider such a method of multi-criteria optimization, widely used in economic problems, as Pareto optimization. To solve problems related to the creation of technical systems, a large number of specific performance criteria are characteristic, expressed, as a rule, by nonlinear functions, and sometimes described by algorithmic procedures. Consequently, the surface of effective Pareto points, on which the best variant of the project is sought, is a complex geometric object in the n-dimensional space of partial criteria. The choice of the best solution is proposed by using the preferences of the designer, formulated in the form of a value function. The value function is also a complex surface in the n-dimensional criterion space. The analytical solution that gives the coordinates of the points of contact of these surfaces is a complex mathematical problem. The paper proposes a numerical method for solving the Pareto optimization problem for a complex technical system, such as a ship.