# Modifications of the method of solving matrices...

## Modifications of the method of decision matrices

When introducing technical, technological, organizational innovations at enterprises, allocating investments for the implementation of large-scale high-cost projects (space, defense, basic scientific research, etc.), the requirements for thorough analysis of factors (including qualitative ones) affecting decision making.

In our country, to solve such large-scale problems, the method of solving matrices, summarized above, was proposed. This method was proposed by G. S. Pospelov to solve the problem of organizing space research, but later found wide application. Later on, based on this method, modifications were developed, which do not always mention the name of the author who proposed the method.

The idea of ​​this method, based on the hierarchical breakdown of large uncertainty into more "shallow", more amenable to investigation, was briefly outlined above. At the same time, this idea can be used in wider applications and options.

Evaluation of the capabilities of the intermediary firm. To ensure the effectiveness of the functioning of the intermediary firm, it is necessary to assess, on the one hand, the product requirements and the capabilities of consumers, and on the other hand, the possibility of obtaining goods from producers.

To simulate this problem, the method of solving matrices G can be modified. S. Pospelov .

Recall that, according to the description of the original variant of the method, the separation of large uncertainty into more observable for the expert was carried out in the form of a stratified model whose levels are allocated according to the "life cycle" solution of the problem: "fundamental R & D - applied R & D - R & D - product (or other result of solving a subproblem)". At the same time, estimates were made of the relative importance of the elements of the lowest level of the model (fundamental R & D) for the upper level (problems) that were obtained by sequentially moving the researcher along the stratified "top-down" model. That is, in the beginning, estimates were made of the relative importance of the subproblems to which the problem was divided; then - assessing the contribution of OCD to the solution of subproblems; further - assessments of the contribution of applied research in the implementation of ROC; and finally - assessments of the contribution of fundamental R & D to the implementation of applied research.

In this problem, the position of an intermediary firm is determined by its name. Therefore, it is necessary to change the sequence of obtaining estimates in comparison with the original method, and obtain them relative to the average level of the stratified model in order to carry out the selection of suppliers and consumers on the basis of the estimates obtained.

You can preliminarily assess the relative needs, and then - the opportunity to purchase products. Then the following strata can be formed in the model (from top to bottom): consumers with relative estimates ; orders - ; suppliers - (Figure 6.5).

Such a model is convenient when an intermediary firm completes orders from products received from suppliers, and then implements these orders to the consumer.

It is also possible to use the model for intermediary enterprises that provide the city or region with agricultural products, consumer goods, etc.

In such a task, first of all, it is necessary to assess the relative importance of customers , fulfilling the rationing condition either in relation to 100%: , as is customary in the original version of the method, or with respect to, as is customary in the PATTERN technique and is more often used in practice.

Estimations can be obtained not only directly in an expert way, but also on the basis of previous (or accumulated) statistics on the implementation of orders.

Then you need to evaluate the possibility (probability) of the implementation of orders. In Fig. 6.5 Probabilities of sales (by own and competing firms) are denoted by and normalized

Fig. 6.5

Now, knowing and using the solving matrix , according to (6.4) -mediaries (including own)

Next, you need to assess the possibility (probability) of purchasing goods to complete orders. In Fig. 6.5 these estimates of the likelihood of the acquisition of products by own and competing firms are designated p ki. Naturally, for each supplier firm, the relative weights are also normalized:

Each line of this decision matrix characterizes the relative possibility (probability in a broad sense) of the acquisition by the i-th intermediary firm of the desired type of products, goods for the acquisition of orders.

Now, knowing and estimating , according to (6.4) you can get the relative weights of the suppliers , controlling the corresponding normalization conditions and

In the model under consideration (see Figure 6.5), the top and bottom strata can be swapped, emphasizing the supplier priority in the model (Figure 6.6).

For example, it may be convenient if the firm is engaged in the supply of foreign computer equipment to the domestic market. A model for solving the problem of ensuring the efficiency of the functioning of such a firm by selecting suppliers and consumers in each specific period of time is shown in Fig. 6.6 (own company is surrounded).

In such a formulation of the problem, firstly, the importance (prestige, reliability) of the suppliers is estimated . These estimates can be obtained not only expertly. First, in assessing the relative importance of suppliers, it is possible to organize a procedure of the type used in the PATTERN methodology, i.e. determine the evaluation criteria (prestige, reliability of the firm, etc.), introduce their weighting coefficients and obtain more accurate estimates taking into account the weighting factors -

Fig. 6.6

criteria criteria. And, secondly, indirect quantitative estimates can be taken into account (for example, based on the experience of communication with a particular firm, assess the reliability of supplies, the number of products supplied, etc.).

You can also use a mixed approach - graphically compare expert and indirect quantitative assessments, identify contradictory and conduct a more thorough analysis of the market of products of this company or product market of the appropriate type, taking into account the importance of similar products of other firms, for which you can apply information models of the market situation, similar to those considered in paragraph 6.4.

Next, you need to evaluate the possibility (probability) of purchasing goods (for example, computers of different types, printers, modems, etc.).

In Fig. 6.6 these estimates of the probability of selling products by own and competing firms are denoted by p ij .

