Presentation of examples of modern scenarios with digital mediametamath
The document discusses modern teaching and learning methods using digital media. It presents examples of how professors in Saxonian universities are using technologies like digital texts, videos, simulations, and online surveys. Specific examples are given of uses like central distribution of materials, flexibility in timing with video lectures, and demonstrations with digital media. Implications for constructive alignment of learning outcomes, assessments and teaching activities are discussed. The use of social learning technologies like wikis, blogs, and video conferencing are also examined. Throughout, implications for integrating these methods into teaching projects are highlighted.
Quality Assurance in Large Scale E-Assessmentsmetamath
The document discusses quality assurance in large scale e-assessments. It outlines a quality assurance process that involves (1) planning assessments according to constructive alignment principles by defining learning outcomes and designing an assessment blueprint, (2) developing assessments by creating test items and compiling tests, and (3) analyzing and evaluating assessments by analyzing item-level metrics like difficulty and discrimination and test-level reliability. The process aims to ensure assessments are valid, objective, and reliable. Quality assurance is about more than just technical issues - it also requires communication and buy-in from students and faculty.
Presentation of examples of modern scenarios with digital mediametamath
The document discusses modern teaching and learning methods using digital media. It presents examples of how professors in Saxonian universities are using technologies like digital texts, videos, simulations, and online surveys. Specific examples are given of uses like central distribution of materials, flexibility in timing with video lectures, and demonstrations with digital media. Implications for constructive alignment of learning outcomes, assessments and teaching activities are discussed. The use of social learning technologies like wikis, blogs, and video conferencing are also examined. Throughout, implications for integrating these methods into teaching projects are highlighted.
Quality Assurance in Large Scale E-Assessmentsmetamath
The document discusses quality assurance in large scale e-assessments. It outlines a quality assurance process that involves (1) planning assessments according to constructive alignment principles by defining learning outcomes and designing an assessment blueprint, (2) developing assessments by creating test items and compiling tests, and (3) analyzing and evaluating assessments by analyzing item-level metrics like difficulty and discrimination and test-level reliability. The process aims to ensure assessments are valid, objective, and reliable. Quality assurance is about more than just technical issues - it also requires communication and buy-in from students and faculty.
Intelligent Adaptive Services for Workplace-Integrated Learning on Shop Floorsmetamath
The document discusses intelligent adaptive services to support workplace-integrated learning on the shop floor. It provides context on Industry 4.0 and the transformation of manufacturing workplaces through digitalization and cyber-physical systems. The APPsist project aims to develop assistance and knowledge acquisition services for smart production environments. Services select appropriate work processes, learning content, and assistance based on the user and machine context to guide operators and support flexible on-the-job learning. The services were implemented and tested in pilot scenarios at industry partners.
Introduction to the e-Learning networ in mathematics in Saxony - E-Assessment...metamath
This document introduces an e-learning network in mathematics across universities in Saxony, Germany. The network shares electronic assessments created using ONYX and MAXIMA. Over 50 authors have created more than 1000 questions across various topics in mathematics. The assessments provide interactive practice and feedback for students and inform instructors. OPAL is the central learning platform used by 80,000 members across 11 universities. ONYX allows for different question types and MAXIMA can analyze student responses with random parameters and expressions as answers. The speaker's university courses use 4 online tests throughout a semester to provide practice for approximately 200 students.
The document describes a project to develop self-directed e-learning mathematics courses on an online platform to help students from diverse educational backgrounds succeed in their university studies, with features like entry tests, short instructional videos, interactive examples, and online exercises with personalized feedback to support learning both individually and collaboratively before classroom lessons.
This document outlines an evaluation methodology for reformed math courses. It proposes conducting a longitudinal study comparing student outcomes between a controlled group taught with old courses and an experimental group taught with new reformed courses. Student outcomes would be assessed using pre-and post-tests, pre-and post-questionnaires, and measures of grades, knowledge gain, drop-out rates, motivation, and student evaluations. Challenges include accounting for differences between groups and ensuring high response rates to electronic questionnaires.
Math-Bridge is an educational software solution that automatically generates math exercises. It uses domain reasoners and a knowledge base to create multi-step exercises that provide feedback, hints, and solutions. Exercises are generated and can be customized through an authoring interface that allows domain experts to construct exercises and feedback for students.
