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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.19 No.1 pp.120-132
DOI : https://doi.org/10.7232/iems.2020.19.1.120

Development of Innovation Infrastructure of Energy Complex Enterprises

Galiya S. Ukubassova*, Adaskhan K. Daribayeva, Aigul N. Toxanova, Darima Zhenskhan, Aigul A. Mukhamejanova
Department of Economics, Kazakh University of Economics, Finance and International Trade, Nur-Sultan, Republic of Kazakhstan
Department of International Trade and Law, Kazakh University of Economics, Finance and International Trade, Nur-Sultan, Republic of Kazakhstan
Department of Economics, Kazakh University of Economics, Finance and International Trade, Nur-Sultan, Republic of Kazakhstan
Department of Management, S. Seifullin Kazakh Agro Technical University Nur-Sultan, Republic of Kazakhstan
Department of Economics, Kazakh University of Economics, Finance and International Trade, Nur-Sultan, Republic of Kazakhstan
*Corresponding Author, E-mail: gal-ukub@murdoch.in
November 13, 2019 December 25, 2019 January 3, 2020

ABSTRACT


The relevance of the study is determined by the fact that energy-saving enterprises are closely related to the implementation of technologies that can fully provide a technological breakthrough for any enterprise. As a novelty of the research, we accept the fact that the innovative development of the enterprise is based primarily on the formation of projects that can carry out a technological change of production or improve its energy efficiency. The article considers the energy efficiency of production as a discrete value that can create additional economic benefits without forming a separate technological transition. The paper presents a mathematical model for the development of enterprise innovations and their stratification based on the equilibrium approach and forecasting the growth of profits. Practical application of the obtained results is possible primarily in the implementation of the program of compliance of modern enterprises to the world energy efficiency standards. The article discusses the main vectors of innovation in the transition period of economic development and forms the basis for the formation of a harmoniously developed industry. The economic model of development is designed.



초록


    1. INTRODUCTION

    The achievement of the projected performance indicators and the implementation of the mission of the enterprise, the realization of its strategic plans are only possible with the detailed execution of business plans (Semenyutina et al., 2018). It is the level of planning that determines the implementation of innovations and, consequently, the achievement of results, at each workplace, on the sites, in workshops and in management units (Chandran Govindaraju, 2016). A study of aspects of energy saving in the innovative development of industrial enterprise and its divisions in business planning must be pursued in the process of examining these types of routine work, focusing on the energy conservation measures that can be reflected in the respective plans in parallel with the actions of innovative character, which will necessitate the translation of the economy on energy efficient path of the industry development, improve the investment climate for attracting business, and will contribute to the competitiveness of domestic production (Sapre, 2017;Abramov et al., 2018a;Abramov et al., 2018b).

    Industrial production is a complex dynamic system that involves many conflicting factors (Kypreos et al., 2003). From the mathematical perspective, a set of problems, which is used to model the influence of the energy factor on the result of economic activity of industrial enterprises can be represented as a multi-criteria optimization problem (Bardsley, 2008). A multi-criteria problem is a model for making an optimal decision on several criteria. These criteria may reflect assessments of the various qualities of the object or process on which a decision is made (Antunes et al., 2002;Dobrowolski et al., 2017).

    In the classical formulation of the problem of mathematical programming, one objective function is assumed, which is quantified. In real economic systems, the role of the criterion of optimality (efficiency) expects several dozens of indicators (Shulenbaeva, 2013). For example, a maximum net income from the sale of production or high profitability, low production costs or low-cost energy resources (Brears, 2018). Also, it is desirable to apply several criteria at the same time, and they may be incompatible (Shtal et al., 2018). For example, the requirement to achieve maximum production efficiency at minimum resource costs from the perspective of mathematical formulation of the problem is incorrect (Allan et al, 2009). Minimum resource costs are zero costs that occur in the complete absence of any production process. Similarly, maximum efficiency can be achieved only if certain volumes (certainly not zero) of resources are used (Seitzhanov et al., 2018). Therefore, it is correct to set tasks of this type: to achieve maximum efficiency at a given cost or to achieve a given effect at a minimum cost (Ryszkowski, 1975). There is no universal criterion of economic efficiency (Walz and Schleich, 2009).

    2. LITERATURE REVIEW

    One usually considers multi-criteria optimization and compromise plans. There are several methods to obtain the trade-offs, among which special attention should be paid to the methods by I. Saski, H. Huttler, methods of successive concessions and relative indicator. To find a compromise plan based on two equal criteria, one can use the method by Shanorov. This method allows us to find a compromise solution in which the deviations of each criterion from the optimal value are equal and minimal (Cavaliere, 2019). When solving problems of this class must satisfy the following conditions (Semenutina et al., 2018):

    • - justification of a set of criteria for a given task;

    • - quantitative assessment of the relative benefits criteria or the construction of a scale of preferences;

    • - determination of the conditions of possible compromise (choice of compromise scenarios) and justification of the method for finding a compromise option.

