ABOUT OPTIMIZING OF INVESTMENTS VOLUME TO IMPROVE THE BASIC INDICATORS OF THE ENTERPRISE EFFECTIVENESS

Purpose. Profit and profitability of any, including transport enterprises are the main economic indicators of the enterprise effectiveness. These indicators reflect the results and successful performance of the enterprise. On the other hand the enterprise effectiveness in the long term, assurance of rapid development and competitiveness is largely determined by the level of investment activity and the range of investment activity. The purpose of this study is the feasibility of the method to determine optimal investments volume for improving these or others (selectable by the management) principal economic indicators of the enterprise effectiveness. Methodology. The basis of the proposed methodology for determining the optimal investments volume is the theory of optimal control, in particular, the procedure of dynamic programming since a managed development process of the enterprise is a multiple stage. This procedure, using a phased plan, allows not only simplifying the solution of optimization problems, but also solving those, which are impossible to apply the methods of mathematical analysis. Findings. The expediency of performing the calculations to determine the optimal investments volume to ensure high rates of enterprise development was proved, it is a key to the effectiveness of the enterprise in the long term and it improves its competitiveness. Originality. It is shown that using methods of the optimum control theory one can calculate the minimum volume of capital investments for the improvement of economic indicators, which determine the enterprise effectiveness. The proposed method of calculation does not depend on the specific content of economic indicators. The effectiveness of this calculation method is demonstrated on a model example. Practical value. The proposed method of calculating the minimum volume of capital investments to improve the economic effectiveness of enterprises is quite simple, but at the same time enables, on the one hand, to determine priority directions of investment activity of the enterprise. On the other hand it improves the manageability and transparency of business enterprises, increases the head's confidence in the correctness of decisions.


Introduction
Income and profitability of any, including transport [5][6][7] enterprise are the main economic indicators of enterprise effectiveness.These indicators reflect the results and successful performance of the enterprise.They will help determine the viability of the realizable business-project and to correlate values of benefits and costs [10].On the other hand the enterprises effectiveness in the long-term prospects, assurance a high rate of development and increasing competitiveness is largely determined by its level and range of investment activity.
The volume of investments depends on many factors.For example, volume of investments depends on the distribution of the earned incomes on consumption and savings.With low per capita incomes most of them are spent on consumption.Revenue growth causes an increase in their share allocated to savings, which are a source of investment resources.Consequently, the share increase of savings causes corresponding increase in the volume of investment and vice versa.Also the expected net profit margin has significant influence on the volume of investments.This is due to the fact that profit is the main motive of investments.The higher expected net profit margin the higher volume of investments will be and vice versa [4,6,11].
As it is known [1][2][3], before the investment one should perform a range of activities to substantiate the effectiveness of investments at the enterprise, called the investment project.Preparation of an investment project is a long and sometimes very expensive process consisting of series of acts and stages.
The main purpose of the investment project, as a rule, is increase the net income and profitability, therefore increasing the efficiency of the enterprise performance to the desired level.Consequently, one of the stages of its preparation may be determining the optimal (minimum) volume of investments.This object can be effectively solved by the methods of optimal management theory.Examples of these methods application in economics are presented in papers [13,14].

Purpose
In this paper we present a method for calculating the minimum volume of investments to achieve the desired values k P -net income and k Rprofitability of the enterprise.It is assumed that the costs are known the change-over from the level ( , ) i j P R magnitudes of income and profitability up to levels 1 ( , ) ( , ) , < i i j j numbers of steps calculations, and a step of calculation are month, quarter or a year.These costs may be calculated by using the discounting method, i.e reduction of nonsimultaneous incomes and expenses, carried out within the framework of investment project to the single (base) moment in time [6,10].All calculations are carried out in basis, anticipated and in the setting prices.

