Українська   Русский
DonNTU   Masters' portal

Abstract

Соntents

Introduction

Health care is one of the main areas that determine the quality of life and social well-being of society. In one of any health comes a point when the update becomes vital medical equipment important need. It is known that during the operation of equipment loses its quality. Moreover, technological progress, which is not in place, facilitated by the relatively rapid obsolescence of the original performance equipment. In order to bring it to the level corresponding to modern requirements for fixed assets, institutions modernizing.

When the need arises for the best option upgrade medical equipment based on the availability of space for equipment and skills medical staff with minimal upgrades. Therefore, the most important assistant manager are decision support systems solutions that allow you to simulate the situation and form the best strategy. In some cases, when making decisions, we assume errors with implications of varying degrees of importance. Therefore, one of the undoubted success of the conditions regardless of the nature and specificity of work is the art of making the right decisions [4].

1. Theme urgency

Master's thesis is devoted to the actual problem to date healthcare modernization. Every year, hospital equipment, with a high rate of medical processes, quickly wear out, become obsolete and out of order and therefore provide a decent standard of medical care equipment needs to be replaced. Modernization of medical equipment is the key to effectively care for patients. When selecting the size and direction of modernization is reasonable to take into account the financial resources, the possibility of practitioners, how doctors are trained to work with new types of equipment, there is a need for space to install the equipment. For the problem of obsolescence of buildings hospitals and the need for their respective modernization as social objects is also very important.

2. Goal and tasks of the research

Aim of this study is to develop a decision support system for the modernization of medical institution.

To achieve this goal the following tasks:

  1. Develop a mathematical model of the modernization plan of medical institution.
  2. Search and identify strengths and weaknesses of existing optimization techniques.
  3. Selecting the best method for solving the problem.

Research object: the process of modernization of medical institution.

Research subject: optimization techniques to help determine the best solution.

3. Scientific novelty

To date, this has not been developed decision support system that would afford the best upgrade options. But there are similar systems used in other areas and are based on ant algorithm. Ant colony algorithm is applicable in many optimization problems, especially on graphs. Mostly it gives a positive effect.

4. The mathematical formulation

The task of constructing a medical institution modernization plan can be formulated as finding the optimal path in space decision-making. The main task is to find the minimum of the functional F under the given constraints. Need to find a solution which would be carried out at all the restrictions and costs were minimal. Decision space can generally be represented as a weighted graph in Figure 1.

We introduce the notion of a weighted graph solutions. Weighted graph solutions (G) graph, each edge of which is mapped to weight of the edge. Such a graph can be represented as:

pic1 (1)

where

V – variety of vertices (actions),

E – variety of arcs (edges),

W – variety of weights.

Arcs can be represented as:

pic2 (2)

Arc connects two vertices. As the edges of the graph are the actions vi vj, which will be performed on objects of modernization equipment, facilities, personnel.

To determine the shortest path from one vertex to another must be able to measure the distance between nodes (actions), so we introduce a distance function defined on the arcs of d: E→R, где R – variety of real numbers.

The weights take into account the degree of risk and cost levels can be represented as:

pic3 (3)

where wij – weight of the arc.

In addition, we introduce the function limitations for each node. Restriction is function on top of the graph.

pic4 (4)

Restrictions:

Consider the following risks:

Criterion need of modernization

Each vertex of the graph we associate an index ranging from 0 to 1. Wear index is a function that depends on time. The larger the index ,the greater the need for modernization.

Minimum of the functional sequence of vertices of F is reached, the sum of weights which gives the lowest possible weight.

pic7 (7)
pic8

Figure 1 – Graph of solutions

Actions on the graph are:

  1. Modernization
  2. Selection of equipment
  3. Buying a new
  4. Adjustment
  5. Installation
  6. Other costs
  7. Renovated old
  8. Do nothing
  9. Selection of placing
  10. Building a new
  11. Renovated old
  12. Do nothing
  13. Selection of personal
  14. Teaching
  15. To hire a new
  16. Not teach

5. Ant algorithm

To solve this problem dealt with the following methods: ant algorithm, the algorithm imitation annealing, dynamic programming, algorithm A *, binary binary search trees. It is supposed to use the ant algorithm to solve.

The idea of ant algorithm – modeling of the behavior of ants associated with their ability to quickly find the shortest path from nest to a food source and to adapt to changing conditions, finding new shortest path. In its motion the ant leaves pheromone in its path, and this information is used other ants to choose path. This is an elementary rule of conduct and determine the ability of ants to find new path, if the old is unavailable.

