Optimal investment decision making on the model of production enterprise with limited resources

ARTICLE INFO Tetiana Ivanenko, Viktor Hrushko and Anatolii Frantsuz (2018). Optimal investment decision making on the model of production enterprise with limited resources. Investment Management and Financial Innovations, 15(4), 61-68. doi:10.21511/imfi.15(4).2018.05 DOI http://dx.doi.org/10.21511/imfi.15(4).2018.05 RELEASED ON Tuesday, 23 October 2018 RECEIVED ON Friday, 31 August 2018 ACCEPTED ON Thursday, 04 October 2018


INTRODUCTION
Investment activity of enterprises is always connected with the problem of limited investment resources. According to statistics, the main source of investments in Ukraine is own funds of enterprises. Rational usage of such funds is a key task. An investor usually can't foresee all possible investment options, but also needs to make decisions, choosing the best strategy to achieve his own goals. In the multi-purpose decision making, a number of goals must be achieved by the selected investment option in the maximum possible degree, measured by several criteria.
The task of making a multi-purpose project selection is to identify and simultaneously optimize several parameters that affect each goal. Such parameters are often not only interrelated, but also controversial. This means that achieving the investor's best values for all parameters is not possible at the same time, because improving one of them leads to a deterioration of the other. Thus, the investor has to make a nonobvious solution, the expediency, and optimality of which must be confirmed by certain calculations. In order to make settlements, the investor, first of all, should formulate the initial conditions of the task, which consists in determining the objectives of decision making and criteria for assessing the degree of achievement of each goal, the possible investor strategies and the state of the economic environment.

LITERATURE REVIEW
Various applications of multi-criteria decision making methods in economic studies are described in the article of Mardani et al. (2015), giving an analysis of 393 scientific publications in peer-reviewed journals for the period 2000-2014. These publications were categorized based on methods of multi-criteria decision making (MCDM), applications, journals etc. Methods of MCDM are classified as discrete and continuous by the fields of application: energy, environmental and sustainability, supply chain management, material, quality management, GIS, сonstruction and project management, safety and risk management, manufacturing systems, information technology management, operation research and soft computing, strategic management, knowledge management, production management, tourism management, and other fields. Metzger and Fehr (2017) conducted a survey of investors concerning attitude toward financial risks and revealed the impact of legal regulations and scientific criteria on investors' behavior. MacNeil (2012) suggests that legal risks must be taken into consideration among other investment risks and also emphasizes the need for regulation of investment to decrease any risks. Pangsri (2015) combines MCDM with Delphi method, AHP, and TOPSIS to analyze decision making in construction enterprise, including expert evaluation of selective criteria.
Problems of optimal decision making in conditions of uncertainty and risk are studied by Vitlinskyi et al. (2002), Kihel (1999). Buz'ko (2014) investigated theoretical approaches to the definition of an investment decision and the conditions for its use in the strategic management of production enterprises. Hlibchuk (2012) analyzes the degree of risk in implementing a long-term investment project and the main principles of the enterprise's investment decision making. Hrydzhuk (2011) examined investment decision making in conditions of multi-criteria uncertainty using statistical methods. Methods of evaluation and key criteria for making investment decisions are considered by Yashkina (2010). Features of making investment decisions are researched by Peresada et al. (2003), Honcharov (2002Honcharov ( , 2009). Risk management in entrepreneurial activity is analyzed in the book of Shehda and Holovanenko (2008).
However, the problem of multi-purpose and multi-criteria optimization in choosing one of several alternative investment projects in a context of limited capital and other resources, as well as personal attitudes of a decision maker, isn't sufficiently examined yet.

Problem
The investment process in Ukraine in the last three years shows a moderate recovery. Capital investment in the period 2015-2017 is characterized by the indicators given in Table 1. The data given in Table 1 show a significant increase in the volume of capital investments in the national currency, for example, in 2016, by almost a third compared with 2015. However, it would be more correct to compare these indicators in a stable currency, as during this period the devaluation of the hryvnia continued. An annual increase in investments calculated in US dollars was 10-12%. The vast majority of capital investments consisted of investments in tangible assets: buildings, structures, equipment, its acquisition, modernization, and major repairs. Own funds of enterprises remain the main source of investment with the share of almost 70%. Foreign direct investments and other sources don't exceed 5-10% of each, namely budgets of different levels, bank loans, and domestic investments. Let's consider the task of making a decision on choosing an investment project for the production enterprise to investits own funds in capital assets.
Investment projectis implemented on production enterprise, the activity of which characterr -ized as follows. The enterprise operates in the food industry exclusively on the domestic market. The last two years of the enterprise's activity have shown that its products are in demand, and there is a possibility to increase sales volumes by increasing the volume of existing production, as well as by expanding the range of products, as well as improving its quality. However, the investment opportunities of the company are limited and an entrepreneur can realize only one project. So, the way of further development of the enterprise must be chosen from the following options: 1) to establish a production plant in the region A with a promising market for products; 2) to establish a production plant in the region B with a significant resource of cheap labor; 3) to expand existing production; 4) to modernize existing production for the immprovement of products quality.
Also, possible states of the economic environment must be taken into account as significant factors of financial outcome of an enterprise's economic activity. Possible states of the economic environiment are described as follows: 1) unfavorable (involves an increase in the rate of inflation, reducing the purchasing power of the population, increasing costs of the enterprise and reducing its profits); 2) neutral (characterized by a stable situation in the market); 3) favorable (it involves lowering the rate of inflation, further growth of demand for products of the enterprise, increase of its profits).

