1. INTRODUCTION
For any enterprise that relates to the field of small or mediumsized business, the smooth functioning is extremely important, which, in addition to the entrepreneurial initiative, is also involved in the formation of finished products (Kingsley and Klein, 1998). In this regard, the task of supporting the enterprise, its development on the basis of entrepreneurial initiative, which in turn forms the possibility of modernization and gradual development in a competitive environment, becomes urgent. It is necessary to analyze the processes supporting the activities of the enterprise in the context of its subsequent modernization (Petukhova, 2011). One of the driving elements of the organization of production in industrial enterprises is their logistic support. In the current economic environment of industrial enterprises, the efficiency and optimality of each process are extremely important (Toxanova et al., 2017;Atanelishvili and Silagadze, 2018;Silagadze, 2019). Along with production, sales, marketing and other processes, logistic support has an extremely large impact on the efficiency of the enterprise; logistic support management of the enterprise plays a special role in the profitability of this enterprise.
For the smooth functioning of the production of the power complex enterprise, it is necessary to systematically establish logistic support, which allows distributing the means of production, establishing connections and concluding transactions between suppliers and consumers (Carlisle, 1998). The values of logistic support include values of cost and labor productivity, the use of production assets, the duration of production – in short, everything that affects its performance. It is proposed to understand logistics as the process of production support of the power complex enterprise with the necessary types of material and technical resources in a timely manner and in the volumes necessary for its regular operating activities (Borisov et al., 2012). By providing interindustry relations in the supply of products, the logistic support structures are helpful to reduce production time, increase its efficiency and product quality. This is due to the rhythmic and timely provision of enterprises with economic lines of various types of raw materials, materials and equipment.
2. LITERATURE REVIEW
2.1 Stages of Planning and Implementation of Logistics
The essence of logistic support is that it is the basis for pricing the manufactured product and the smooth production flow. The logistic support system is a set of enterprises producing material and technical reresources, trade and intermediary organizations, service units, and government bodies that regulate relations in the field of technical and engineering support (Higgott, 1980). In modern conditions, the main functions of the logistic support of the power complex enterprise are (Farakhov et al., 2015):

 organization of the procurement of materials, raw materials and semifinished products necessary for the production;

 organization of effective feedback from consumers to production, including consideration of consumer complaints and aftersales service.
The listed functions generate the following tasks for logistic support (Tarasova et al., 2018):

 determination of tasks of other structural units aimed at improving the position of the enterprise on the market.
The planning of logistic support of the power complex enterprise is based on the logistic support scheme, which is formed at the corresponding stages. Let us analyze them in more detail (Kolegov et al., 2012).

1. Analysis of resource efficiency in the reporting period. At this stage, adjustments are made to the production program and the volume of sales of the products in the planning period. Norms for consumption of materials, terms of wear of the tools, spare parts are calculated. Calculations of the needs of internal units for auxiliary materials are performed. The information on the material stocks in the production facilities, in incomplete production at the beginning and at the end of the planning period is analyzed. Terms of delivery of certain types of products are considered. Actual material stocks in warehouses are recorded.

2. Calculation of the need for material and technical resources. It is carried out on the grounds of basic values of resource consumption and according to the planned production volume (it determines the amount of materials that the enterprise needs to implement the production plan, for repair and operational needs).

3. Research of the market of raw materials. At this stage, the market of raw materials is analyzed, the instock balance forecast at the end of the current year and carryover stocks at the beginning of next year are developed, decisions on suppliers are made.

4. Drawing up a procurement plan for material resources. Needs are determined before the delivery of material resources based on the logistic support balance.
The tasks of planning the logistic support of the power complex enterprise are as follows (ErnstJoachim, 2000):

 timely and complete supply of the needs of the power complex enterprise for highquality material and technical resources;

