Abstract

Theme: Development of computer subsystem of planning of load of cement mills on the basis of brief-case of orders

Plan

Introduction
1. The characteristic of object of a computerization
2. The purpose and problems of working out of a subsystem
3. An urgency
4. Mathematical statement of a problem
5. Decision methods
Conclusion
List of literature

Introduction

Factory HeidelbergCement Ukraine is one of the largest cement factories which is present on the market of Ukraine since 2001. Factory makes a wide spectrum of high-quality cement, concrete and sand-gravel mixtures mixes. Economic targets is the constant increase in profit at the expense of management of expenses and the long-term income focused on reception. The factory aspires to creation of long-term mutual relations with clients who are based on reliability and honesty.

The characteristic of object of a computerization

For today the factory uses all capacities for cement manufacture round the clock as orders of clients arrive daily and demand for a building material doesn't decrease. Cement manufacture is carried out by means of 4 mills of a grinding. The factory makes 12 marks of cement. Available degree of a freedom of use of the electric power is very limited and basically is reduced to a site of a grinding of cement. On the given site now scheduling, i.e. definition when to make certain type of cement, and on what mill, it is made manually, using heuristic rules and relying on experience of the operator. However, a considerable quantity of mills, types of cement and bunkers plus various operational and contractual restrictions, create the big problem. Too often, the choice of the operator is far from the rational. Using orders of the client (the basic information– Volume of the ordered cement and performance terms), it is necessary to create the basic schedule of work of all guild of grade, defining, when and that each mill will make.

In a kind of that orders of clients are non-uniform and monthly the output of certain mark changes, there is a necessity for switching of mills for manufacture of necessary mark of cement. Switching of mills increases enterprise expenses. Having conducted researches of similar systems, the conclusion has been drawn that the considered systems place emphasis on minimization of the expenses connected with current consumption and quantity of made low-grade cement (the cement made during switching from one type on another). Curtailment of production of low-grade cement, electric power expenses is reached by reduction of quantity of switchings of manufacture.

The purpose and problems of working out of a subsystem

The purpose of working out of a computer subsystem – creation of a subsystem which will allow to automate process of creation of the schedule of loading of cement mills at enterprise HeidelbergCement Ukraine in which base principles of management taking into account specificity of manufacture of cement on the basis of the output plan are realized.

Tasks in view concern:

• Construction of the network schedule by methods of network planning;
• Definition and minimization of switchings of each mill;
• Working out of the algorithm based on application of modern algorithm for reception of the optimum plan of loading of mills which will allow to consider the imposed technological restrictions at the maximum loading of the equipment and the maximum use.

An urgency

Creation of a subsystem of planning of loading of cement mills is of great importance at the enterprise as it will lead to reduction of expenses. We will result the list of expenses, which are born by the enterprise at manual planning to be convinced of necessity of creation of a subsystem:

• idle time of mills that conducts to essential losses of the enterprise at the expense of reduction of volumes of output increases.
• at switching of mills the expenses connected with additional expenses of the electric power for start of a mill grow.
• at switching of mills there is a deterioration of a reducer depending on which the quantity of made cement, and also the expenses connected with repair of a reducer decreases.

The analysis of existing systems in the given subject domain has been carried out. In connection with a small number of the cement enterprises on territories of Ukraine, a question of switchings of mills it is not investigated to the full. Whether to address to workings out of the western countries is a question of the enterprise, and everyone solves for itself(himself), whether it is necessary for it or it is possible to carry out this problem to 3-4 experts of department of logistics. In the cement industry the given theme is actual and the decision of a problem on planning of loading of mills will allow to reduce enterprise expenses.

Mathematical statement of a problem

Generalizing told, problem formalization, considering problems in the field, it is possible to present in the form of formulas on which basis optimization methods will get out.

Зпр= k * P * tпр                    (1)

where Зпр – enterprise expenses at idle time of mills, P – the sum of expenses at mill idle time equal one hour, k – quantity of switchings of mills, tпр – a mill idle time.

Зэ = k * P * Q                    (2)

where Зэ – expenses of the enterprise for the electric power demanded at start to a mill, P – cost 1Kvt/hour, k – quantity of switchings of mills, Q – quantity of the electric power necessary for start of a mill.