The document provides steps for installing and configuring the Math-Bridge system, including installing Java, copying system files, compiling, configuring the system properties and ports, adding courses, starting and stopping the server, and finalizing the administrator user configuration. It also provides tips for production settings like adjusting JVM settings and enabling caching.
- Math-Bridge is an education solution that provides teacher tools in its platform.
- The teacher tools allow teachers to manage users and user groups, content like books and tests, and generate reports on student activity.
- Specifically, teachers can edit user parameters, assign roles, import and export user lists, create and assign user groups, restrict access and assign tutors to groups. Teachers can also create and edit books and tests to include as content.
This document discusses assessment and reporting features in Math-Bridge. It describes two assessment modes: exams, which allow multiple attempts with feedback, and tests, which can be structured in pages or questions and include time constraints. Reporting provides overall user performance, individual attempt details, exercise activity, aggregated user and content feedback, and event logs. The document also mentions a search tool to access learning objects directly or through semantic or smart search, and a course assembly tool to create course books and tests.
This document provides instructions for authoring basic math exercises using the Math-Bridge education solution. It explains the structure of interactive exercises as graphs consisting of tasks, interactions and transitions. It then provides a step-by-step guide to creating the simplest possible exercise with one task node, one interaction node, and two transitions connecting to feedback nodes for correct and incorrect answers. The instructions cover adding and connecting the different node types, authoring their content, and testing the created exercise. More complex exercise graphs are also possible within this authoring tool.
This document provides instructions for translating the user interface of a math training program called Math-Bridge. It explains that interface phrases are saved in Java properties files labeled Phrases_LANG.properties using UTF-8 encoding, and that translators should open the file, translate the phrases, save it, and run an 'ant i18n' target to restart the system with the new translations.
Math-Bridge is an education solution that uses an event framework to facilitate communication between its components. The event framework allows components to publish events about actions taken, which other interested components can subscribe to and listen for. Events contain information about the action, timestamp, and source. Example events include a page being presented in a book, an exercise being started or completed, and individual exercise steps. The event framework supports listening, subscribing, and publishing events to allow components like the student model and exercise subsystem to share information and update each other.
The document describes a new authoring workflow and environment for creating and editing learning objects. The new authoring environment is web-based, WYSIWYG, and integrated with the rest of the platform. It allows authors to create new learning objects, edit existing ones, and automatically populates metadata. When publishing a modified learning object, it will either overwrite the existing one if the author is a contributor, or create a new copy with the author attributed if they are not previously a contributor.
This document provides instructions for using the jEdit text editor with the OQMath plugin to author and transform content using Math-Bridge. It describes how to configure jEdit and OQMath, enter mathematical formulas, browse available symbols, transform content to omdoc format, and common errors that may occur. Examples of different types of exercises that can be authored using this process are also provided, including fill in the blank, single choice, and multiple choice exercises.
This document describes the Math-Bridge education solution which provides pre-recorded math courses covering basic to advanced mathematics topics. The courses include videos, exercises, and assessments. Content areas include numbers, arithmetic, algebra, functions, geometry, trigonometry, calculus, probability, and more. The content is organized into collections and designed to be reusable across programs and institutions. Some content has been implemented at Leuphana University in Lüneburg, Germany for a bridging mathematics course.
Intelligent Adaptive Services for Workplace-Integrated Learning on Shop Floorsmetamath
The document discusses intelligent adaptive services to support workplace-integrated learning on the shop floor. It provides context on Industry 4.0 and the transformation of manufacturing workplaces through digitalization and cyber-physical systems. The APPsist project aims to develop assistance and knowledge acquisition services for smart production environments. Services select appropriate work processes, learning content, and assistance based on the user and machine context to guide operators and support flexible on-the-job learning. The services were implemented and tested in pilot scenarios at industry partners.
Introduction to the e-Learning networ in mathematics in Saxony - E-Assessment...metamath
This document introduces an e-learning network in mathematics across universities in Saxony, Germany. The network shares electronic assessments created using ONYX and MAXIMA. Over 50 authors have created more than 1000 questions across various topics in mathematics. The assessments provide interactive practice and feedback for students and inform instructors. OPAL is the central learning platform used by 80,000 members across 11 universities. ONYX allows for different question types and MAXIMA can analyze student responses with random parameters and expressions as answers. The speaker's university courses use 4 online tests throughout a semester to provide practice for approximately 200 students.
The document describes a project to develop self-directed e-learning mathematics courses on an online platform to help students from diverse educational backgrounds succeed in their university studies, with features like entry tests, short instructional videos, interactive examples, and online exercises with personalized feedback to support learning both individually and collaboratively before classroom lessons.