    The set of possible criteria is determined by the characteristic properties of the economic process and justified based on logical analysis (Pohlmann, 2018). After determining the required set of criteria and their relative advantage, one can proceed to the choice of a compromise option (Qi et al., 2016).

    The condition of compromise can be formulated in different ways:

    • - minimization of relative deviations from optimal values over the entire set of criteria;

    • - fixing one of the criteria at a given level and further optimization by the following criteria.

    In accordance with the conditions of the com-promise formulation, the methods for finding solutions to multi-criteria problems have been developed (Vinod Kumar and Dahiya, 2017). We apply these methods of finding solutions to multi-criteria problems to substantiate the factors of influence on the decision-making process regarding the optimal strategy of innovative development of industrial enterprises based on energy saving (Tsuchiya, 2001). In our case, industrial enterprises must find an optimal solution for an energy-saving innovative development strategy in which the value of the target functions is acceptable (Tereshkin, 2018). Based on this decision, it is necessary to analyze the obtained result and determine the feasibility of implementing various directions of in-novative development of industrial enterprises based on energy saving (Kar et al., 2015). At the same time, it is necessary to consider the impact factors of the macro environment, which can be classified as follows: political, regulatory, economic, social, energy and technological (Stroev et al., 1999). Only in this way it is possible to fully assess the possibility of efficient use of energy resources in industrial enterprises and to make the right decisions.

    3. MATERIALS AND METHODS

    The tasks of energy saving at industrial enter-prises should be solved on the basis of activation of innovation by using the resource-saving technologies and the actions providing the decrease in prime cost of production, and, as a consequence, the increase in its competitiveness. In this context, it is important to distinguish the innovations by the categories of targeted activities. We consider the main ones (Table 1).

    The first category of innovation can be attributed to the local level activities with relatively low costs, implementation time, and minimal risks. These include modernization and replacement of individual units or groups of equipment within the existing technology, automation of management, control, and accounting processes (Akhmetshin, 2017). They can be called narrow or local modernization. As a result of such measures, production costs and resource costs are reduced. The second category is the measures related to more radical changes in existing production. Specifically, it can be the replacement or reconstruction of shops, divisions within the operating enterprise, the restoration of the whole technological complexes, expansion of production at the increase in volumes of production. Such changes are long-term and require significant financial resources. The third category refers to radical technological innovations, structural changes in production, usually across the enterprise or even at the industry level. It is clear that the resource provision, duration of works, level of guarantees and results will be much more serious and longer in comparison with the first two categories.

    The development of business plans, considering the consequences of resource savings for each category of innovation introduced in the workplace, is necessary and important. The effects of savings, particularly energy savings that should be included in the business plan categories of innovation, must be submitted to the potential investors and the partners of the enterprise with the necessary information regarding the innovation activity of the enterprise. The participation of enterprises in the innovative programs is not something exceptional, and therefore it is necessary to consider such activities as objectively justified, necessary both from the perspective of the marketing factor and competition, and participation in energy-saving activities of the enterprise team, community, territory, and state. It is important to form a positive attitude to energy saving and the use of resource-saving technologies in the minds of society, industry leaders, and businessmen.

    We propose to use the mathematical apparatus of quantitative methods to build a business plan for the implementation of innovations of the first category, namely, we will set the goal of saving production resources by reducing their use. Let us call savings for a period of under-utilization. Let us present function y = f(x) of the admissible variants of production plans and their efficiency (Figure 1).

    Obviously, there are three points for a given function x 1 , x 2 , x 3 , in which it reaches its maximum value. The optimal plan will be the plan with the highest level of efficiency, that is, x1. However, a minor change Δx1 of the conditions of plan implementation x1, which occurs as a result of saving the resource base, leads to the formation of a valid plan x 1 * . At the same time its effectiveness y 1 * is largely below the optimum ( y 1 * < y 1 ) . Plan x2, with the most stable character, corresponds to the level of efficiency y2, however y2<y1. At the same time there is a variant of the plan x3 with the efficiency y3, which is very different from y1 and simultaneously y3<y2. However, this business plan is resistant to possible changes. So, it is the most elastic. The elasticity of the production schedule is its resistance to the deformation without significant loss of the potential for the implementation of the goal, and the degree of achievement of the planned indicators, considering the changes in the initial conditions.