 selection of appropriate suppliers and maintenance of communications with them; assurance of quality of material resources;
An important step in the development strategy of the power complex enterprise is the formation of a system of goals. In this aspect, qualimetric, hierarchical and divergent methods are applied (McNall, 1974). The application of a divergent and convergent approach to solving this problem will make it possible to expand the list of possible development goals, expose them to verification and, as a result, provide rationalization for the development strategy of the enterprise in general (Frolov, 2011). The sequence of goalsetting of the power complex enterprise can be represented as a spiral. It expands and then narrows, or as two pyramids of goals that are closed by their foundations and at each level they have corresponding models of comparison with competitors, or models for assessing the importance and achievability of goals (Kiseleva and Fonotov, 2017). The general scheme of the proposed divergent and convergent approach to the competitive goalsetting of the power complex enterprise has the form shown in Figure 1.
At the first stage of the divergent phase, the performance of the enterprise under study is compared with the performance values of competitors. The result of this stage is the establishment of performance target value at the level of the best competitors. Thus, the basis is set for further research on the prospects of the power complex enterprise and the construction of a wider “fan” of goals (Glamazdin et al., 2008). As values of the performance of competing enterprises, it is proposed to use the following (Sherin, 2017):
Moreover, values of profitability and net profit are the main ones, and the volume of sales is auxiliary. Profitability is used when analysis is necessary using relative values, and net profit is used in the analysis of absolute values of competitors’ performance (Klimov, 2009). When comparing the performance values with competitors, it is proposed for each of the competing enterprises to establish its importance in terms of impact on the business segment of the enterprise in general (Kruzhilin et al., 2018). In other words, for each competitor, its weight is set, and the total minimum value of performance that an industrial enterprise should try to achieve is calculated as a weighted average of the corresponding competitors’ values (Shapira and Youtie, 1998). A generalized model of the system of planning the need for logistic support of the power complex enterprise is shown in Figure 2. The management of logistic support of production covers a whole range of activities on coordinating the operation of all departments, employees and officials (Ramzaev et al., 2015).
Particular attention should be paid to suppliers management and procurement management, the set of their responsibilities and the quality of tasks (Figure 3), because their implementation has a certain sequence in the process of logistic support of industrial enterprises (Korel and Kombarov, 2012). This sequence can be represented in the following way:
2.2 Supplier Selection Inventory and Procurement Management Process
When choosing a supplier, remoteness, availability of reserve capacities can also be taken into account; terms of fulfillment of current and urgent orders, creditworthiness and financial situation, risk of strikes, etc.
The algorithm for selecting a supplier of material and technical resources is formed according to the following parameters:
Figure 4 shows a diagram of such an algorithm that takes into account the main and additional quantitative and qualitative criteria for the selection of a supplier. The main and additional criteria are determined each time by the customer, based on the current economic situation and factors (external and internal) that may assert influence on it (Shtal et al., 2018). The type and specialization of production, its spatial location, volumes and materialsoutput ratio of manufactured products determine the corresponding type of structure of the supply agencies (Platonov et al., 2017). In small enterprises that consume small amounts of material resources in a limited range, supply functions are assigned to small groups of individual employees of the economic department of the enterprise. At most medium and large enterprises, which include enterprises of the power complex, this function is performed by special departments of logistic support, which are formed on a functional or material principle. The organizational structure of the supply department is shown in Figure 5.
This structure makes it possible to rationally organize procurement strategies, it contributes to an increase in the responsibility of employees, and to an improvement in logistic support of production. The procurement process takes the following form (Seliverstov, 2014): fulfillment of an order; receipt of supply objects; conclusion of contracts with suppliers; receipt of commercial offers and benefits; receipt of applications; settlements with suppliers. The procurement management department should perform the following tasks:
Effective procurement management should bring cost savings that can be achieved by:
The procurement management process has certain stages and functional configuration (Figure 6). At the power complex enterprise, for every percent of reduction in procurement costs, there is a 12% profit growth. If the structure of the prime cost of production of the power complex enterprise is analyzed, it can be found out that the share of materials accounts for a significant percentage of all funds spent on the production of finished products. Thus, at the disposal of logistic support agencies there is a large part of the estimated cost of the completed project order. So, one of the main reserves for reducing the cost of production of the power complex is the improvement of the logistic support system for such production. Today, the power complex enterprises are characterized by order production, so the efficiency of using material resources is carefully determined:

 for the purpose of an objective assessment of the state of resource consumption in the main and auxiliary production, reserve volumes;

 for the purpose of making decisions on issues of resources saving and developing ways of rational use;
3. MATERIALS AND METHODS
The task is to optimally distribute a limited resource with a previously selected optimality criterion. They apply for mathematical methods in solving problems of optimizing the functioning of production systems, in the allocation of material and labor resources. The statements of the above problems are of an optimization nature, where various objective functions that are recorded analytically are used as performance criteria. However, a distinctive feature of the statement of problems of system analysis is the fact that, along with a rigorous mathematical apparatus, heuristic methods are used based on the intuition of the researcher, his/her experience in solving problems of this type. This is due to the difficulties of formalization of models of complex systems and processes.
On the basis of the work performed, an analysis was made of the current state of models in the method of analysis and minimization of risks in distributed production systems (Shtal et al., 2018;Ramzaev et al., 2015;Klimov, 2009). Too the inadequacy of models by modern technological and production systems was revealed. It was determined that simulation modeling allows us to model various situations with the possibility of assessing the consequences of decisions made under conditions of transformational changes in external conditions. Therefore, it is advisable to apply simulation modeling technology to solve the problems of the allocation of a limited resource in the process of logistic support for the production of the power complex.
Simulation modeling does not exclude the use of analytical models in the process of a computational experiment with incomplete information about the initial state of the system and its input operations. Thus, simulation modeling does not reduce the importance of analytical models, but is a way to expand the scope of their application in accordance with the research conditions, which are complicated during the implementation of the project. Thus, using works devoted to applied problems of resource management as applied to organizational and technical systems, it is proposed to combine system analysis technologies, game theory, and simulation modeling to solve problems of optimizing the allocation of material resources (Petukhova, 2011;Klimov, 2009;Platonov et al., 2017).
In the process of logistic support for the production of the power complex, significant amounts of funds are spent in the form of materials, semifinished products, components, this fact makes the task of efficient allocation of resources relevant in order to satisfy some optimality criterion. The term “resources” can be understood not only as financial, but also as specific material flows to be allocated. In this case, it is necessary to move from a scalar quantity describing financial resources to a vector quantity characterizing material resources. The dimension of a vector describing a set of allocated material resources is determined from the conditions of a specific task. In general, the logistic support function associated with the allocation of a limited resource can be considered as the task of managing several projects that are related to each other only by common resources.
4. RESULTS AND DISCUSSION
The maximum value at which the enterprise can consider itself a leader should be equal to the maximum of all competitors’ values, taking into account the correction coefficient (Equation 1):
where G^{R} : target value of the performance of the power complex enterprise (profitability, net profit, or other);

ε : correction coefficient, which may be more than one if the enterprise is trying to become the undisputed leader in the industry, or less than one if the enterprise's capabilities do not allow it to become a leader;
The next stage of the divergent phase is a comparison with competitors' business processes and the formation of goals for the reorganization of their business processes. In this case, the range of the value of main goal established at the previous stage is basic. When forming the goalsetting model at this stage, the assumption was established that each business process under consideration has an influence on the main goal and this influence can be estimated. As a model for reforming the business processes of the power complex enterprise, the corresponding business processes of competing enterprises are selected. When forming a system of auxiliary goals for each business process, the influence of the sphere to which the business process belongs on the main goal and the difference between the efficiency of the business process at the industrial enterprise and at competing enterprises are analyzed. An auxiliary goal is included in the goalsetting system if (Equation 2, 3, 4):
where