Зрем = k * Pред/100                  (3)

where Зрем – of the enterprise connected with repair of a reducer, Pред – cost of repair of a reducer k – quantity of switchings of mills. We receive the formula for the general expenses:

Зобщ = Зэ + Зрем + Зпр                   (4)

Proceeding from formulas, it is possible to draw a conclusion that in each formula there is a variable k – quantity of switchings of mills, and the it is more, the more expenses bears the enterprise. Thus, having minimized quantity of switchings, we will aspire to minimization of expenses. For this purpose it is necessary to increase as much as possible an operating time of mills without switchings, proceeding from a portfolio of orders of clients. Proceeding from formulas, it is possible to draw a conclusion that in each formula there is a variable k – quantity of switchings of mills, and the it is more, the more expenses bears the enterprise. Thus, having minimized quantity of switchings, we will aspire to minimization of expenses. For this purpose it is necessary to increase as much as possible an operating time of mills without switchings, proceeding from a portfolio of orders of clients.

Decision methods

From the point of view of the optimization, all decisions received as a result of development of plans, it is possible to divide into the following: optimum by all criteria; optimized by one/several criteria; comprehensible on all restrictions. Process of construction of the industrial schedule can be divided on two subtasks: the finding of possible schedules of industrial works on the basis of various priority rules and allocation from them the best (optimum or very near optimal), agrees demanded criteria. According to results of the majority of the researches, the determined problems of scheduling concern NP-difficult problems of streamlining and have combinatory character [2]. The choice optimum, or "close" to optimum, schedules will be carried out by means of one of four approaches: combinatory, mathematical programming, heuristic and statistical modeling. The choice of the optimum schedule of the set set of works on the available equipment is investigated for a long time already, but optimum decisions are received only for the elementary cases.

Algorithms of construction of schedules without carrying out of full or partial search of variants are solving heuristic rules and play an important role in the applied theory of schedules. However heuristic algorithms are based on reception which is called as "decrease in requirements». It consists in refusal of search of the optimum decision and a finding instead «the good decision» for comprehensible time. From described above 4 approaches, the combinatory method and mathematical programming won't be considered in connection with great volume of variants of decisions and unacceptable time of search of the decision. The methods applied to construction of algorithms of this kind, strongly depend on specificity of a problem.[3] That is the universal algorithm doesn't exist also use of this or that heuristic rule it is necessary to begin after the concrete industrial problem has been solved by different methods and more suitable decision, according to expert estimations taking into account demanded restrictions and criteria of an optimality is chosen.

Network schedules it is realized by methods of network planning. Network planning apply to the organization and drawing up of planned schedules of realization of the big complexes of works. The essence of network planning consists in drawing up of logical-mathematical model of operated object in the form of the network schedule or the model which are in a computer memory in which the interrelation and duration of a certain complex of works are reflected. Management of all these works can be carried out by means of a method of a critical way. Use of this method allows to find out rather simply when it is necessary to begin and finish performance of separate operations as the delay of a course of performance of some operation influences time of end of all project. The schedule representing interrelation of separate works of the project, is called as the network schedule. Works are put on the schedule and events. Event - the fact of the termination of one or several works necessary and sufficient to start the subsequent works. Events are represented by a circle and numbered. The event which does not have previous works, name initial; the event which does not have the subsequent works, - final. They it is designated by pair the bracketed numbers (i, j), where i - event number which work leaves, and j — event number into which it enters. Work - the production demanding expenses of time and resources. Work is coded by numbers of two events: previous and the subsequent. It is designated by a continuous line between two events, and the arrow direction is given from left to right. Over a line the name of works, under a line (below) - operation time in days (from above) is written.[4]

Thus, each event characterizes end or the work beginning, and work means action, which needs to be made to pass from previous event to the subsequent. Work can't begin earlier, than event which it leaves will come true. Each work has certain duration t (i, j).

In drawing 1 the bright example of the count of manufacture of cement on one mill, where Ti – time of manufacture of cement i marks, i Є [1 is presented; 12]; Tп – time of switching of a mill. Increasing time of manufacture of cement of one mark, we increase probability of reduction of switching of a mill if only there will be no new orders for the made mark.