    4. RESULTS AND DISCUSSION

    4.1 The Mechanism for the Formation of an Optimal Business Plan for Enterprises in the Energy Sector

    The mechanism for the formation of the optimal production schedule is known. Then the relationship between under-production of the i product and under-use (economy) of the j type of resource can be represented as follows:

    ( Δ A i A i ; Δ B j B j ) = 0
    (1)

    where

    • i : index of product type,

    • i I ; I: set of product types;

    • j : index of resource type,

    • j J ; J: set of resource types;

    • Ai : production schedule i-product type;

    • ΔAi : volume of under-production of production schedule of i-product type;

    • Bj : stock volume of j-resource type;

    • ΔBj : volume of subsoil use (savings) of j-resource type.

    Relationship between relative under-production of i-product type ( Δ A i A i ) and relative savings of j-resource type ( Δ B j B j ) is a characteristic of elasticity (stiffness) of production schedule. That is, for each value of the delineated relationship there is a relation ε i j = Δ B j B j : Δ A i A i , which characterizes elasticity, and the reverse to it q i j = 1 ε i j – the rigidity of the schedule. Considering the entered designations, the scenario of the production schedule in the form of the following task is made. It is necessary to find such a solution { x i k l 0 , i I , k K , l L k } , which will provide maximum function (profits):

    Z = k K i I l L k C i k l x i k l i l C i Δ A i m a x
    (2)

    when conditions are met:

    • 1) on production considering the market de-mand

    k K l L k a i k l x i k l A i Δ A i , i I
    (3)

    • 2) for the resources of the production schedule

    k K i I l L k b i k l j x i k l B j Δ B j , j J
    (4)

    • 3) on the boundary limits of maneuverability of the production schedule

    a i k l x i k l β i k l , i I , k K , l L k
    (5)

    where

    • k : index of structural division of the enter-prise

    • k K ; K : set of production units of the enter-prise;

    • l : index of the technological mode

    • l L k ; L k : set of technological methods of production with available k structural subdivision;

    • aikl: i-product type output from the units of intensity of l technological method of production for k subdivision of the enterprise;

    • Ai : the value of market demand (target) for the i type of product;

    • xikl: unknown value reflecting the intensity of using the l technological method of production of the i-product type in k subdivision;

    • ΔAi: volume of under-production planned target (short supply to market) of i-product type;

    • biklj: the costs of j-resource type per unit of intensity of using the l technological method of production of i-product type in k subdivision;

    • Cikl : quantifying the effectiveness of a unit of intensity of using l technological method for manufacture of i-product type in k subdivision;

    • Ci : the amount of the penalty for failure to issue a unit of i-product type;

    • Bj : the total planned volume of supply of j-resource type;

    • ΔBj : the amount of under-utilization of j-resource type;

    • αikl, βikl : accordingly the lower and upper limits of maneuverability intensity of using l technological method for manufacture of the i product type in k subdivision.

    Under the influence of uncontrolled and random factors on the production process, the parameters undergo significant changes: C i k l , a i k l , x i k l , b i k l j and Δ B j . Using the simulation procedure of the conditions of the economic-mathematical model (Equations 2, 3, 4, 5), a set of opti-mal solutions is obtained considering different levels of resource use. After that, we carry out the procedure of economic and mathematical analysis of the received plans and, as a result, we have a profitable production schedule. The elasticity function of a profitable production schedule can be defined in the following way:

    Δ A i A i = ( Δ B j B j ) , i I , j J
    (6)

    If it is not possible to set the rate of elasticity in the production schedule, the following method can be used to build elastic production schedules. Let us get the optimal production schedule according to which it is proposed to produce i type of products in the amount of A i О P . For this purpose, Bij units of j-resource type are used. The conditions of production will be changed, that is, reduce the use of j-resource type for the output of i-product type in the amount of Δ B i j . Through the economy of j-resource type the level of production will decrease, i.e. the following relationship will take place:

    A i * = ( Δ B i j ) , i I , j J
    (7)

    where A i * : the level of the i-product type manufacture at saving (underutilization) of j-resource type in the amount of Δ B i j .

    Figure 2 presents the relationship between the i-product type volume input at the underutilization of j-resource.