L^{S} : the minimum value of the efficiency indicator at which the industrial enterprise can consider the value of the effectiveness of a particular sphere as satisfactory;

$M\left\{{B}_{d1},\dots ,{B}_{d{K}^{d}}\right\}$ : median of the set of effectiveness of individual business processes;

$\left\{{B}_{d1},\dots ,{B}_{d{K}^{d}}\right\}$ : a set of efficiencies of individual business processes that relate to the dth sphere of activity of the power complex enterprise;

K^{D} : the number of business processes that belong to the dth sphere of activity of the power complex enterprise;

$F\left({S}_{d},{G}^{R}\right)$ : function reflecting the relationship between the effectiveness of the dth sphere of activity of the power complex enterprise and its global goal;

L^{G} : the value at which the relationship between the effectiveness of the dth sphere of activity of the power complex enterprise and its global goal can be considered significant (in the general case, equal to 0.7 or more).
The stage of formation of the hierarchy of goals makes it possible to ensure the development of the power complex enterprise in each sphere of activity. With this aim in view, it is proposed to establish dependencies between auxiliary goals, that is, those which must be completed earlier, and which later. In this case, auxiliary goals of the second order arise, which were not established directly at the previous stage, but the achievement of which is necessary to implement the auxiliary goals of the first order. The hierarchy of auxiliary goals of the first and second orders is proposed to be carried out using graph theory, and the analysis of the relationships between goals using the critical path method (CPM). Moreover, each goal is described as a list of related goals necessary for its achievement and time spent on achieving these goals (Equation 5, 6, 7):
where G^{R} : the main goal of the power complex;

$\left\{{G}_{s}^{1},{T}_{s}^{1}\right\}$ : a set of auxiliary goals of the first order which must be achieved in order to achieve the main goal of the power complex enterprise, and an evaluation of the time required to achieve them;

$\left\{{G}_{{e}^{1s}}^{1},{T}_{{e}^{1s}}^{1}\right\}$ : a set of auxiliary goals of the first order $\left({G}_{{e}^{1s}}^{1}\right)$ which must be achieved in order to achieve the goal ${G}_{s}^{1}$, and evaluations of the time $\left({T}_{{e}^{1s}}^{1}\right)$ required to achieve them;

$\left\{{G}_{{e}^{2s}}^{2},{T}_{{e}^{2s}}^{2}\right\}$ : a set of auxiliary goals of the second order $\left({G}_{{e}^{2x}}^{2}\right)$ which must be achieved in order to achieve the goal ${G}_{s}^{1}$, and evaluations of the time $\left({T}_{{e}^{2s}}^{2}\right)$ required to achieve them;

$\left\{{G}_{{e}^{2h}}^{2},{T}_{{e}^{2h}}^{2}\right\}$ : a set of auxiliary goals of the second order $\left({G}_{{e}^{2h}}^{2}\right)$ which must be achieved in order to achieve the goal ${G}_{h}^{2}$, and evaluations of the time $\left({T}_{{e}^{2h}}^{2}\right)$ required to achieve them;

${e}^{1s}=1,\dots {E}^{1s}$ : indices of auxiliary goals of the first order, which are necessary to achieve the sth auxiliary goal of the first order (E^{1s} – number of such goals);

${e}^{2s}=1,\dots ,{E}^{2s}$ : indices of auxiliary goals of the second order, which are necessary to achieve the sth auxiliary goal of the first order (E^{2s} – number of such goals);

${e}^{2h}=1,\dots ,{E}^{2h}$ : indices of auxiliary goals of the second order, which are necessary to achieve the hth auxiliary goal of the second order (E^{2h} – number of such goals).
Evaluation of time spent on achieving goals allows us to divide the goalsetting into strategic, operational and tactical. In turn, the existence of temporary goalsetting plans is the basis for the analysis of the resources, sources and schedules for their receipt necessary to achieve these goals. Thus, after the formation of the maximum possible fan of goals, a transition to the convergent stage of goalsetting can be made. At the first stage of this phase, it is proposed to assess the cost of resources to achieve the goals set at the previous stage. It is proposed to divide the resources that can be used by the power complex enterprise into financial and others. Moreover, other resources can be transferred to financial. This approach is justified by the fact that all other types of resources (material, production, personnel) can be acquired, the main issue is the price that will have to be paid for this resource. The description of the cost of resources for each goal has the following form (Equation 8, 9, 10):
where V^{R} : a set of resources which are required to achieve the main goal of the power complex enterprise;

${F}_{s}^{1}$ : a set of financial resources which are required to achieve the main goal of the power complex enterprise;

$\left\{{\widehat{F}}_{s}^{1},{R}_{s}^{1}\right\}$ : a set of nonfinancial resources which are required to achieve the main goal of the power complex enterprise ($({R}_{s}^{1})$) and these resources in monetary terms $({\widehat{F}}_{s}^{1})$;

${V}_{s}^{1}$ : a set of resources which are required to achieve the sth auxiliary goal of the first order;

${F}_{{e}^{1s}}^{1}$ : a set of financial resources which are required to achieve the sth auxiliary goal of the first order;