Mathematical model
To formulate in mathematical terms the problem of multi-purpose multi-criteria investor decision making, let's introduce the system of three sets: a functional of evaluation : F ( ) 12 ,,, , where n -the number of criteria for assessing the problem; 1) a set of investor strategies ( ) 12 ,,, , In reality, variable l is continuous, because environment smoothly changes its state. But in order to simplify the model, investor must pick out indicators of discrete environmental states seaquence t P ( ) 1,..., . tl = Let us denote D the set of matrices, each of which corresponds to the investor's partial goal: where k is the number of goals. The elements of these matrices ( ) r ij d are numbers that characterrize the degree of achievement by an enterrprise of the partial r-th goal in the application of the current strategy of the і-th strategy in j-th state of the economic environment ( ) In this sense, the problem of multi-purpose multi-criteria investor decision making is to construct a set of matrices D based on the data sets , F , S and P followed by its analyysis and decision making on choosing an investment strategy to achieve the best result, that is, maximally possible to achieve all the goals simultaneously. It should be noted that the sets D and F are interconnected: that is, the degree of achievement of a partial goal depends on which criterion to evaluate it. Each project is characterized by different amounts of expected profits, as well as varying degrees of uncertainty, and hence risk. Thus, the investor seeks to achieve two goals: maximizing profits and simultaneously minimizing the risk. Consequently, The link between the objectives and criteria for evaluating projects of this task is as follows: NPV determines project outcome in a peiriod of time in absolute units of measurement (thousands UAH, i.e. Ukrainian hryvnia). Therefore, this criterion evaluates the extent to which goal of maximizing profits , IRR which is relative and is measured as a percentage. The criterion of discounted payback period DPP determines the term of return of invested funds and is measured by periods of time (in years, months, days). The faster the investment is paid, the more predictable is the process of project implementation. Therefore, this indicator can also be taken as a criterion for project and goal

DATA FOR ANALYSIS
The feasibility study for all projects under different conditions of the economic environment has provided data for analysis and decision making on project selection, as shown in Tables 2-5.
For the further calculations, matrix ingredients must be aligned and units of measurement of the matrix elements must be coordinated. An ingredient of a matrix of partial goals is the rule for evaluating the change of matrix elements. If the increase of the elements of the matrix is estimated by the investor as a positive trend, the matrix has a positive constituent, otherwise, it is negative. In the problem under consideration, matrices  .
At the next stage, the priorities of the partial goals should be determined and taken into account. The fact is that not all criteria are equally important for an investor. An entrepreneur may prefer one criterion, consider it more important than others. For this purpose, the investor must determine the vector of weight coefficients

RESULTS
The optimal investment strategy must be chosen according to the matrix * . D The results of the calculations are given in Table 6.
Let's evaluate the risk of each project by the Savage criterion, considering as the risk a value of unearned profit in the case of choosing a nonoptimal strategy. According to the Savage criterion, it is minimal element between maximum elements chosen in each line of the matrix of diversion, denoted here as

DISCUSSION
In view of performed calculations, the next recommendations may be given to the investor. All criteria indicate that the optimal solution under these conditions is the choice of the first strategy, that is, the investor should establish a production plant in the region A with a promising market for products. Although this project will bring the highest absolute profit in comparison with others, it has less efficiency, the highest payback period and the highest marginal cost of capital. Hurwitz's criterion, defining the indicator β according to pessimistic expectations. When applying the Laplace criterion, the investor believes that all the states of the economic environment are equally possible; instead, the Bayes-Laplace criterion uses a certain probabilistic distribution of environmental states ( ) and the Hodges-Lehman criterion takes into account the degree of confidence in this probabilistic distribution ( ).
γ In any case, one criterion must be chosen to assess alternative strategies and give recommendations.

CONCLUSION
Studying the application of optimal decision making theory in investment management, we considered an investment project selection problem in the case of four available projects, varying on characteristics of efficiency and riskiness. This problem was formalized, a mathematical model was developed for multi-purpose multi-criteria optimization. In result, it is shown that the first project according to its parameters fits the best to all investor's requirements. Of course, it isn't the best by the all parameters: only the profitability of project implementation, measured by net present value (NPV), prevails over the rest of the projects for all the states of the economic environment. But values of discounted payback period (DPP), investment rate of return (IRR) and profitability index (PI) of the first project are inferior to other projects. However, calculations show that the first project is optimal for this investor, because the mathematical model also takes into account personal attitudes, expressed by an investor's priorities. In our model investor preferred the NPV, considering the rest of the indicators less significant, but for another investor optimal choice could be different.