This document outlines an evaluation methodology for reformed math courses. It proposes conducting a longitudinal study comparing student outcomes between a controlled group taught with old courses and an experimental group taught with new reformed courses. Student outcomes would be assessed using pre-and post-tests, pre-and post-questionnaires, and measures of grades, knowledge gain, drop-out rates, motivation, and student evaluations. Challenges include accounting for differences between groups and ensuring high response rates to electronic questionnaires.
Math-Bridge is an educational software solution that automatically generates math exercises. It uses domain reasoners and a knowledge base to create multi-step exercises that provide feedback, hints, and solutions. Exercises are generated and can be customized through an authoring interface that allows domain experts to construct exercises and feedback for students.
The document provides steps for installing and configuring the Math-Bridge system, including installing Java, copying system files, compiling, configuring the system properties and ports, adding courses, starting and stopping the server, and finalizing the administrator user configuration. It also provides tips for production settings like adjusting JVM settings and enabling caching.
- Math-Bridge is an education solution that provides teacher tools in its platform.
- The teacher tools allow teachers to manage users and user groups, content like books and tests, and generate reports on student activity.
- Specifically, teachers can edit user parameters, assign roles, import and export user lists, create and assign user groups, restrict access and assign tutors to groups. Teachers can also create and edit books and tests to include as content.
This document discusses assessment and reporting features in Math-Bridge. It describes two assessment modes: exams, which allow multiple attempts with feedback, and tests, which can be structured in pages or questions and include time constraints. Reporting provides overall user performance, individual attempt details, exercise activity, aggregated user and content feedback, and event logs. The document also mentions a search tool to access learning objects directly or through semantic or smart search, and a course assembly tool to create course books and tests.
This document provides instructions for authoring basic math exercises using the Math-Bridge education solution. It explains the structure of interactive exercises as graphs consisting of tasks, interactions and transitions. It then provides a step-by-step guide to creating the simplest possible exercise with one task node, one interaction node, and two transitions connecting to feedback nodes for correct and incorrect answers. The instructions cover adding and connecting the different node types, authoring their content, and testing the created exercise. More complex exercise graphs are also possible within this authoring tool.
This document provides instructions for translating the user interface of a math training program called Math-Bridge. It explains that interface phrases are saved in Java properties files labeled Phrases_LANG.properties using UTF-8 encoding, and that translators should open the file, translate the phrases, save it, and run an 'ant i18n' target to restart the system with the new translations.
Math-Bridge is an education solution that uses an event framework to facilitate communication between its components. The event framework allows components to publish events about actions taken, which other interested components can subscribe to and listen for. Events contain information about the action, timestamp, and source. Example events include a page being presented in a book, an exercise being started or completed, and individual exercise steps. The event framework supports listening, subscribing, and publishing events to allow components like the student model and exercise subsystem to share information and update each other.
The document describes a new authoring workflow and environment for creating and editing learning objects. The new authoring environment is web-based, WYSIWYG, and integrated with the rest of the platform. It allows authors to create new learning objects, edit existing ones, and automatically populates metadata. When publishing a modified learning object, it will either overwrite the existing one if the author is a contributor, or create a new copy with the author attributed if they are not previously a contributor.
This document provides instructions for using the jEdit text editor with the OQMath plugin to author and transform content using Math-Bridge. It describes how to configure jEdit and OQMath, enter mathematical formulas, browse available symbols, transform content to omdoc format, and common errors that may occur. Examples of different types of exercises that can be authored using this process are also provided, including fill in the blank, single choice, and multiple choice exercises.
This document describes the Math-Bridge education solution which provides pre-recorded math courses covering basic to advanced mathematics topics. The courses include videos, exercises, and assessments. Content areas include numbers, arithmetic, algebra, functions, geometry, trigonometry, calculus, probability, and more. The content is organized into collections and designed to be reusable across programs and institutions. Some content has been implemented at Leuphana University in Lüneburg, Germany for a bridging mathematics course.
Статья «Формирование универсальных требований к пользовательским программам п...ph.d. Dmitry Stepanov
предлагается обобщенная структура описания программ. Используя предложенную структуру, формулируются универсальные требования, применимые к любым пользовательским разработкам и необходимые в процессе подготовки функционально-технической спецификации на разработку программы.