Figure 1 – The count of manufacture of cement on one mill

In a considered problem it is required so to make the schedule, on the one hand, to execute the order of the set volume of each mark, and on the other hand – to keep within order terms. But thus it is necessary to execute an overall objective – decrease in losses as reduction of quantity of switchings of mills in the given problem will lead to increase in work of a mill in one mode, but taking into account restrictions on volume and terms of performance of the order.

Thus, network planning creates finally conditions for performance of all complex of works in their logic sequence. By means of network schedules the system approach to questions of the organization of management is carried out by the set processes as collectives of various divisions participate in them as the links of uniform difficult organizational system united by a generality of a problem.

The network schedule after its optimization by means of applied mathematics and computer facilities is used for an operational administration by works. In drawing 2 the real schedule of work of a mill within a month which is necessary for receiving in result of optimization and the task in view decision is represented.

Figure 2 – The schedule of work of a mill within a month

Genetic algorithms, using analogy between natural selection and process of a choice of the best decision of set possible, are one of the most widespread variants of realization of evolutionary algorithms. Modeling selection of the best plans as evolution process in population of individuals, it is possible to receive the decision of a problem of optimization, having set entry conditions of evolutionary process. In modern conditions local search on the basis of genetic algorithms is realized simply enough. Advantage of genetic algorithms before others is simplicity of their realization, rather high speed of the work, parallel search of the decision at once the several individuals, allowing to avoid hit in "trap" of local optimum (a finding of the first comer, but not the most successful optimum). Lack – complexity of a choice of the scheme of coding, that is a choice of parameters and a kind of their coding in "chromosomes", possibility of degeneration of population, complexity of the description of restrictions of planning.[5]

Conclusion

Having analysed similar foreign systems, and also methods of optimization and mathematical modeling which allow to solve a task in view, necessity of working out of the computerized subsystem of planning of loading of mills which can be introduced at the enterprise for reduction of expenses is proved.

At the task in view decision it is necessary to use an evolutionary method which solves multicriteria problems, and also will allow to receive an optimum solution of a problem of real industrial situations for small time.

On the basis of the analysis of existing workings out in the field of evolutionary methods the perspective decision of difficult combinatory problems of optimization is use of genetic algorithm. It will allow to improve essentially operational planning system, thereby having reduced time of reception of optimum or comprehensible industrial schedules. Also at occurrence of the casual events influencing process of manufacture, will allow to react to change and entering of corrective amendments into the initial data quickly.

Thus, working out of the software product is necessary for development of systems of planning, allowing to build optimum production plans, using tools of evolutionary methods.

List of literature

1. Сайт швейцарской компании АББ [электронный ресурс]/ Интернет-ресурс. - Режим доступа: http://www.abb.com/

2. Маляренко И., Планирование и оптимизация [nекст]/Корпоративные системы. – 2006. – № 27. – С. 29-32.

3. Павлов А. А. Основы системного анализа АСУ [nекст]/ А.А. Павлов – К.: Техника, 1990. – 367с.

4. Модер Дж., Филлипс С., Метод сетевого планирования в организации работ, пер. с англ.[текст]/ Дж.Модер, С.Филлипс - М. — Л., 1966.

5. МакКоннелл Дж. Основы современных алгоритмов [текст]/ Дж.МакКоннелл – М.: Техносфера, 2004. – 368 с.

6. Матиас Боллигер, Эдуардо Галлестей, Габриэла Кросли, Михель Киенер, «Как регулировать потребление энергии при производстве цемента» [электронный ресурс]/ Интернет-ресурс. – Режим доступа: Оптимизаторы энергопотребления

7. Журнал компании АBB «Экспертный оптимизатор системы Optimize» [электронный ресурс]/ Интернет-ресурс. – Режим доступа: Экспертный оптимизатор

When writing the abstract the Master's work was not completed yet. The date of completion is the December 1st 2011. Full text of the work and materials on the topic can be obtained from the author or his supervisor of studies after the date.

© DonNTU 2011, Gryshkovets V.A.