Base formic algorithm, regardless of modifications can be represented as a circuit (Figure 2).

Figure 2 - Generalized ant algorithm

Figure 2 – Generalized ant algorithm

Conclusion

To date, upgrading health facilities is extremely important and topical issue in terms health system development. Using outdated technology in medicine, late replacement inventory results to frequent breakdowns of equipment, appearance of unavoidable situations and high risk for people undergoing treatment in hospitals. so development and implementation of the designed system will find the most effective solution modernization of medical institutions, taking into account the budget and time.

At the time of writing this essay was carried out as follows:

  1. Developed a mathematical model of the modernization plan of medical institutions.
  2. Based on an analysis of literary sources highlighted key algorithms that may be used in solving the tasks.

Based on the comparison of different methods for solving this problem is supposed to use the ant algorithm.

Important Notice

In writing this essay master's work is not yet complete. Final completion: December 2014. The full text of the work and materials on the topic can be obtained from the author or his head after that date.

References

  1. Касьянов В.Н., Евстигнеев В.А. Графы в программировании: обработка, визуализация и применение СПб. БХВ-Петербург, 2003. – 1104 c.
  2. Russel S., Norvig P. / Рассел С., Норвиг П. – Artificial Intelligence. A Modern Approach, Second Edition / Искусственный интеллект. Современный подход (2-е издание),2006. – 1408 с.
  3. Томас Х. Кормен, Чарльз И. Лейзерсон, Рональд Л. Ривест, Клиффорд Штайн Алгоритмы: построение и анализ, 3-е издание – М.: Вильямс, 2013. – 1328 с.
  4. Терелянский П.В. Системы поддержки принятия решений. Опыт проектирования: монография / П. В. Терелянский; ВолгГТУ. – Волгоград, 2009. – 127 c.
  5. Скобцов Ю.А. Основы эволюционных вычислений. – Донецк: ДонНТУ, 2008. – 326 с.
  6. Штовба С.Д. Муравьиные алгоритмы, Exponenta Pro. Математика в приложениях. 2004. № 4, C. 70 – 75.
  7. Поиск в пространстве состояний [Электронный ресурс]. – Режим доступа: http://habrahabr.ru/company/abbyy/blog/217839.
  8. Википедия. Алгоритм поиска А* [Электронный ресурс]. – Режим доступа: http://ru.wikipedia.org/wiki/Алгоритм_поиска_A*.
  9. D. Goldberg. Genetic Algorithms in Search, Optimization and Machine Learning. Reading, MA: Addison-Wesley, 1989. – 412 c.
  10. Харчистов Б.Ф. Методы оптимизации: Учебное пособие. / Б.Ф. Харчистов – г. Таганрог: Изд-во ТРТУ, 2004. – 140 с.
  11. Информационные управляющие системы и компьютерный мониторинг 2010/ Сборник материалов к I Всеукраинской научно-технической конференции студентов, аспирантов и молодых ученых. – Донецк, ДонНТУ – 2010, C. 12 – 16.
  12. Электронный учебник Экономико-математические методы. Динамическое программирование [Электронный ресурс]. – Режим доступа: http://math.mrsu.ru/text/courses/method/dinamicheskoe_programmirovanie1.htm.
  13. Муравьиные алгоритмы [Электронный ресурс]. – Режим доступа: http://habrahabr.ru/post/105302/.
  14. Скиена С. Алгоритмы. Руководство по разработке 2-е изд.: Пер. с англ. – СПб.: БХВ-Петербург. 2011. – 720 с.
  15. Системы поддержки принятия решений [Электронный ресурс]. – Режим доступа: https://tpl-it.wikispaces.com/системы+поддержки+принятия+решений.
  16. Введение в оптимизацию. Имитация отжига [Электронный ресурс]. – Режим доступа: http://habrahabr.ru/post/209610/.
  17. Поиск пути [Электронный ресурс]. – Режим доступа: http://ru.wikipedia.org/wiki/Поиск_пути.
  18. Классификация методов поддержки принятия решений [Электронный ресурс]. – Режим доступа: http://www.ipiran.ru/niap/pages/st_19.pdf.
  19. Алгоритмы муравьиной колонии [Электронный ресурс]. – Режим доступа: http://ru.science.wikia.com/wiki/Алгоритмы_муравьиной_колонии.
  20. Динамическое программирование [Электронный ресурс]. – Режим доступа: http://ru.wikipedia.org/wiki/Динамическое_программирование.