Третья часть тренинга по решению задач оптимизации в пакете GLPK. На примере решения транспортной задачи рассматриваются операции с множествами, доступные в MathProg
Применение статического анализа кода в преподавании и в разработке свободного ПОAndrey Karpov
В своём докладе я расскажу, как использование татического анализа может помочь преподавателям и студентам обучать и обучаться. Также я расскажу, как именно стоит наладить процесс анализа для использования в студенческих роектах разработки СПО, чтобы удовлетворить специфике работы в рамках учебного заведения.
В работе приведен обзор 7 классов метрик и более 50 их представителей, дано детальное описание и используемые алгоритмы вычисления, описана роль метрик в разработке программного обеспечения.
TMPA-2015: The dynamic Analysis of Executable Code in ELF Format Based on Sta...Iosif Itkin
The dynamic analysis of executable code in ELF format based on static binary instrumentation
Mikhail Yermakov,ISP RAS
12 - 14 November 2015
Tools and Methods of Program Analysis in St. Petersburg
Юрий Бабин -- многокритериальная оптимизация в инженерных проектахAnatoly Levenchuk
Доклад Юрия Бабий "Опыт применения инструментария многокритериальной оптимизациии для повышения эффективности сложных технических систем" на 65 заседании Русского отделения INCOSE, 24 октября 2012г.
Модели в профессиональной инженерии и тестировании программ. Александр Петрен...yaevents
Александр Петренко, ИСП РАН
Профессор, доктор физико-математических наук, заведующий отделом технологий программирования Института системного программирования (ИСП РАН), профессор ВМК МГУ. Основные работы в областях: формализация требований, генерация тестов на основе формализованных требований и формальных моделей (model based testing – MBT). Приложения: тестирование операционных систем и распределенных систем, тестирование компиляторов, верификация дизайна микропроцессоров, формализация стандартов на API операционных систем и телекоммуникационных протоколов. Сопредседатель оргкомитетов International MBT workshop (http://www.mbrworkshop.org/), Spring Young Researcher Colloquium on Software Engineering – SYRCoSE (http://syrocose.ispras.ru), городского семинара по технологиям разработки и анализа программ ТРАП/SDAT (http://sdat.ispras.ru/).
Тема доклада
Модели в профессиональной инженерии и тестировании программ.
Тезисы
Model Based Software Engineering (MBSE) является расширением подхода к разработке программ на основе моделей. В MBSE в отличие, например, от MDA (Model Driver Architecture) существенное внимание уделяется не только задачам собственно проектирования и разработки кода, но и задачам других фаз жизненного цикла – анализу требований, верификации и валидации, управлению требованиями на всех фазах жизненного цикла. Model Based Testing (MBT) хронологически возник гораздо раньше, чем MBSE и MDA, однако его место в разработке программ в полной мере раскрылось вместе с развитием MBSE. По этой причине MBT и MBSE следует рассматривать в тесной связке. В докладе будут рассмотрены концепции MBSE-MDA-MBT, основные источники и виды моделей, которые используются в этих подходах, методы генерации тестов на основе моделей, известные инструменты для
Завершающий доклад дня будет посвящён реализации и верификации разработанных алгоритмов обработки сигналов на конечных целевых платформах. Мы продемонстрируем современный подход к решению этой задачи в рамках концепции МОП, подразумевающий активное использование поведенческой модели алгоритма, а также автоматизацию многих этапов разработки и тестирования.
Similar to KNRTU course 1 optimisation methods (20)
Probability Theory and Mathematical Statistics in Tver State Universitymetamath
Project MetaMath outlines a probability theory and mathematical statistics course offered at Tver State University. The course is offered over two semesters for a total of 9 credits. It includes lectures, laboratory work, seminars, course projects each semester, and exams. The goal of the course is to present basic information about probability models that account for random factors. Upon completing the course, students should have mastered key probability and statistics concepts and techniques. The course also discusses modernizing elements like pre-testing students and incorporating online homework assignments.
This document compares the Discrete Mathematics curricula and courses between OMSU (National Research Ogarev Mordovia State University) in Russia and TUT (Tampere University of Technology) in Finland. It analyzes the competencies, topics, and learning outcomes covered in the Discrete Mathematics courses based on three levels of difficulty. Overall, the OMSU course covers more topics like set theory, combinatorics, algebraic structures, and coding theory over a longer duration, while the TUT course focuses more on number theory over a shorter period. The document proposes increasing engineering applications and using an online learning system to help modernize the Discrete Mathematics courses.
