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Abstract

Content

Introduction

Currently the business is growing rapidly, increasing competition in the various areas of trade. Entrepreneurs fight hard for different markets, spheres of influence. Speed, accuracy, timeliness business decisions – the key to success in this type of activity. To keep beeing competitive, you need to innovate and take advantage of advanced technologies.

1. Description of the research

The research object is the process of opening the fixed number of trade points. Every point must be done by exact date. Separately the organization of trade point contains list of operations which can be done in parallel or consequentially considering technology and real opportunities. The investment is made in fixed period of time according to funding schedule. It’s made by a manager.

The enlarged list of works:

  1. Computing of number of trade points.
  2. Finding an area.
  3. Projecting the structure of trade point.
  4. Fixing operations.
  5. Searching of staff.
  6. Teaching of staff.
  7. The licensing process.
  8. Obtaining permits for trade.
  9. Formation of inventories:

    • approval a range;
    • making conracts for supply of goods;
    • delivery of goods (when trade point is done);
    • reception of goods(possible only after item number 12).

  10. Ordering of trade equipment.
  11. Ordering of IT-equipment, office equipment, installing of software.
  12. Fitting of equipment.
  13. Purchase of expendable materials.[1]

2. Actuality

When you are planning your business, the development of production strategies needs to control their costs, monitor graphics of outputs, the schedules of various manufacturing operations. Deadlines are extremely important, in a competitive environment possible strategic mistakes and losing market competitor. This can result in huge financial losses, and in the worst case - bankruptcy and the inability to restore former position of influence in the sector. The financial component is also crucial, as failure of some obligations, for example, by proxy or other companion may incur a penalty for fines and penalties. [2]

In this situation, the way out is the effective production planning, production of outputs, schedule of various jobs.

3. Existing methods for solving problems

This problem relates to the direction of scheduling.

Scheduling is developing and bringing to the structural units and workplaces operational targets for output and ensure their necessary resources. [3]

Calendar plan of production is a document that establishes the sequence and timing of production operations and identifies the requirements for human resources and time.

Scheduling in project management is a key and important process, the result of which is approved by the leadership of the project schedule (often also called the schedule, project management plan). The purpose of scheduling is to get an accurate and complete project schedule considering the list of operations, their durations, required resources, which serves as the basis for the execution of the project.

Timetable - a graphical interpretation of the schedule, concretizing it related to it's consist, volume, consequence, performance time. In constructing the timetable it's necessary to consider the availability of resources, as the parallel execution of certain operations due to limitations associated with employees, equipment and other kinds of resources, it may be impossible. [3]

4. Analysis of similar systems

Nowadays, many companies are trying to solve the problem of scheduling. Next, we will briefly review the companies and their software products.

Easy Projects is a product developed by Logic Software Inc., which is situated in Toronto and develops software. In 2003 company needed a system to manage the project for their own purposes. They decided to develop their own system. As a result, the system was so comfortable that she was transferred to a commercial basis and began to spread in the market of such systems. [4]

On the figure 1 one of the key function is presented. It's composing of Gantt chart.

Figure 1 – Composing of Gantt chart in Easy Projects

As we can see there is the function to form list of operations, to group them.

A feature of this system is that it is a web application. In some cases this is disadvantage because Internet access is required, on the other hand - if there is the Internet it performs all of the necessary actions for planning.

Microsoft Project 2013 is Microsoft sofrware can plan resources of company. On the figure 2 functions of the system are presented.

Figure 2 – Microsoft Project 2013 functions
(animation: number of frames – 3, delay – 1000 ms, size – 110 kilobytes)

If it's necessary, each stage can be deployed by "+" button and we can see all of the stage. Although mapping the network schedule in Microsoft Project 2013 is different from the usual type of work and events, this does not cause any inconvenience. [5]

PlanWIZARD – software for automation of planning economic department work. It allows to enter planned operations and form Gantt chart. On the figure 3 main functions of the software are presented.

Figure 3 – Operations and Gantt chart in PlanWIZARD

VisualData Планирование производства работ is software to improve the efficiency of enterprise management by automating the processes of formation of schedules of work and then oversee their implementation, using visual data representation forms. The software is aimed at directors and production planning department primarily enterprises of the construction industry, although it can also be used in other industries. [6]

These packages are similar in functionality. Their main task - the construction schedule in a Gantt chart or a network schedule. But all of then do not solve the main problem - the optimization of the schedule of works for the effective distribution of funds.

The future system will solve this problem, but this requires a closer look at the project.

5. Goals and objectives

The main purpose of the developed system is to minimize the time of the project in order to optimize the use of funds allocated to the project.

The criteria for achieving the goals are:

To achieve this goal the system must make schedule which is the main task of calendar planning. [7]

6. Formalization of the task

Operation is an action which is necessary to open a trade point by exact date. Every operation has the following characteristics:

  1. Duration.
  2. Cost.
  3. Set of previous operations. It's operations must be done by the start of operation. Set could be empty.
  4. Start date.
  5. Finish date.

