Экономические науки/10.Экономика предприятия

Cand.Tech.Sci Parshin Y.I.

«National mining university», Dnepropetrovsk, Ukraine

Distribution of resources in global companies and corporations

Rational distribution of resources is one the most important economic problems of today. Distribution of such limited means as capital investments, equipment, primary material etc. among enterprises of corporation or big company is topical issue. Hence distribution which will ensure peak efficiency is considered as urgent one. The paper objective is to develop efficient procedure as to resource distribution within specific company or corporation.

In this context we can not hazard any conjectures on effectiveness function nature. Depending upon nature of processes the functions can be nondifferentiable, discontinuous, and lend themselves to the requirement of integrality. Besides, the functions may be shown as tabulated ones. Consider that user may introduce effectiveness functions as he/she finds it expedient. However developing symbolic model we will issue from the following:

) When the resource is used in some definite process then definite effectiveness is reached, and it depends on nature of process and amount of dedicated resource

) Effectiveness of each process results only from amount of resource dedicated to the process. It can not depend on the amount of resource dedicated to other processes (independence of effectiveness of processes)

) Income from different processes can be measured with the help of universal unit (availability of unified measure)

) General effectiveness is equal to total of effectiveness’s from independent processes (additivity of effectivenesses).

In this context it mathematically will mean that some dedicated resource which amount is , should be divided into members

; (1)

Effectiveness of i th process because of condition of process independence is expressed as functions of one variable . Common effect of resource is a function of , which because of and conditions is expressed as their total:

(2)

Formulate definition of nonnegative numbers as a problem

, (3)

and this will fulfill condition (1), and maximize function (2).

It should be noted that solving problem of resource distribution in this arrangement (under variable resource and arbitrary effectiveness functions) is possible with the help of dynamic programming method. Thereby effectiveness functions should meet following requirements resulting from substance of the matter:

а) means that modicum of dedicated resource is unprofitable

b) is monotone no decreasing function as when amounts of dedicated resource increase effectiveness either rises or at least stays invariable

с) Rates of function growth decay if rises as increase in resource amount being higher than certain level results in saturation effect.

Symbolize peak efficiency as . It is obtained if optimum distribution of resource over the first th enterprises:

,

and .

Following equations are to determine the functions:

1. .

Because of demand maximum is obtained if and .

2. is peak efficiency obtained from optimum distribution of the whole resource between enterprises 1 and 2. To do that, enterprise 2 is dedicated resource units which bring return units, and remaining amount is dedicated to enterprise 1, and return units are available. With it effectiveness of resource use is

.

Function depends on one variable which may vary within . Find absolute peak of the function within which identifies :

.

Preliminary proper value name as conditionally optimal:

.

3. means peak effectiveness obtained from optimum distribution of the whole resource among the first three enterprises. Enterprise 3 is obtained resource units where it brings of return units, and remaining amount is dedicated to enterprises 1 and 2 where under optimum distribution is brings returns. With it total effect is:

.

In this connection depends only on varying within . Find absolute peak of function within which will determine:

.

Proper value of is conditionally optimal too.

4. Analogously under any means peak effectiveness obtained if the whole resource is distributed ideally among the first th enterprises. th enterprise is dedicated resource units which bring returns. Remaining amount is dedicated to the first th enterprises where under ideal distribution it brings return units.

Total effect is:

.

In this context depends on one argument varying within . Find absolute peak of function within , which determines :

; (4)

.

Determined value is conditionally optimal.

Equation (4) is correct if .

means total effect obtained under ideal distribution of resource among all th enterprises, and proper value maximizing is optimum one.

Apropos th determine absolutely optimum value maximizing when resource is distributed among enterprises. Hence we verge towards correcting. As a result we obtain ideal distribution of resources into parts (optimum strategy), and maximum effect of distribution .

Suppose that it is required to distribute resources for three subsidiaries of corporation. In this context effectiveness functions of the enterprises are: ; and . Accordingly, our problem is to maximize:

,

If and .

If the whole resource is dedicated to the first enterprise then maximum is obtained under :

.

Distribute the whole resource between the first two enterprises:

.

Setting derivative to zero, and solving the equation we obtain following conditionally ideal distribution of resources between the first two enterprises d: the resource is divided in ratio .

In this context:.

When the whole resource is divided into three enterprises:

.

Solving the problem with the help of functional equations we obtain .

Hence the third enterprise should be dedicated 0,207792 of the whole resource, and the first and the second – 0,792208 of the resource part.

In this context total effect is:

.

To find ideal distribution of resource correction is made on the first two enterprises:

, and .

Hence in spite of resource amount dedicated to subsidiaries optimum behavior is to divide it in such a way: . It will ensure peak efficiency of capital investments.

The procedure of resource distribution within large corporation or global company gives ability to take into account operational efficiency of individual subsidiaries, and to use such available reserves as capital investments, equipment, primary material etc. with peak efficiency. Future research is planned in the line of the procedure adaptation to specific production methods to use them within decision support system.