This document outlines a course of calculus for IT students at Lobachevsky State University of Nizhni Novgorod. The course is divided into 3 terms covering sequences, differential calculus, integral calculus, and series. Tests and exams are given throughout each term to assess student competency in mathematical thinking and problem solving. The course aims to develop skills in applying modern mathematical tools. Plans are discussed to modernize the course by adding an introductory section to address low student preparation, using online tools like METAMATH to support independent work, and testing key concepts to address educational problems.
The document discusses the discrete mathematics curriculum at Saint-Petersburg Electrotechnical University. It provides an overview of which discrete math topics are covered in each year of study for different degree programs. It also compares course parameters like credits and hours between the university and TUT. Key modules covered in the second year Math Logic and Algorithm Theory course are outlined. Competencies addressed in the curriculum are mapped to SEFI levels, with additional competencies covered uniquely at the university. Suggested modifications to improve the curriculum structure are presented.
Probability Theory and Mathematical Statisticsmetamath
This document provides information about a Probability Theory and Mathematical Statistics course taught at KNITU, Russia. It includes details about the course such as the number of students, preliminary courses required, distribution of working time, topics covered in lectures and workshops/laboratories. It also compares the methodology and topics studied in this course to a similar course taught at TUT, Finland. Key differences highlighted include the use of Matlab at TUT and more emphasis on practical work/tutorials versus lectures. Overall competencies covered are also summarized and compared between the two courses based on the SEFI framework.
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The KNITU course is mandatory, has fewer credits (3 vs 5), and less time spent (108 student hours vs 138). Key topics are similar but KNITU spends less time on lectures (10 vs 28) and nonlinear optimization.
The main difference is KNITU has fewer lectures, almost half that of TUT. This could be addressed by using an online math platform like Math-Bridge to provide additional lecture material and practice problems. Mid-term tests on Math-Bridge could help evaluate knowledge gained from the extra online content.
This document summarizes the course content and structure for Discrete Mathematics at the National Research Ogarev Mordovia State University. The course is divided into 4 modules covering set theory, graph theory, algebraic structures, and coding theory. Students take exams and write 3 essays throughout the semester to assess their understanding of each module. Pedagogical methods include lectures, practice problems, subgroup work, computer programming assignments, and a final exam to evaluate students on a 100 point scale.
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1. МЕТОДЫ ОПТИМИЗАЦИИМЕТОДЫ ОПТИМИЗАЦИИ
Пример модернизации курса
Направление «Информатика и вычислительная техника»
Магистерская программа подготовки
«Разработчик-программист (информатика как вторая компетенция)»
2. Изучаемые разделы дисциплиныИзучаемые разделы дисциплины
«Методы оптимизации»«Методы оптимизации»
2
Тема 1. Введение
1.1. Предмет и задачи дисциплины
1.2. Математическое моделирование в оптимизации
Тема 2. Методы одномерной оптимизации
2.1. Математическая модель одномерной
оптимизации
2.2. Классический метод одномерной оптимизации
2.3. Прямые методы одномерного поиска
•Метод равномерного перебора.
•Метод поразрядного поиска.
•Методы исключения отрезков.
•Метод дихотомии.
•Метод золотого сечения.
3. Изучаемые разделы дисциплиныИзучаемые разделы дисциплины
«Методы оптимизации»«Методы оптимизации»
3
Тема 3. Методы безусловной минимизации функций многих переменных
3.1. Математическая модель многомерной оптимизации
3.2. Прямые методы безусловной оптимизации
•Минимизация по правильному симплексу.
•Методы покоординатного спуска.
3.3. Методы безусловной оптимизации, использующие производные
•Метод градиентного спуска.
•Метод наискорейшего спуска.
3.4. Градиентные методы второго порядка
•Метод Ньютона.
Тема 4. Методы оптимизации при наличии ограничений
4.1 Математическая модель конечномерной оптимизации при наличии
ограничений
4.2 Классический метод решения задачи на условный экстремум
•Правило множителей Лагранжа.
4.3 Методы последовательной безусловной оптимизации
•Метод штрафных функций.
•Метод барьерных функций.
•Последовательность барьерных функций.
•Комбинированный метод штрафных функций.
•Методы случайного поиска.