To determine the sequence of works the following features must be considered:

  1. Each job has a lot of previous works, which does not allow to perform all work in parallel, except in the case when each job has an empty set of predecessors.
  2. At the start of the k parallel work their total cost can not exceed the amount of funds available at time t (1)

    3. где Mt – funds in moment t, pi – cost of operation i.

  3. Two operations Wi и Wj can be done in parallel, if Wi ∉ PSj and Wj ∉ PSi

Mathematical formulation of the problem can be formulated in the next way.

Project P contains set of trade points T{t1, t2, …, tn}, where n is the number of trade points. Funding is made at regular intervals t equal of M monetary units. Each trade points has:

Each operation wk has:

The expression of optimization function is the following one

where P is total duration of project.

Graphoanalitical model will be the following: graph G(W,E), where node Wi – executing of operation i, Eij – edge which characterises the way between Wi and Wj. The task is to find optimal way in graph.

As an example we can review the sequence of passing the graph for one trade point:

  1. Analysing of operations which are available in this moment of time (dashed arrows).
  2. Selection of operations considering budget limits (W1 and W5).
  3. Executing of W1 and W5.
  4. Analysing of operations which are available in this moment of time (dashed arrows).
  5. Selection of operations considering budget limits (W2 and W4).
  6. Executing of W2 and W4.
  7. Analysing of operations which are available in this moment of time (dashed arrows).
  8. Selection of operations considering budget limits (W3).
  9. Executing of W3.

Figure 4 – Graph
(animation: number of frames – 7, delay – 1500 ms, size – 109 kilobytes)

This task is similar to travelling salesman problem but this is one distinction. The way can be consequent. It has dendritic structure.[8]

7. Supposed algorithm

Modified ant colony optimization algorithms will be used for finding the optimal way. We need to define the ant.

Ant consists of the set of brigades B {b1, b2, …, bm}, where m is the number of brigades.

It's necessary to make a modification for the algorithm under this task. Steps of algorithm are following:

  1. Generation of an ant colony.
  2. Sequential passage of ants on a graph with the deposition of pheromones on the edges.
  3. Changing the level of pheromones on the edges depending on the number of ants that passed along the edge.
  4. Evaporation of pheromones to avoid local optimal solutions.
  5. Checking the stopping criterion of the algorithm. [9]

Step #2 is the key step of algorithn. Ant has complicated structure. That means that it's passing though the graph is complicated too. Limits of budget and time must be considering too.

Conclusions

For this problem has been collected and processed information to solve it. A description of the object has been made. During the formulation of the problem revealed the following problems:

  1. Sequence of operations.
  2. Allocation of financial resources.

During the analysing the disadvantages of calendar scheduling methods and comparison their task with the task of researches it was found that the best way of solving this problem is heuristic approach namely ants colony algorithm with it's modification.[10]

For the final completion of the algorithm is necessary to determine the behaviour of ants. The standard formula for calculating the probability of transition does not consider the specifics of the problem. It must be transformed and introduce into it the parameters that characterize the optimal solution.


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

References

  1. Дрыкин В.А., Светличная В.А., Шумаева Е.А. Разработка функциональной схемы компьютеризированной подсистемы распределения временных ресурсов при управлении проектом. Збірка матеріалів V всеукраїнської науково-технічної конференції студентів, аспірантів та молодих вчених Информатика и компьютерные технологии–2013 Донецьк, ДонНТУ 2013, Том 1, с. 28–36.
  2. Бизнес-планирование фирмы/В.И. Захарченко, Н.В. Халикян, 4-е изд., перераб. – О.: Наука и техника, 2007, c. 90–100.
  3. Ильин А.И. Планирование на предприятии: учеб.пособие/А.И. Ильин. – 7-е изд., испр. и доп. – Мн.: Новое знание, 2006, c. 349–356.
  4. About us, EASYPROJECTS/ [Электронный ресурс]. – Режим доступа: http://www.easyprojects.net/about/.
  5. Портал по Microsoft Project / [Электронный ресурс]. – Режим доступа: http://www.microsoftproject.ru.
  6. PlanWIZARD – программа для календарного планирования/ [Электронный ресурс]. – Режим доступа: http://www.wizardsoft.ru/product/planwizard.
  7. Зуй К.Б., Светличная В.А., Ченгарь О.В. Разработка диаграммы деятельности с синхронизацией параллельных действий при создании компьютеризированной системы управления проектом. Збірка матеріалів VI всеукраїнської науково-технічної конференції студентів, аспірантів та молодих вчених Информатика и компьютерные технологии–2014 Донецьк, ДонНТУ 2014, Том 1, с. 112–117.
  8. Экспертные системы: принципы разработки и программирование, 4-е издание. : Пер. с англ. – М.: ООО И.Д. Вильямс, 2007. – с. 508–521.
  9. Штовба С. Д. Муравьиные алгоритмы, Exponenta Pro. Математика в приложениях. 2004. № 4.
  10. Борзов В.О. Исследование эвристического метода решения задачи коммивояжера // Электронный журнал Исследовано в России. – 2008. – http://zhurnal.ape.relarn.ru/articles/2008/028.pdf.