Methodology
The proposed methodology is a dynamic programming procedure [8,9].This procedure, using a phased plan, not only let simplify the solution of optimization problems, but also solve those of them to which it is impossible to apply the methods of mathematical analysis.
Accordingly to this procedure, the process of decision-making concerning investments begins from the last k -step.On this step one choose the solution that allows obtaining the greatest effect (reaching the final level ( , ) P R of the enterprise on ( 1) k − -step is unknown, then one consider the various levels at this step.For each possible level is selected so-called conditionally optimal solution on the last, k -step.
Let us plan k -step-by-step investment process and On the last step we will find conditionally optimal solution for each of them.Thus, k -step has been planned.Really, whatever level ( , ) P R on the penultimate step was, we already know what solution should be applied on the last step.We proceed similarly to ( 1) k − -step, only conditionally optimal solutions should be chosen, taking into account already selected suboptimal solutions on k -step and so on.As a result, we are on the original level 0 0 ( , ) P R of net income and profitability.
For the first step of assumptions about the possible level ( , ) P R we do not do, as the level 0 0 ( , ) P R is known, but we find the optimal solution, taking into account all conditionally optimal solutions, which have been found for the second step.When passing from 0 0 ( , ) P R to ( , ) P R , we obtain the desired optimal solution that provides minimum volume of investments and their best distribution on the steps of calculating.

Findings
As we have defined the performance level of the enterprise with two parameters ( , ) P R , then the optimal solution is convenient to search with the geometric method on the plane POR , or rather on bounded with lines 0 , P P = P R levels are well defined as two points of the plane (Fig. 1).
Fig. 1 On fig. 1 vertical segments show profitability increase at a constant value of income, horizontal segments show income increase at a constant value of profitability, and diagonal segments show simultaneously increase of income and profitability.
It is assumed that in one step one can increase either net income on the amount P ∆ , or profitability on the amount R ∆ or it is possible simultaneous increase both income and profitability.Here where 1 2 , n n -numbers of steps, accordingly, horizontally and vertically.Obviously, there are many trajectories (solutions) that are represented as broken lines ( , ) P R on which the point can be moved around from 0 0 ( , ) P R to ( , ) k k P R .Thus, from solution set we have to choose the single one that will minimize funds expenses equal to the amount of funds expenses for each stage corresponding to the broken line.
To demonstrate the efficiency of the above mentioned algorithm one should construct an optimal solution for the investment process, shown in Fig. 2.
Suboptimal solutions will be represented by the arrows coming out of circles, and the minimum expenditure of funds will be recorded in circles.If the point ( , ) P R is on the line k , that pass through the ( , ) P R , then one can be moving around only vertically to this point.This is the only solution possible and optimal.
In our case there are four points on the straight line k ( , , , ) A A A A , for which a path of motion in ( , ) k k P R vertically is the only thing, and funds expenditure are 10, 17, 25 and 30 units accordingly.On the straight line k point ( , ) P R may be from points ( , , , , ) B B B B B of straight line 1 k − .Considering these points, we choose the conditionally optimal solution for each of them, taking into account conditionally optimal solutions that have been found for points.If the point ( , ) P R is in the point 1 B as a result of previous step, then single (horizontally) funds expenditure is 4 units.
Three ways are possible from the point 2 B in to the point ( , ) k k P R : through point 1 B and funds expenditure is 9 units; through point 1 A , and funds expenditure is 19 units; diagonally (and funds expenditure is 10 units.).In this case the conditional optimal solution is jump in vertical direction (through the point 1 B ). Similarly, we find suboptimal solutions for points 3 4 5 , , B B B .Then subsequently find suboptimal solutions for points on other lines, until we are at a point 0 0 ( , ) P R , for which we establish the optimal solution, therefore, the optimal solution for the entire process.The final optimal solution is shown in Fig. 2 with two parallel arrows.Number 32, standing next to the point 0 0 ( , ) P R , mean minimum funds expenditure for jump from this point in to the point ( , )

Originality and practical value
It is shown that using the theory methods of optimal control one can calculate the minimum volume calculation of capital investments for improving the economic indicators which are determine the enterprise effectiveness.The proposed method of calculation does not depend on the specific content of economic indicators.The effectiveness of this calculation method is demonstrated on the model example.
Suggested calculation method of minimum volume of capital investments in order to improve the economic indicators of the enterprise effectiveness is quite simple, but at the same time it allows, on the one hand, determining major priorities for investment activity of the enterprise.On the other hand it increases the manageability and transparency of economic activity at the enterprise, enhances the confidence of the head concerning the correctness of decisions.

Conclusions
If for some node point there are several (two or three) conditionally optimal solutions, then they are all marked by arrows, and after that any of them is selected.In these cases, the problem has several solutions, if such nodal points belong to the optimal trajectory.
We should note that the above mentioned calculation algorithm can be applied for any pair of the economic indicators operating efficiency at any enterprise.

Fig. 2 .
Fig. 2. On the horizontal, vertical and diagonal lines are given the model parameters 1, i i j