$\left\{{\widehat{F}}_{{e}^{1s}}^{1},{R}_{{e}^{1s}}^{1}\right\}$ : a set of nonfinancial resources which are required to achieve the auxiliary goal of the first order $\left({R}_{{e}^{1s}}^{1}\right)$, which is associated with the sth auxiliary goal, and monetary estimates of these resources $\left({\widehat{F}}_{{e}^{1s}}^{1}\right)$;

${F}_{{e}^{2s}}^{2}$ : a set of financial resources which are required to achieve the auxiliary goal of the second order of the power complex enterprise which is associated with the sth auxiliary goal;

$\left\{{\widehat{F}}_{{e}^{2s}}^{2},{R}_{{e}^{2s}}^{2}\right\}$ : a set of nonfinancial resources which are required to achieve the auxiliary goal of the second order $\left({R}_{{e}^{2s}}^{2}\right)$ which is associated with the sth auxiliary goal, and monetary estimates of these resources (${\widehat{F}}_{{e}^{2s}}^{2}$);

${V}_{h}^{2}$ : a set of resources which are required to achieve the hth auxiliary goal of the second order;

${F}_{{e}^{2h}}^{2}$ : a set of financial resources which are required to achieve the hth auxiliary goal of the second order;

$\left\{{\widehat{F}}_{{e}^{2h}}^{2},{R}_{{e}^{2h}}^{2}\right\}$ : a set of nonfinancial resources which are required to achieve the hth auxiliary goal of the second order of the power complex enterprise $\left({R}_{{e}^{2h}}^{2}\right)$), and monetary estimates of these resources $\left({\widehat{F}}_{{e}^{2h}}^{2}\right)$;

${e}^{1s}=1,\dots ,{E}^{1s}$ : indices of the auxiliary goals of the first order which are required to achieve the sth auxiliary goal of the first order (E^{1s} – number of such goals);

${e}^{2s}=1,\dots ,{E}^{2s}$ : indices of the auxiliary goals of the second order which are required to achieve the sth auxiliary goal of the first order (E^{2s} – number of such goals);