    If to reduce the j-product type production schedule from the optimal level to a profitable ( A i p r f ) , then at the underutilization of j resource type by the volume Δ B i j we’ll obtain the following dependence:

    A i p r f = 1 ( Δ B i j ) , i I , j J
    (8)

    The analysis of the diagram in Figure 2 shows us that at the section of j-resource type saving ( 0 , Δ B i j к р ) with an optimal plan, the manufacturer receives more products than with a profitable one, i.e. with Δ B i j ( 0 , Δ B i j к р ) there is А i О P > A i p r f . However, at the segment ( Δ B i j к р , Δ B i j g р ) one may observe the opposite picture. The closer the solution of the problem is to the optimal one under some conditions, the more it can deviate from it in others. There is a need to perform the process of optimization of production schedule systems, considering possible resource savings. Each level of saving of j resource type corresponds to a certain volume of i output, which can be specified as a sequence { A i j τ , τ T } , where τ – index of investment volumes; T – set of options for the volume of investments. Then, for each A i j τ one may build the following econometrical model:

    A i τ = τ ( Δ B i j ) , i I , j J , τ T
    (9)

    Quantitative expressions of this function (Equation 9) can be found by finding the solutions to the optimization problem of calculating the production schedule at different values ΔBij. The basis of the modeling algorithm of the simulation process is the model (Equations 2, 3, 4, 5). Using the mathematical apparatus of econometric methods and simulation results, dependences of the form (Equation 9) are obtained. Next, the value of the expected (mathematical expectation) volume of i output is found for each set A i τ in case of underutilization of j resource type, i.e.:

    M ( A i τ ) = 0 Δ B i j г р τ ( Δ B i j ) d Δ B i j , i I , j J , τ T
    (10)

    Next, we find as follows:

    A i p r f = m a x τ { M ( A i τ ) } , i I , τ T
    (11)

    where A i p r f   : a profitable variant of the production schedule release-product type with a flexible business plan.

    Thus, we can start innovative activities without significant investment and loss of time. The practical implementation of the considered technique was preceded by the simulation of the production schedule of industrial production, calculated based on the mathematical model (Equations 2, 3, 4, 5). The input parameters were the volume of investment (3650, 3550, 3450 and 3350 USD thousand) in addition to the optimal value of 3700 USD thousand invested in the production process and the level of resource savings (0%, 1%,..., 20 %). As a result of simulation, a set of optimal variants of production schedule was obtained (Table 2).

    Analysis of the simulation results (Table 2) shows that for each level of resource savings there is a profitable amount of investment.

    Econometric analysis of the simulation results makes it possible to conclude that between the volume of production and the level of resource savings for a certain variant of the investment volume, there is the following relationship:

    τ ( Δ B ) = b 0 τ + b 1 τ Δ B
    (12)

    where

    • ΔB : level of saving (underutilization) of the resource (%);

    • τ : index option size of investments,

    • τ = 1 , 5 ¯ ;   τ ( Δ B ) : the volume of output in the case of the investment volume

    • τ ; b 0 τ , b 1 τ : econometric model parameters for investment option τ.

    With the help of the STADIA software product for the corresponding investment sizes the following econometric models are obtained:

    37 00  USD thousand : φ 1 ( Δ B ) = 17 , 143 0 , 149 Δ B , R = 0 , 9932 ;
    (13)

    365 0  USD thousand : φ 2 ( Δ B ) = 17 , 501 0 , 084 Δ B , R = 0 , 9856 ;
    (14)

    355 0  USD thousand : φ 3 ( Δ B ) = 17 , 481 0 , 077 Δ B , R = 0 , 9861 ;
    (15)

    345 0  USD thousand : φ 4 ( Δ B ) = 17 , 082 0 , 074 Δ B , R = 0 , 9867 ;
    (16)

    335 0  USD thousand : φ 5 ( Δ B ) = 116 , 478 0 , 059 Δ B , R = 0 , 9774 ;
    (17)

    According to the proposed methods of building business plans of production determine the expectation function of output τ ( Δ B ) of random variable ΔB with distribution density fB), which for the case of the normal distribution law has the following form:

    f ( Δ B ) = 1 σ 2 π e ( Δ B a ) 2 2 σ 2
    (18)

    where

    • a : expectation of resource saving level;

    • σ : its standard deviation.

    The mathematical expectation of the output function:

    M [ τ ( Δ B ) ] = + τ ( Δ B ) f ( Δ B ) d Δ B
    (19)

    Substituting in (Equation 8) the real limits of in-tegration and replacing ( Δ B ) for specific mathematical models, we obtain as follows:

    M [ τ ( Δ B ) ] = 0 20 ( b 0 τ + b 1 τ Δ B ) 1 σ 2 π e ( Δ B a ) 2 2 σ 2 d Δ B = b 0 τ σ 2 π 0 20 e ( Δ B a ) 2 2 σ 2 d Δ B + b 1 τ σ 2 π 0 20 Δ B e ( Δ B a ) 2 2 σ 2 d Δ B = b 0 τ [ Φ ( 20 a σ ) + Φ ( a σ ) ] + b 1 τ σ 2 π 0 20 Δ B e ( Δ B a ) 2 2 σ 2 d Δ B
    (20)

    where Φ ( y ) – Laplace integral function of y parameter.