Of course, for each supplier firm, the relative weights are also normalized: each row of the decision matrix characterizes the relative probability (probability in the broad sense) of acquiring by the i-th firm -mediary of the desired type of goods of the corresponding firm.

Now, knowing and using the solving matrix , you can, according to (6.4), get the relative Possibilities of intermediary firms (including own)

Unlike the traditional method of solving matrices in this modification, the procedure for obtaining is interesting to repeat for different types of purchased products in order to choose the most advantageous option for your own company. At the same time, it is useful to supplement such an analysis with economic estimates of costs for one or another variant of interaction with supplier firms. You can also consider options for mutually beneficial agreements with competing firms and take this into account in the model.

Next, you need to evaluate the feasibility of implementing specific types of products, interviewing consumers (which, of course, is not always possible) or estimating the probability of sales of equipment of a particular type to consumer groups (enterprises, universities, schools, etc.) based on either the previous experience, or opinions of experts who studied the market of the relevant type of goods. These estimates in Fig. 6.6 denoted

Similar to the above approach, knowing and estimating , you can get the relative weights

You can supplement the model with the fourth stratum, detailing the groups of consumers, and obtain updated estimates of the probability of sales . In this case, unlike the traditional method, the lower level should be formed not as an unordered set of consumers, but in the form of elements of the previous level of the hierarchy, which are combined into nodes , 0 src="images/image892.jpg">, and first assess the relative opportunity (for example, the purchasing power) of specific consumers within the group (for example, the probability of purchasing computers by commercial schools may be more likely to purchase the same computers by schools with government funding Niemi), and then to perform normalization conditions multiply the estimates for appropriate evaluation of consumer groups, i.e., to the corresponding estimates from the set .

If a satisfactory option is not obtained, then the whole procedure should be repeated, changing the types of goods purchased, and, possibly, agreements with competing intermediary firms.

In applying this approach, the formation and location of strata depends on the specific task, the problem situation. In real conditions, it is necessary to create databases and accumulate in them information about possible suppliers and their characteristics, on the potential capabilities of consumers. In the long term, the database may require information (taking into account the availability of its appropriate computer technology) about competing intermediary enterprises, etc. It is also useful to keep the solutions available in the modeling process in order to analyze trends in the market situation.

It is clear that the implementation of this approach is a fairly laborious task and is practically impossible without automation. Therefore, it is necessary to develop appropriate automated dialog procedures that should provide the user with the ability to enter the number of levels (strata) of the model, the number and name of the components and estimates for each of the strata. And when applying the evaluation method, taking into account the weighting factors of the criteria, it should be possible to enter the number and the name of the evaluation criteria and their weights, the dialogue with the user and presentation of the final results in a convenient form for the decision maker. The procedures are implemented by students of SPbSPU with various software tools - TURBO-SI, FOXPRO, DBMS, CLIPPER [4].

Planning the activity of small-scale enterprises producing consumer goods. In a market economy, it is necessary to plan the activity of an enterprise producing new technical means of general consumption (for example, for an enterprise that assembles computational or audio video products equipment from the purchased components, including foreign ones).

The model should allow (see Figure 6.7) to first determine the effective demand for consumer products, and then the opportunity to purchase the necessary components, taking into account the behavior of competitors (own company in Figure 6.7 is circled).

You can also set a task for a manufacturing company that picks up and uses loans for manufacturing products, setting the task of repaying a loan and obtaining additional funds from the sale of products for the development of the enterprise.

In this task, there are banks on the top stratum, which can be accessed to obtain a loan (Figure 6.8). Banks can be

Fig. 6.7

Fig. 6.8

evaluate in terms of their rating, reliability, the possibility of obtaining a loan, etc. characteristics. Evaluations are obtained expertly and on the basis of accumulated experience of communication with the banks of the enterprise in question and competing firms.

Then, in contrast to previous examples of the lower stratum is implemented in the form of two parallel, as it were, because it is necessary to evaluate the contribution to the efficient operation of the enterprise as component suppliers and consumers of manufactured products of computer and audio-video equipment.

The program procedure can be similar to that considered considering that you need to repeat the reference to the module for assessing the relationship of the enterprise with the lower level twice, assessing the relationships with suppliers and consumers.

Using the method of solving matrices and its modifications and forming a multi-level structure of factors affecting the creation and operation of enterprises (organizations), it is possible to conduct a more thorough analysis of the contribution of specific factors of the lower level of this structure to the process of designing and operating the enterprise. Moreover, along with estimates of the relative importance of the underlying components on the higher-lying, at each level, components can be quantified using deterministic or probabilistic characteristics obtained from an analysis of the previous experience. These estimates can be considered as indirect quantitative estimates.

Even more objective analysis can be obtained using methods of organizing complex examinations based on the use of an information approach.

[...]

[...]

[...]

[...]

[...]

[...]

[...]

[...]

[...]

[...]

[...]

[...]

[...]

[...]

## Other services that we offer

If you don’t see the necessary subject, paper type, or topic in our list of available services and examples, don’t worry! We have a number of other academic disciplines to suit the needs of anyone who visits this website looking for help.

## How to ...

We made your life easier with putting together a big number of articles and guidelines on how to plan and write different types of assignments (Essay, Research Paper, Dissertation etc)