${e}^{2h}=1,\dots ,{E}^{2h}$ : indices of the auxiliary goals of the second order which are required to achieve the hth auxiliary goal of the second order (E^{2h} – number of such goals).
Already at this stage, we can narrow down many of the goals of the power complex enterprise if, when assessing the resources, it turns out that the necessary resources can be obtained even with sufficient financial soundness (for example, the necessary technology is protected by patents, the owner of which does not agree to sell it). But the main stage of the convergent phase is the stage of goals cuts in accordance with available resources. At the same time, the availability of resources or the possibility of attracting them is assessed, and goals that cannot be achieved in the current conditions are canceled. Moreover, the cancellation of goals of the second and first orders necessitates a review of goals that are at the higher level of the hierarchy in accordance with what has been withdrawn. Higher hierarchy goals can be adjusted (for example, the planned volume of sales is reduced) or completely canceled. The cuts of goals of the power complex enterprise according to the available resources can be carried out in the mode of individual viewing of each goal for which there may not be enough resources, with the subsequent analysis of the entire chain of goals that are associated with the reduced goal. The cuts of goals can also be carried out in an automated mode, when all possible combinations of canceling goals are considered in accordance with available resources, and a set of alternatives is provided to analysts and managers for making a decision. The main characteristic of each alternative is the expected value of the indicator characterizing the strategic goal of the power complex enterprise. Thus, the result of this stage is a reduced set of goals, the structure of which is given in Table 1.
The final stage of the convergent phase of goalsetting of the power complex enterprise is the formation of a schedule for achieving goals. The purpose of this stage is to narrow down the diversity of goals at each time horizon. Due to the estimated time spent on the formation of the goal hierarchy, the time to achieve each auxiliary goal can be linked to a specific calendar date, which makes it possible to further monitor the achievement of goals. Presentation of the schedule for achieving goals of the power complex enterprise can be carried out using standard tools to display the implementation of projects, for example, Gantt charts. When modeling the procedure for the supply of material and technical resources and their procurement, it will be assumed that there are two players in the goods market. The first player represents the enterprises supplying resources, the second player represents the industrial enterprises receiving resources. And, as already noted, each enterprise can be both a supplier and a buyer of resources. A player who can supply resources determines their supply in the goods market; a player who can buy resources determines their demand in the goods market. Therefore, in the future, it will be considered that the first player controls the offer of resources (supply), and the second player controls the demand for resources (procurement).
Let x(0) be the value of the supply of material resources in national currency, which is planned to be offered to the counterparty (the second player) in the resource market in the period [0,T] (T is a natural number). y(0) is the value of demand for resources in national currency, which the second player plans to satisfy in the resource market in the period [0,T]. Let us denote by α^{pr} – the growth rate of the supply of resources during the planning period of time $\left[t,T\right]\left(t=0,1,\dots ,T1\right),{\beta}_{pr}$ – the growth rate of the demand for resources during the planned period of time $\left[t,T\right]\left(t=0,1,\dots ,T1\right)$. For the sake of simplicity, we believe that the growth rate, α_{pr}, β_{pr} are constants. In addition, let us denote by ${p}_{1}^{pr}$ – the offer price of resources in national currency, by ${p}_{2}^{pr}$ – the price of demand for resources in national currency, by ${\gamma}_{1}^{pr}$ we denote the relation ${p}_{1}^{pr}/{p}_{2}^{pr}$, and by ${\gamma}_{2}^{pr}$ – the ratio ${p}_{2}^{pr}/{p}_{1}^{pr}$.
Let us describe the process of supply and demand in the resource market. At time t, it is assumed that the value of the supply x(t) of resources in national currency, which the first player planned to offer to the second player in the interval [t,T] is multiplied by the growth rate of the supply of resources in national currency in the interval $\left[t,T\right]\left(t=0,1,\dots ,T1\right)$. After that, the first player selects the value $u\left(t\right)\in \left[0,1\right]$ which determines the value of the supply $u\left(t\right)\times {a}_{pr}x\left(t\right)$ of goods in national currency to the second player.
The second player acts in a similar way. At time t, the value of demand y(T) for resources in national currency which the second player planned to satisfy on the interval [t,T] is multiplied by the growth rate of the demand for resources in national currency in the interval $\left[t,T\right]\left(t=0,1,\dots ,T1\right)$. After that, the second player selects the value $\nu \left(t\right)\in \left[0,1\right]$ which determines the value of the demand $\nu \left(t\right)\times {\beta}_{pr}y\left(t\right)$ for resources in national currency, which the second player planned to satisfy in the interval $\left[t,t+1\right]\left(t=0,1,\dots ,T1\right)$.
The value of the supply $u\left(t\right)\times {\alpha}_{pr}x\left(t\right)$ of resources in national currency, which the first player supplies to the second player, will allow the second player to satisfy his/her demand for resources in national currency by the value ${\gamma}_{2}^{pr}\times u\left(t\right)\times {\alpha}_{pr}x\left(t\right)$ (in accordance with the law of equilibrium: (supply price) x (supply volume) = (demand price) x (demand volume)). The value of the demand $\nu \left(t\right)\times {\beta}_{pr}y\left(t\right)$ for resources in national currency, which the second player planned to satisfy in the interval $\left[t,t+1\right]\left(t=0,1,\dots ,T1\right)$, will allow the first player to offer the second player a value ${\gamma}_{1}^{pr}\times \nu \left(t\right)\times {\beta}_{pr}y\left(t\right)$ of resources in national currency (according to the law of equilibrium: (supply price) x (supply volume) = (demand price) x (demand volume)).
Thus, at time t+1 the value of supply x(t+1) and demand y(t+1) will be written in the following way (Equation 11, 12):
At once it will be noticed that the situation fits into the framework of the considered scheme: one enterprise that is interested in buying resources for its functioning is a group of enterprises supplying resources, which can be either one enterprise or a group of enterprises. In the case when the demand and supply procedure is considered not only in the domestic market, but also in the external one, it is necessary to make additions due to this factor. That is, taking into account the fact that players, in addition to supply and demand for resources in national currency, also supply resources in foreign currency, and are also in demand for resources in foreign currency. Let us introduce additional notations. We denote by ${\beta}_{1}^{pr}\left({\beta}_{1}^{pr}\in \left[0,1\right]\right)$ – the value characterizing the proportion of the value of the first player’s supply of resources in national currency in the domestic and foreign markets in the interval [t,t+1]; i.e. ${\beta}_{1}^{pr}\times u\left(t\right)\times {\alpha}_{pr}x\left(t\right)$ – the value of the first player’s supply of resources in national currency in the domestic and foreign markets in the interval [t,t+1], then $\left(1{\beta}_{1}^{pr}\right)$ will mean the share of the first player’s supply of resources in foreign currency in the domestic and foreign markets in the interval [t,t+1]; i.e. $\left(1{\beta}_{1}^{pr}\right)\times u\left(t\right)\times {\alpha}_{pr}x\left(t\right)$ – the value of the first player’s supply of resources in foreign currency in the domestic and foreign markets in the interval [t,t+1].