    To find the integral 1 2 2 π 0 20 Δ B e ( Δ B a ) 2 2 σ 2 d Δ B assume that x = Δ B a σ and accept x for the new variable. Thus, we have Δ B = x σ + a , moreover d Δ B = σ d x . After replacing the variables, we get as follows:

    1 σ 2 π 0 20 Δ B e ( Δ B a ) 2 2 σ 2 d Δ B = σ σ 2 π a / σ ( 20 a ) / σ ( x σ + a ) e x 2 2 d x = σ 2 π a / σ ( 20 a ) / σ x σ e x 2 2 d x + a 2 π a / σ ( 20 a ) / σ e x 2 2 d x = σ 2 π a / σ ( 20 a ) / σ e x 2 2 d ( x 2 2 ) + a [ Ф ( 20 a σ ) + Ф ( a σ ) ] = σ 2 π [ e a 2 2 σ 2 e ( 20 σ ) 2 2 σ 2 ] + a [ Ф ( 20 a σ ) + Ф ( a σ ) ]
    (21)

    The final formula for finding the desired expec-tation of output is as follows:

    M τ = M [ ( Δ B ) ] = b 0 τ [ Φ ( 20 a σ ) + Φ ( a σ ) ] + b 1 τ { a [ Φ ( 20 a σ ) + Φ ( a σ ) ] + σ 2 π ( e a 2 2 σ 2 e ( 20 a ) 2 2 σ 2 ) }
    (22)

    The calculated value of the expectation for each investment option is the following {15,44; 15,47; 15,28; 15,04; 14,69. The maximum value is as follows:

    M E L = m a x { M 1 ; M 2 ; M 3 ; M 4 ; M 5 } = m a x { { 15 , 44 ; 15 , 47 ; 15 , 28 ; 15 , 04 ; 14 , 69 } } USD million = 15 , 47
    (23)

    This means that by investing 3650 USD thou-sand, we get a profitable elastic business plan and save resources at the same time. The proposed approach to identify and plan the consequences of innovative devel-opment of industrial enterprises based on energy saving will allow considering the factor of saving resources for each category of innovations introduced in production, as well as taking measures to improve energy efficiency, and creating a favorable investment climate for attract-ing business. Given the above advantages of multi-criteria optimization, it can be concluded that the ra-tionale for the factors influencing the decision-making process on the optimal strategy of innovative develop-ment of industrial enterprises based on energy saving require further research. The structural and logical scheme of the mathematical model of decision-making on the optimal strategy of innovative development of industrial enterprises based on energy saving is shown in Figure 3. The decision-making process consists of two stages of modeling.

    For example, the information about the manu-facture of products by the enterprise Vector, LLP will be used. The company will be developed the appropriate economic and mathematical models, taking into account the norms of the cost of resources (natural gas, electricity, coal, fuels and lubricants) for the production of natural stone, sand, fine stone, and facing stone. The data for the construction of economic and mathematical models of the tasks is shown in Table 3.

    4.2 Formation of Alternatives for Implementing the Innovation Development Strategy of Industrial Enterprises

    Let us consider the formulation of the problem for optimizing the production program of the enterprise, the purpose of which is to maximize profits in the case of reducing the costs of available resources. It is necessary to calculate the compromise version of the production program of the enterprise considering two criteria:

    • 1) getting the maximum profit;

    • 2) minimum energy costs for production.

    To organize the production of four types of products, Vector, LLP uses four types of energy resources with the set volumes and norms of their use per unit of output. Known the market demand for products, the profit from the sale of a unit of production and energy intensity per unit of output.

    Let us introduce the following values: i – index of the resource type, i = 1 , n ¯ ; j – index of the product type j = 1 , m ¯ ; k – index of the optimality criteria, k = 1 , K ¯ ; a i j – utilization rate of i type of resource per unit output for j type; Ai – volume of the available i resources; Bj – value of contractual deliveries of j product; cjK – indicator of efficiency criterion; xj – unknown value, which means the volume of j type output; M1 – many types of products for which the lower and upper limit of market demand is set; M2 – many types of products for which there are fixed contractual deliveries; α j , β j – accordingly, the lower and upper limits of market demand for products of j type. Provided the entered notation, the mathematical model will take the form. To find the solution { x j 0 , j = 1 , m ¯ } , which will provide

    Z k = j = 1 m C k j x j m a x ( m i n ) , k = 1 , K ¯
    (24)

    under specified conditions:

    • 1) constraints on the use of available types of resources

    Z k = j = 1 m α k j x i A , i = 1 , n ; ¯
    (25)

    • 2) constraints on the implementation of the terms of delivery of products

    x j = B j , j M 1
    (26)

    • 3) constraints on production considering market demand

    α j x j β j , j M 2
    (27)

    Vector of profit from the sale of a production unit {4; 4,5; 4,7; 4,8} USD. Energy intensity vector per unit of production {4,197; 0,9733; 0,484; 2} USD.

