Theme of master's work:

The research of methods of multiobjective optimization for estimation and choice of partners for enterprises of wholesale

1.1 Actuality

In the tasks of the mathematical programming with one criterion it is needed to define the value of having a special purpose function, proper, for example, to the minimum expenses or maximal income. However, a bit thinking, we practically in any real situation will find out a few aims, conflicting with each other. We will show, as far as the range of problems which can be adequately formulated as a multicriterion is wide, and what descriptions it is necessary to use as criteria.

The methods of decision of tasks of the mathematical programming with one criterion were intensively developed last 60 years. The study of such methods, however, reflected the earliest and stand the stage in development of the mathematical programming. As we gradually enter into age of informatics, becomes clear that practically any serious real task is characterized more than one criterion. Persons, decisionmaking (LPR), in a considerably greater degree, what when that was not by, feel a necessity to estimate alternative decisions from point of a few criteria.

The results of research of tasks of planning and management show that in the real raising these tasks are a multicriterion. So, often meeting expression to «attain a maximal effect at the least expenses» already means a decision-making at two criteria. Functioning of enterprises possesses the large spectrum of descriptions, therefore determination of his future parameters is essential in regard to perspective of production. Such tasks often meet on enterprises, being in the crisis state, and a necessity of choice of partners with the proper parameters can be basic at determination strategy and tactic for a certain enterprise. It will allow to promote efficiency of functioning of enterprise, that can result in growth of volumes of realization and improvement of his financial state on all of indexes.

Thus, for an effective decision it is necessary any of problem data above all things to build a multicriterion mathematical model which after needs to be optimized, preliminary choosing the most suitable for this purpose method.

One of the most essential features of the applied tasks of choice is unclear character of criteria of choice of alternatives, their parameters, limitations, laid on on possibility of choice of one or another variants and etc Hereupon, the construction of adequate mathematical model of the probed problem appears in many cases impossible, that entails the necessity of the use of expert estimations which often appear the unique information for making a decision. Naturally, there is a necessity of development of methods, allowing effectively to get and process unclear expert information.

A purpose of work is a study of algorithms and mathematical principles of decision of multicriterion tasks of choice and consideration most widespread and effective from them for optimization of choice of partners for the enterprises of wholesale.

It is required to estimate clients, proranzhirovat' them, and on that ground to set the system of discounts, the amount of orders, their sum, debt, payment and duration of collaboration, will be taken into account here.

Application of vehicle of multicriterion optimization is assumed to the concrete process of realization of auction operations with optimization of his parameters. The construction of multicriterion mathematical model of process and decision of task of the multicriterion programming is thus planned as it applies to this model. It is planned to conduct optimization with the use of software which also will be by us it is developed in accordance with the applied method of optimization.

This work is devoted consideration of problem of estimation of partners of enterprises with the use of methods of multicriterion optimization. It will be realized in a software product, on the basis of database, taking into account seven selected criteria. For an analysis information is utillized about purchases for two years, here are approximately 250 buyers and 2000 records.

Approaches for the decision of tasks on the finite set of alternatives which the put task will decide through, include the followings methods: choice on an absolute preference, method of main criterion, a construction of linear is packages, construction of great number of effective decisions (nedomeniruemykh), choice of the best by rule majority.

In the beginning we build a mathematical model:

First we will make passing to the ball indexes, to bring them over to the single scale and do everything on a maximum. For passing to the marks utillize the method of count of range of values: A scale gets out from 1 to 100 marks, and then indexes are counted in pairs.

Choice on an absolute preference: the best variants get out on all by indexes. If no variant dissatisfies all of indexes, decision to find it is impossible, it is a standard situation for multicriterion tasks.

In obedience to the method of absolute preference get a result in such kind: on every criterion choose the best variants. In the program get the lists of the best variants for every criterion.

Choice of main criterion: one criterion gets out main, and on other the limitations are set. A that decision is considered the best, which satisfies limitations and is the best on a main criterion.

Choice of the best by rule majority: on every index some threshold value is on every private criterion; for every variant the amount of indexes, exceedings a threshold for maximums is considered, and for minimums – not excelling a threshold; the best is consider a decision with the maximal value of amount of such indexes.

In obedience to the results of method of main criterion and the rule of majority can be developed system of discounts. An user sets maximal and minimum possible discount, chooses a method and sets the parameters of method. In obedience to the got decisions discount distributed evenly: maximal – to the best, minimum – to worst.

Construction linear packages are foreseen by adding up of marks on all of criteria for every enterprise. Thus, get the well-organized list of enterprises, each of which has the total mark. An answer will be an enterprise with a maximal mark, and the proranged list of enterprises will be used for the construction of the system of discounts.

Discount system algorithm

Animated image. Format: gif. Sise: 53 КБ. Slides: 14. Repeats: 12. Changing slides: 1slide/sec

1) National Science Foundation (USA)

It is an independent federal agency, created in 1950. Engaged in support of many universities and colleges in industries of mathematics, komp'yuternoy science. Supports the branches of fundamental science and engineering, and also engaged in new developments.

2) Institute of information technologies – BAS (Bulgarian Academy of Sciences)

This Bulgarian academy of sciences is engaged in a komp'yuternym design, complex analysis. Its employees wrote a lot of the useful advanced studies

3) Institute of Electrical and Electronics Engineers (IEEE)

World leading organization on technologies. It is volonterskaya organization. Unites authors from the different corners of the world in area of komp'yuternoy, telecommunication, electronic developments. Members are exchanged the professional researches, divided new developments

3.1 Developments and researches

Decision of problem of estimation of partners of enterprises with the use of methods of multicriterion optimization, it will be realized in a software product, on the basis of database, taking into account seven selected criteria. For an analysis information is utillized about purchases for two years, here are approximately 250 buyers and 1500 records. Summary table, with the selected criteria on all of enterprises shown.

Passing to the marks

Choice on an absolute preference

Choice of the best by rule majority

A construction of linear is packages

We get the well-organized list of enterprises, each of which has the total mark. An answer will be an enterprise with a maximal mark. The proranged list of enterprises will be used for the construction of the system of discounts.

In this work existent problems and ways of their decision were in detail considered through the methods of multicriterion opitimizatsii. Some of methods were realized programmatic.

In future we will conduct a few testing of the developed methods through the written program, will analyse results and will generalize research results, will bring in recommendations on further developments.

Presently work in the process of development. A revision is expected to December, 2007. With questions concerning dissertation to speak to the author.

Literature