By ${\beta}_{2}^{pr}\left({\beta}_{2}^{pr}\in \left[0,1\right]\right)$ – the value characterizing the share of the second player’s demand for resources in national currency in the domestic and foreign markets in the interval [t,t+1], i.e. ${\beta}_{2}^{pr}\times \nu \left(t\right)\times {\beta}_{pr}y\left(t\right)$ – the value of the second player’s demand for resources in national and foreign currencies in the domestic and foreign markets in the interval [t,t+1]. Then $\left(1{\beta}_{2}^{pr}\right)$ means the share of the second player’s demand for resources in foreign currency in the domestic and foreign markets in the interval [t,t+1], i.e. $\left(1{\beta}_{2}^{pr}\right)\times \nu \left(t\right)\times {\beta}_{pr}y\left(t\right)$ – the value of the second player’s demand for resources in foreign currency in the domestic and foreign markets in the interval [t,t+1]. In addition, by k_{d} we denote the exchange rate in relation to the national currency, i.e. 1$ = k_{d}; by ${q}_{1}^{pr}$ we denote the price of supply of goods in foreign currency, by ${q}_{2}^{pr}$  the price of demand for goods in foreign currency (dollars); by ${\delta}_{1}^{pr}$ we denote the ratio ${q}_{1}^{pr}/{q}_{2}^{pr}$, by ${\delta}_{2}^{pr}$ – the ratio ${q}_{2}^{pr}/{q}_{1}^{pr}$. So, the record for values $x\left(t+1\right)\u0438y\left(t+1\right)$ has the following form (Equation 13, 14):
Let us comment on the process of supply and demand of products and services in the resource market, which includes both the domestic and foreign markets. At time t, it is assumed that the value of the supply x(t)) of resources in national and foreign currencies that the first player planned to supply to the second player in the interval [t,T] is multiplied by the growth rate of the supply of resources in national and foreign currency in the interval $\left[t,T\right]\left(t=0,1,\dots ,T1\right)$. After that, the first player selects the values ${\beta}_{1}^{pr}\in \left[0,1\right],\left(1{\beta}_{1}^{pr}\right)\in \left[0,1\right],u\left(t\right)\in \left[0,1\right]$ that dedetermine the value of the supply ${\beta}_{1}^{pr}\times u\left(t\right)\times {\alpha}_{pr}x\left(t\right),\left(1{\beta}_{1}^{pr}\right)\times u\left(t\right)\times {\alpha}_{pr}x\left(t\right)$ of resources in national and foreign currencies, respectively, to the second player. The second player acts in a similar way. At time t, the value of the demand y(t) for resources in national and foreign currencies, which the second player planned to satisfy in the interval [t,T] is multiplied by the growth rate of demand for resources in national and foreign currencies in the interval $\left[t,T\right]\left(t=0,1,\dots ,T1\right)$. After that, the second player selects the value ${\beta}_{2}^{pr}\in \left[0,\hspace{0.17em}1\right],\hspace{0.17em}\hspace{0.17em}\left(1{\beta}_{2}^{pr}\right)\in \left[0,1\right],\hspace{0.17em}\nu \left(t\right)\in \left[0,1\right]$ that determine the value of the demand ${\beta}_{2}^{pr}\times \nu \left(t\right)\times {\beta}_{pr}y\left(t\right),\hspace{0.17em}\left(1{\beta}_{2}^{pr}\right)\times \nu \left(t\right)\times {\beta}_{pr}y\left(t\right)$ of national and foreign currencies, which the second player planned to satisfy in the interval $\left[t,t+1\right]\left(t=0,1,\dots ,T1\right)$.
The value of the supply ${\beta}_{1}^{pr}\times u\left(t\right)\times {\alpha}_{pr}x\left(t\right)$ of resources in national currency, which the first player supplies to the second player, will allow the second player to satisfy his/her demand by the value ${\gamma}_{2}^{pr}\times {\beta}_{1}^{pr}\times u\left(t\right)\times {\alpha}_{pr}x\left(t\right)$ (according to the law of equilibrium: (supply price) x (supply volume) = (demand price) x (demand volume)). The value of the supply $\left(1{\beta}_{1}^{pr}\right)\times u\left(t\right)\times {\alpha}_{pr}x\left(t\right)$ of resources in foreign currency, which the first player supplies to the second player, will allow the second player to satisfy his/her demand by the value ${\delta}_{2}^{pr}\times \left(1{\beta}_{1}^{pr}\right)\times u\left(t\right)\times {\alpha}_{pt}x\left(t\right)$(according to the law of equilibrium: (supply price) x (supply volume) = (demand price) x (demand volume)).
The value of the demand ${\beta}_{2}^{pr}\times \nu \left(t\right)\times {\beta}_{pr}y\left(t\right)$ for resources in national currency, which the second player planned to satisfy in the interval $\left[t,t+1\right]\left(t=0,1,\dots ,T1\right)$, will allow the first player to supply to the second player the value ${\gamma}_{1}^{pr}\times {\beta}_{2}^{pr}\times \nu \left(t\right)\times {\beta}_{pr}y\left(t\right)$ of resources in national currency (according to the law of equilibrium: (supply price) x (supply volume) = (demand price) x (demand volume)). The value of the demand $\left(1{\beta}_{2}^{pr}\right)\times \nu \left(t\right)\times {\beta}_{pr}y\left(t\right)$ for goods in foreign currency, which the second player planned to satisfy in the interval $\left[t,t+1\right]\left(t=0,1,\dots ,T1\right)$, will allow the first player to supply to the second player the value ${\delta}_{1}^{pr}\times \left(1{\beta}_{2}^{pr}\right)\times v\left(t\right)\times {\beta}_{pr}y\left(t\right)$ of resources in foreign currency (according to the law of equilibrium: (supply price) x (supply volume) = (demand price) x (demand volume)). Then, at the time t + 1 < T one of four conditions is possible (Equation 15, 16, 17, 18):
If the first condition is met, then the second player managing the demand ahead of schedule realized his/her demand at the time t+1, and the first player managing the supply did not implement his/her offer at the time t+1. The supply and demand procedure is considered completed as a result of the realization of demand by the second player ahead of schedule. If the second condition is met, then the first player managing the supply prematurely realized his/her supply at the time t+1 and the second player managing the demand did not realize his/her demand at the time t+1. The supply and demand procedure is considered completed as a result of the realization of the supply by the first player ahead of schedule. If the third condition is met, then the players managing both supply and demand, realized their supply and demand at the time t+1 ahead of schedule. The supply and demand procedure is considered completed as a result of the realization of demand by players ahead of schedule. If the fourth condition is met, then the players managing both supply and demand did not realize their supply and demand at the time t+1 and, therefore, the supply and demand procedure continues for the times larger than t+1. And, at the point in time t = T  1 players make the last move and determine the values x(T) and y(T) that show the supply and demand at the time t = T as a result of the realization of the demand and supply of players.
Note 1. Both supply and demand for resources include both resources in national currency and in foreign currency. If V_{1} – the amount of resources in national currency that can be supplied, and V_{2} – the amount of resources in foreign currency, for example, in the currency that can be offered, then the total amount of resources (“valued” in national currency) that can be offered is equal to the amount ${V}_{1}+{k}_{d}\times {V}_{2}$. Thus, the share ${\beta}_{1}^{pr}$ of resources in national currency that can be supplied is equal to ${V}_{1}/\left({V}_{1}+{k}_{d}\times {V}_{2}\right)$, and the share $\left(1{\beta}_{1}^{pr}\right)$ of resources in foreign currency can be supplied equal to ${k}_{2}\times {V}_{2}/\left({V}_{1}+{k}_{d}\times {V}_{2}\right)$. That is, the choice of shares ${\beta}_{1}^{pr},\left(1\beta {1}_{1}^{pr}\right)$, when substantiating the dynamics of changes in the volumes of supply and demand, can occur in the manner described above, which means that for fixed volumes V_{1}, V_{2} the change of values ${\beta}_{1}^{pr},\hspace{0.17em}\left(1{\beta}_{1}^{pr}\right)$ is due to changes in the exchange rate k_{d}. With the growth of the exchange rate, the value ${\beta}_{1}^{pr}$ decreases, and the value $\left(1{\beta}_{1}^{pr}\right)$ increases, with a decrease in the exchange rate, the value ${\beta}_{1}^{pr}$ grows, and the value $\left(1{\beta}_{1}^{pr}\right)$ – decreases.
A game theory toolkit that allows us to determine the areas of possible initial states of supply and demand (in the resource market). If the process of supply and demand begins with these states, then at one point in time the supply or demand can be realized. It makes it possible to obtain the necessary result of the supply and demand realization process and find optimal (rational) strategies for managing the supply and demand realization process. To find such areas, a multistep game with two terminal surfaces is solved. The solution of which is to determine the sets of initial states of supply and demand, as well as strategies (control actions) of players, using which it is possible to obtain results that are desirable for each player (the realization of demand or supply).