    Considering the market demand, the imposed constraints on the minimum volume of all types of products are as follows x 1 15 ; x 2 20 ; x 3 22 ; x 4 18 ; x 1 40 ; x 2 50 ; x 3 40 ; x 4 25 .

    At the first stage the construction of a compro-mise plan is carried out.

    Mathematical model of problem No. 1.

    The objective function of the problem is to find such a solution { x j 0 , j = 1 , 4 ¯ } , which will provide the company with maximum profit (Z1):

    Z 1 = 0 , 4 x 1 + 0 , 45 x 2 + 0 , 47 x 3 + 0 , 48 x 4 m a x
    (28)

    • 1. Consideration of constraints on the volume of available types of energy resources:

      • - natural gas volume limit

        250 x 1 + 252 x 2 + 235 x 3 + 256 x 4 40000 ;

      • - limit on the volume of electric energy

        220 x 1 + 222 , 2 x 2 + 223 x 3 + 224 , 4 x 4 40000 ;

      • - limit on coal reserves

        3 , 1 x 1 + 3 , 15 x 2 + 3 , 19 x 3 + 3 , 22 x 4 750 ;

      • - limit on volumes of fuels and lubricants

        3 x 1 + 3 , 2 x 2 + 3 , 1 x 3 + 3 , 4 x 4 500 ;

    2. Consideration of the market demand con-straints

    x 1 15 ; x 2 20 ; x 2 22 ; x 4 18 ; x 1 40 ; x 2 50 ; x 3 40 ; x 4 25

    The solution of the problem was obtained using the Solver EXCEL utility.

    Z 2 = 69 , 3 ; x 1 = 15 ; x 2 = 20 ; x 3 = 22 ; x 4 = 18
    (29)

    In the production of 40 tons of natural stone, 50 tons of sand, 40 tons of fine stone and 25 tons of cladding stone, the company can get a maximum profit of 69.3 USD thousand.

    Mathematical model of problem No. 2.

    The objective function of the problem is to find such a solution { x j 0 , j = 1 , 4 ¯ } , which will provide the company with minimum energy costs for production (Z2):

    Z 2 = 4 , 197 x 1 + 0 , 9733 x 2 + 0 , 484 x 3 + 2 x 4 m i n
    (30)

    • 1. Consideration of constraints on the volume of available types of energy resources

      • - natural gas volume limit

        250 x 1 + 252 x 2 + 253 x 3 + 256 x 4 40000 ;

      • - limit on the volume of electric energy

        220 x 1 + 222 , 2 x 2 + 223 x 3 + 224 , 4 x 4 40000 ;

      • - limit on coal reserves

        3 , 1 x 1 + 3 , 15 x 2 + 3 , 19 x 3 + 3 , 22 x 4 750 ;

      • - limit on volumes of fuels and lubricants

        3 x 1 + 3 , 2 x 2 + 3 , 1 x 3 + 3 , 4 x 4 500

    • 2. Consideration of the market demand con-straints:

      x 1 15 ; x 2 20 ; x 3 22 ; x 4 18 ; x 1 40 ; x 2 50 ; x 3 40 ; x 4 25

    The solution of the problem was obtained using the Solver EXCEL utility.

    Z 2 = 129 , 069   x 1 = 15 ; x 2 = 20 ; x 3 = 22 ; x 4 = 18
    (31)

    In the production of 40 tons of natural stone, 50 tons of sand, 40 tons of fine stone and 25 tons of cladding stone, the company can get a maximum profit of 129,069 USD thousand.

    Mathematical model of problem No. 3.

    Z 1 ( x ) = 0 , 4 x 1 + 0 , 45 x 2 + 0 , 47 x 3 + 0 , 48 x 4 ( m a x )
    (32)

    Z 2 ( x ) = 4 , 197 x 1 + 0 , 9733 x 2 + 0 , 484 x 3 + 2 x 4 ( m i n )
    (33)

    As a result of solving the problems (Equations 28, 30) we got: Z 1 * = 69 , 3 USD thousand; Z 2 * = 129 , 069 USD thousand. The mathematical model of the third problem will consist the main constraints of the problems (Equations 28, 30) and additional constraints. Constraints towards the profit are as follows:

    | Z 1 * Z 1 ( x ) Z 1 * | Z { Z k ( x ) + Z k * Z Z k * Z k ( x ) Z k * Z Z k *
    (34)

    Considering value Z 1 * = 69 , 3 and the inequali-ty system (Equation 34), two additional constraints are obtained:

    Z 1 + 69 , 3 × Z 69 , 3
    (35)

    Z 1 69 , 3 × Z 69 , 3
    (36)

    Provided that problem No. 2 was investigated at a minimum, additional constraints on the volume of available types of energy resources Z 2 * = 129 , 069 are as follows:

    Z 2 + 129 , 069 × Z 129 , 069
    (37)

    Z 2 129 , 069 × Z 129 , 069
    (38)

    Z m i n
    (39)

    Z 1 + 69 , 3 × Z 69 , 3
    (40)

    Z 1 69 , 3 × Z 69 , 3
    (41)

    Z 2 + 129 , 069 × Z 129 , 069
    (42)

    Z 2 129 , 069 × Z 129 , 069
    (43)

    0 , 4 x 1 + 0 , 45 x 2 + 0 , 47 x 3 + 0 , 48 x 4 Z 1 = 0
    (44)

    4 , 197 x 1 + 0 , 9733 x 2 + 0 , 484 x 3 + 2 x 4 Z 2 = 0
    (45)

    250 x 1 + 252 x 2 + 253 x 3 + 256 x 4 40000
    (46)

    220 x 1 + 222 , 2 x 2 + 223 x 3 + 224 , 4 x 4 40000
    (47)

    3 , 1 x 1 + 3 , 15 x 2 + 3 , 19 x 1 + 3 , 22 x 4 750
    (48)

    2 x 1 + 3 , 2 x 2 + 3 , 1 x 3 + 3 , 4 x 4 500
    (49)

    x 1 15 ; x 2 20 ; x 3 22 ; x 4 18 ;
    (50)

    x 1 40 ; x 2 50 ; x 3 40 ; x 4 25
    (51)

    Obtained results for the solution of problem No. 3 are reflected in Table 4. By applying the calculations for the implementation of the optimal innovation strategy of an industrial enterprise based on energy saving, it is important to note some recommendations for its implementation:

    • 1. Built compromise version of industrial pro-duction makes it possible to decide on reducing the use of natural gas thanks to the following: the introduction of new energy-saving technologies used to reduce the energy intensity of production and to increase the competitiveness of products; engineering, scientific, and implemented measures.

    • 2. In modern conditions of the world economy development, the industrial enterprises should consider energy efficiency as an important com-ponent of innovative development of the industry in optimum implementation of innovative strategy of the industrial enterprise based on energy saving.

    • 3. The use of coal is appropriate, where the scheme of coal cooking and its conveying are partially preserved and in the area with local fuel resources.

    • 4. Increasing the volume and scope of renewable energy, which will partially replace natural gas.

    The rise in the price of natural gas and the task of reducing its consumption has put on the agenda topical issues, which is the use of renewable energy. The choice of the optimal management solution for the transfer of industrial production to renewable energy resources is proposed based on the method of hierarchy analysis developed by the famous American mathematician Thomas Saati (2011). This method is used to solve many practical problems at different levels of planning. The method has become widespread in the last decade. According to this method, the choice of priority decisions is carried out by means of paired comparisons, which make it possible to compare the relative importance of any quantified and uncertain factors. To represent the results of evaluations in quantitative terms, T. Saati introduced a scale of paired comparisons. According to this scale, we will not be in-terested in the absence of physical or objective units of measurement. The main advantage of this method is that it is limitless and there is no problem in bringing to the same units of measurement. The validity of this scale is proved theoretically and practically when compared with many other known data. Experience has shown that when conducting paired comparisons, the following questions are mainly raised: Which element is more important? What’s the most likely? Which one is the most attractive? The hierarchy analysis method includes the procedures for synthesizing many statements, prioritizing criteria, and finding alternative solutions. What is important is that the values thus obtained are estimates in the relationship scale but correspond to so-called hard estimates. The solution of the problem is the process of gradual formation of priorities. At the first stage, one identifies the most important elements of the problem, at the second – the best way to verify the allegations and assess the elements. The whole process is subject to review and rethinking until it is established that it has covered all the important characteristics of the solution to the problem. So, the first step of the hierarchy analysis method is to decompose and present the problem in a hierarchical form. We consider dominant hierarchies that are built from the top (goals from a management perspective) through intermediate levels (criteria on which the next levels depend) to the lowest level, which is usually a list of alternatives. A hierarchy is considered complete if each member of a given level functions as a criterion for all the members of the level below it. That is, the hierarchy can be divided into sub-hierarchies that share the highest element. The law of hierarchical continuity requires that the elements of the lowest level be pairwise equalized with respect to the elements of the next level, and so on to the top of the hierarchy. As an indicator of the elements’ consistency degree of the matrix D in the framework of the hierarchy analysis method, the consistency index (CI) is used

    C I = λ m a x m m 1
    (52)

    which characterizes the deviation of a value λ m a x (maximum weight indicator) from value m, which corre-sponds to the ideal variant.