4.4. Постановка задачи линейного программирования
4.5. Графический метод решения ЗЛП
4.6. Симплекс-метод решения ЗЛП
4. Модернизация темыМодернизация темы
««Методы одномерной оптимизацииМетоды одномерной оптимизации»»
4
Основное направление модернизации: добавление примеров и
приложений, непосредственно связанных с инженерной
специальностью.
ПРАКТИЧЕСКИЙ ПРИМЕР (для инженеров нефтехимических специальностей):
Химический завод производит некоторое вещество. Количество продуцируемого
вещества определяется температурой реакции: у = F (T).Температура может
изменяться в определенных пределах: T1 <T <T2. Вид функции F заранее не известен,
она зависит от используемого сырья. Поступила очередная партия сырья, необходимо
найти температуру Т, при которой производство наиболее выгодно, то есть функция
F(T) достигает своего максимального значения.
Разработано 5 прикладных примеров для инженеров различных
специальностей по каждому из пяти изучаемых методов.
5. Реализация примеров в программных пакетах.Реализация примеров в программных пакетах.
Перспектива использованияПерспектива использования Math-BridgeMath-Bridge..
Реализация в прикладном программном комплексе MainOp2012 (метод дихотомии)
5
Реализация в пакете MatLab (метод золотого сечения)
M – функция, вычисляющая f(x)
function y=ext(x) y=arctg(sin(x)- cos(x)); end
%------------------------------------------ %
Построение графика
>> x=-5:0.1:6;
>> y=ext(x);
>> plot(x,y,'-k') > [x,y]=fminbnd(@ext(-3.14, 3.14)
x = 2.35619
y = 0.9817
>>
6. Модернизация темыМодернизация темы
««Методы безусловной минимизации функций многихМетоды безусловной минимизации функций многих
переменныхпеременных»»
6
Основное направление модернизации: реализация инженерных
примеров в программных пакетах.
ПРАКТИЧЕСКИЙ ПРИМЕР (для инженеров самолетостроительных специальностей):
Разработка программной реализации 5 прикладных примеров для
инженеров различных специальностей по каждому из пяти изучаемых
методов.
7. Реализация примеров в программных пакетах.Реализация примеров в программных пакетах.
Перспектива использованияПерспектива использования Math-BridgeMath-Bridge..
7
Реализация в пакете MatLab (Simulink)
8. Модернизация темыМодернизация темы
««Методы оптимизации при наличии ограничений»Методы оптимизации при наличии ограничений»
нелинейная оптимизациянелинейная оптимизация
8
ПРАКТИЧЕСКИЙ ПРИМЕР (для инженеров машиностроительных специальностей):
Основное направление модернизации: добавление примеров и
приложений, непосредственно связанных с инженерной
специальностью.
Разработано 4 прикладных примера для инженеров различных
специальностей по каждому из четырех изучаемых методов.
Контактные задачи для узлов экипажной части подвижного состава
железных дорог с учетом и без учета трения, шероховатости
поверхностей, а также с большими перемещениями.
9. Модернизация темыМодернизация темы
««Методы оптимизации при наличии ограничений»Методы оптимизации при наличии ограничений»
линейная оптимизациялинейная оптимизация
9
ПРАКТИЧЕСКИЙ ПРИМЕР (для инженеров-логистиков):
Основное направление модернизации: добавление примеров и
приложений, непосредственно связанных с инженерной специальностью, и
их программная реализация.
Разработано 2 прикладных примера для инженеров различных
специальностей по каждому из изучаемых методов.
Имеется транспортная сеть, связывающая заводы-
изготовители, оптовые базы и пункты розничных продаж.
Расположение и возможные пути перевозок между ними
указаны на схеме. Ежемесячные объемы выпуска товара на
заводах и имеющиеся к настоящему времени остаточные
запасы на оптовых базах указаны в таблице 1 и таблице 2. С
некоторых оптовых баз также осуществляется
непосредственная продажа товара в объемах, указанных в
таблице 3. Ежемесячный объем продаж в каждом магазине
указан в таблице 4. Стоимости перевозок указаны в табл. 5.
Найти план перевозки продукции с заводов через оптовые
базы в магазины так, чтобы весь товар с заводов и баз с
излишками продукции был вывезен на базы и в магазины
розничных продаж. При этом суммарная стоимость
перевозки должна быть минимальной.
10. Реализация примеров в программных пакетах.Реализация примеров в программных пакетах.
Перспектива использованияПерспектива использования Math-BridgeMath-Bridge..
10
Реализация в специализированном программном комплексе (графический метод)