The above realization process of the supply and demand procedure will be considered within the framework of the positional multistep game scheme with full information. Within the framework of this scheme, the process “generates” two tasks: from the point of view of the first ally player and from the point of view of the second ally player. Due to the symmetry, it will suffice to be limited to considering one of them, for example, from the point of view of the first ally player. Let us denote by ${T}^{*}=\left\{0,1,\dots \right\}$ a discrete set characterizing the area of change of the time parameter.
Definition. The pure strategy of the first ally player is called the function ${T}^{*}\times {R}_{+}^{2}\to \left[0,1\right]$ that puts to the state of information (position) $\left(t,\left(x,y\right)\right)$ the value $u\left(t,\left(x,y\right)\right)\in \left[0,1\right]$. That is, the pure strategy of the first ally player is a function (rule) that sets to the state of information at time t the value $u\left(t,\left(x,y\right)\right)$, which determines the value of the supply of material resources, which he/she supplies in the planning period $\left[t,t+1\right]$. Regarding the awareness of the opponent player (within the framework of the positional game scheme), no assumptions are made, which is equivalent to the fact that the opponent player chooses his/her control influence ν(t), which determines the amount of demand for material resources, based on any information.
After defining the strategies in task 1, it is necessary to identify many “benefits” W_{1} for the first player. W_{1}  a set of such initial states $\left(x\left(0\right),y\left(0\right)\right)$ which are the value of supply and demand. For such initial states, there is a strategy of the first player that controls the supply of material resources, which for any realization of the strategy of the second player “brings” the state $\left(x\left(t\right),y\left(t\right)\right)$ at one point in time t wherein condition (1) is satisfied. Moreover, the second player does not have a strategy that can “lead” to the fulfillment of conditions (2) or (3) at one of the previous points in time. The strategy ${u}_{*}\left(.,.\right)$ of the first player with this property is called optimal.
The solution to problem 1 is to find a set of “advantages” of the first player and his/her optimal strategies. Similarly, the problem is posed from the point of view of the second ally player. Due to the symmetry, it is enough to be limited to the solution to problem 1, since the solution to Problem 2 is found in exactly the same way. The solution to problem 1 is found using the tools of the theory of multistep games with complete information, which allows us to find it with different ratios of game parameters. Here is a solution to the game, that is, a lot of advantage W_{1} and optimal strategies for the first player. Note the following: a set of benefits W_{1} is a union of sets W_{1} of states $\left(x\left(0\right),y\left(0\right)\right)$ which have the property that if the supply and demand procedure begins with them, then the first player has a strategy ${u}_{*}\left(.,.\right)$ which allows him/her to obtain the fulfillment of condition (1). At the time t=i, no matter how the second player acts, and the second player has a strategy ${v}_{*}\left(.,.\right)$ which does not allow the first player to obtain the fulfillment of condition (1) in less time. Let us denote by S_{1} – the value ${\gamma}_{1}^{pr}\times {\beta}_{1}^{pr}+{\delta}_{1}^{pr}\times \left(1{\beta}_{1}^{pr}\right)$, i.e.
and by S_{2} the value ${\gamma}_{2}^{pr}\times {\beta}_{2}^{pr}+{\delta}_{2}^{pr}\times \left(1{\beta}_{2}^{pr}\right)$, i.e.
We write the sets ${W}_{1}^{i}$ and optimal strategies ${u}_{*}\left(.,.\right)$ for any ratios of game parameters (Equation 21, 22, 23, 24, 25).
On the basis of this, Inequality (26) is formed:
The first player cannot “force” the second player to satisfy demand at any given time. $\alpha >\beta ,{s}_{1}\times {s}_{2}\ge 1;$ In this case, a set of advantages of the first player W_{1} will be the union of a finite number of sets W_{1}, namely (N+2) of sets where (Equation 27, 28, 29):
Optimal strategy (Equation 30, 31) is defined as follows.
and not defined – otherwise (Equation 32),
at $\left(x,y\right)\in {R}_{+}^{2},\alpha \times y>{s}_{2}\times \beta \times y,$, and not defined – otherwise}; $t=0,\dots ,N+1\}$. $\alpha >\beta ,\hspace{0.17em}{s}_{1}\times {s}_{2}<1;$ In this case, a set of advantages of the first player W_{1} will also be a union of finite number of sets ${W}_{1}^{i}$, namely $\left(N+{i}_{*}+2\right)$ of sets, where $N:k\left(i\right)>\alpha /\beta ,i=0,\dots ,N1;k\left(N\right)\le \alpha /\beta ;$; i – the minimum nonnegative number determined by the inequality (Equation 33):
Then
If ${i}_{*}=0$, then
The record of the optimal strategy in this case is exactly the same as in case 2.
The optimal strategy (Equation 39, 40) is defined as follows.
and not defined – in another case, $t=0,1,\dots ,{i}_{*}$,
at $\left(x,y\right)\in {R}_{+}^{2},\alpha \times y>{s}_{2}\times \beta \times y,i\ge {i}_{*}+1$, and not defined  otherwise}.
Note 2. If the supply and demand procedure is considered as a onestep procedure, then according to the classification of game theory such a procedure can be embedded in the framework of an infinite antagonistic game with zero sum, that matters (“saddle point”) in the class of mixed strategies. For example, in case 1) the set ${W}_{1}^{i}$ are sets of states $\left(x\left(0\right),y\left(0\right)\right)$ which have the property. If a onestep procedure for the realization of supply and demand begins with them, then with probability (1/i) the first player managing the supply in the resource market will “lead” the demand and supply management process to the realization of the supply in one step, if the second player managing the demand in the resource market will use its optimal mixed strategy. If the second player uses a nonoptimal mixed strategy, the realization probability of supply will increase in one step.
Note 3. In reality, the process of managing supply and demand in the resource market can run differently over time. For example, players can make their decisions in turn, or simultaneously, but with a greater frequency, which is modeled to some extent by a continuous model of managing supply and demand in the market resources in which the dynamics of control is given by differential equations. In each case, there is a solution to the corresponding game. Then, using the results of the decisions of the corresponding games, the results of the real process of supply and demand in the resource market can be predicted.
Note 4. Since some of the parameters in this model are endogenous, and some are exogenous, so we can exert influence on the result of the procedure, trying to improve it (from the position of a player) by controlling both endogenous and exogenous factors.
Note 5. When solving problems with the proposed gaming technologies, in the space of variables (x,y), there are either areas of equation or rays of equation, i.e., if the procedure for managing supply and demand in the resource market begins with them, then the players have strategies that allow them to remain either in the field of equation or in the ray of equation. Therefore, for any condition $\left(x\left(0\right),y\left(0\right)\right)$ it is possible to determine the parameters of the procedure under which this state will be either on the ray of equation, or in the field of equation.
A typical model of the allocation of limited resources is considered when implementing an arbitrary number of independent projects (the essence of each project, its relationship with others is taken into account only at the level of total resources consumed). The basic ratios are made in a general way, which allows us to switch from financial flows to material ones. Let us formulate the problem of the allocation of limited material and technical resources in the most general setting.
Consider n project orders that meet the necessary conditions of efficiency, each of which is characterized by a set of parameters: Q_{f} – the required amount of funding for the ith project; ${T}_{{t}_{i}}$ – the duration of the ith project; P_{i} – the expected profitability of the ith project. The valuable thing in the algorithms under consideration is that the sources of project financing are studied, while own and borrowed funds are allocated. This leads to the need to solve two problems depending on the sources of financing. The notation is introduced:

V – a set of project orders requiring appropriate resources (project portfolio); ${Q}_{f\left(own\right)}$ – the amount of funding regarding the necessary material and technical resources from own funds; Q_{f} – total funding for the necessary material and technical resources. If ${Q}_{f}{Q}_{f\left(own\right)}$ then the difference ${Q}_{f}{Q}_{f\left(own\right)}$ is financed by means of loans, which naturally increases the cost of the project; profitability of the portfolio of projects and each project:
The effectiveness of the Ith project (reduced to the period under consideration):
The complexity of solving the problem largely depends on the nature of the profitability functions of the set of project orders under study: as a rule, the more restrictions are imposed on the nature of the function, the more difficult the decision procedure is. A minimal requirement is introduced that follows logically from the nature of this problem; it is believed that a function must possess the additivity property. In this case, the cost of resources required to realize a set of project orders taking into account the interest rate for the loan (a – the interest rate) will be determined in the following form (Equation 44):
then the effectiveness of the set of project orders V will be characterized by Equation (45):
Therefore, the expression represents the objective function of the problem of finding the optimal allocation of limited resources available. Specific material flows in the framework of managing the logistic support of power projects, which can be written in the classical form of a nonlinear programming problem (Equation 46, 47):
The solution of the formulated problem depends on the type of objective function. If we restrict ourselves to the previously introduced requirement of additivity of the objective function, then in this case the most effective way will be the application of the dynamic programming method.
5. CONCLUSION
Thanks to the developed model of the competitive goalsetting of the power complex enterprise, which is based on the formation of an excessive list of possible goals that are set as a result of comparison with competitors at the divergent stage, and further reduction. At the convergent stage, the enterprise management is provided with the opportunity to set goals and obtain a hierarchy and a schedule for achieving goals of the power complex enterprise, which take into account the characteristics of the competitive environment.
Thus, a resource allocation model has been developed within the framework of a methodological approach to managing the logistic support of the production of the power complex enterprise. Into account the limited resources available, specific material flows, which makes it possible to find their optimal allocation and ensures the efficiency of production processes at the enterprise.
The novelty of the work is determined by the fact that economic activity in the field of entrepreneurial business is determined by the format and planning measures for the long term, which is formed on the basis of the costs of small and mediumsized enterprises in the production of industrial products. The practical significance of the study is determined by the possibility of forming a highquality component that will create an instrument for the development of small and medium enterprises in the regions.