    The acceptability assessment of the consistency degree for the elements of the matrix is carried out by calculating the value of the consistency ratio (CR)

    C R = C I C I S
    (53)

    where CIS is average consistency index.

    Exceeding the threshold value of CIS is a reason to revise the considerations adopted in the process of comparing the elements. The method for analysis of hierarchies is applied to determine the strategy of transition to an alternative form of energy. Figure 4 shows the hierarchical structure of the task.

    To implement the strategy of innovative devel-opment of industrial enterprises based on energy saving, we are guided by the following criteria: cost, availability, performance and reliability of a renewable energy sources. Renewable energy sources for the enterprise can be as follows: wind energy, solar energy, biofuel, energy of secondary energy resources. The dimension of the matrix D = 4 × 4. Random consistency or threshold CIS = 0, 9. To construct the matrices, the scale of relative advantages by T. Saati is used. The matrix of pairwise comparisons for such criteria as “cost”, “performance”, “availability”, and “reliability” is presented in Table 5. Consistency index λ m a x = 4 , 1213 ; C I = 0 , 0404 ; C R = 0 , 0449 .

    Let us calculate the matrix of pairwise comparisons for alternatives with the “cost” criterion (Table 6). Index λ m a x = 4 , 0356 ; C I = 0 , 0119 ; C R = 0 , 0132 .

    Let us calculate the matrix of pairwise comparisons for alternatives with the “availability” criterion (Table 7). Consistency index λ m a x = 4 , 0675 ; C I = 0 , 0225 ; C R = 0 , 025 .

    Let us calculate the matrix of pairwise comparisons for alternatives with the “performance” criterion (Table 8). Consistency index λ m a x = 4 , 0694 ; C I = 0 , 0232 ; C R = 0 , 0257 .

    Let us calculate the matrix of pairwise comparisons for alternatives with the “reliability” criterion (Table 9). Consistency index λ m a x = 4 , 0836 ; C I = 0 , 0289 ; C R = 0 , 0310 .

    In our case, the maximum, considering all the criteria, is the assessment for the first alternative – the use of secondary energy resources, which has a maximum priority value. On the other hand, this task gives us the opportunity to allocate available resources among the alternatives according to their priorities. The next priority alternative is the use of biofuels, then – the use of solar energy and the fourth position is taken by wind energy.

    Resumptive priority assessments at the choice of the alternatives are shown in Table 10.

    5. CONCLUSION

    Based on the calculations on the implementation of the innovative strategy of the industrial enterprise on the basis of energy saving, it is important to note some recommendations for its implementation:

    As renewable fuels, which will partially replace natural gas, can serve as waste (secondary energy re-sources). While processing, a large amount of organic waste is accumulated. All these industrial wastes can be processed into biogas.

    Biogas production from the production of waste will reduce the consumption of natural gas and at the same time significantly improve the environmental situation. The organization of such production provides not only the joint use of auxiliary equipment and services, but also has several organizational and economic advantages.

    Solar and wind energy can be used in industrial plants to produce hot water for technological, economic and household needs, and to produce electric energy (with the introduction of “green” tariff for electricity generation, the development of industrial production of electricity through solar panels has become financially sound). Large power consumption of electric energy and significant energy consumption of outdated equipment will not allow completely switching to the autonomous power supply with this type of energy, since solar installations and wind turbines are low-power and operate with low efficiency and require special natural conditions, large areas and large capital expenditures.

    Figure

    IEMS-19-1-120_F1.gif

    Function of efficiency.

    IEMS-19-1-120_F2.gif

    Diagram of the relationship between output and the level of resource use.

    IEMS-19-1-120_F3.gif

    Structural and logical scheme of mathematical model of decision-making concerning optimum strategy for innovative development of the industrial enterprises based on energy saving.

    IEMS-19-1-120_F4.gif

    Hierarchical structure of the decision-making task.

    Table

    Characteristics of Innovative Projects

    Set of optimal variants of production schedule

    Resource intensive standards to manufacture products by vector, LLP

    Variants of the production program considering optimality criteria

    Pairwise Comparison Matrix for Criteria and Its Numerical Estimates

    Matrix of pairwise comparisons for alternatives and their numerical estimates by the “cost” criterion

    Matrix of pairwise comparisons for alternatives and their numerical estimates by the “availability” criterion

    Matrix of pairwise comparisons for alternatives and their numerical estimates by the “performance” criterion

    Matrix of pairwise comparisons for alternatives and their numerical estimates by the “reliability” criterion

    Resumptive priority assessments at the choice of the alternatives

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