On Analytical Approach to Estimate Proceeds of Industrial Enterprises
Subject Areas : International Journal of Mathematical Modelling & ComputationsKeywords: Optimization, analytical approach for modelling, prognosis of proceeds of industrial enterprises, maximization of volume of manufactured products,
Abstract :
In this paper we presents a model to prognosis of proceeds of industrial enterprises. The model gives a possibility to analyze proceeds of enterprises with account of changing of quantity of manufactured products. The model gives a possibility to analyze proceeds of enterprises with account of changing of quantity of manufactured products. At the same time the model gives a possibility to take into account various expenses (raw materials, transportation costs, ...). An analytical approach for analysis of the influence of various parameters on the considered proceeds has been introduced.
1
On analytical approach to estimate proceeds of industrial enterprises
Abstract
In this paper we presents a model to prognosis of proceeds of industrial enterprises. The model gives a possibility to analyze proceeds of enterprises with account of changing of quantity of manufactured products. The model gives a possibility to analyze proceeds of enterprises with account of changing of quantity of manufactured products. At the same time the model gives a possibility to take into account various expenses (raw materials, transportation costs, ...). An analytical approach for analysis of the influence of various parameters on the considered proceeds has been introduced.
Keywords: prognosis of proceeds of industrial enterprises; maximization of volume of manufactured products.
Introduction
To optimize functioning of industrial enterprises they should be accounted following factors: increasing of profits and decreasing of overhead costs [1-4]. In this situation, it is necessary to develop effective methods of innovative development and changing the market situation leading to price changes depending on the volume of products on the market [5-8]. In this paper we introduce a model for prognosis of proceeds of enterprises with account of changing of volume of production. We also introduce an analytical approach to analyze of dependence of revenue on various factors.
Method of solution and discussion of results of analysis
In this paper we used the following expression as the model of proceeds
Q =V×P- V×R-V×T-V×S. (1)
Here V is the quantity of manufactured product; P is the price of a unit of the product; R is the price of raw materials, consumed per unit of production; T is the transportation costs per unit of product; S is the salary paid to employees per unit of production. The price of products may vary depending on its quantity. In this paper, we consider the simplest (linear) model of such a dependence P (V) =A-B×V, where A and B are the parameters of the approximating function, taking into account the actual price change [9]. Taking this approximation into account, relation (1) takes the following form
Q =V×(A-B×V)- V×R-V×T-V×S. (1a)
Proceeds Q depends on parameters R, T, S, A, B monotonically. These dependences of proceeds Q on the volume of product V is non-monotonous. Extreme value of proceeds could be defined framework standard procedure, i.e. framework the condition of equality of corresponding partial derivative to zero: ¶ Q/¶ V = 0 [10]. Accounting of relation (1a) into equation ¶ Q/¶ V = 0 could be written as
¶ Q/¶ V =A-2B×V-R-T-S=0. (2)
Solution of the above equation gives a possibility to obtain the extreme value of the volume of manufacturing product Vextr
Vextr=(A -R-T-S)/2B. (3)
Dependences of proceeds of industrial enterprise and extreme values of the product are shown in the figures below. Figure 1 shows typical dependences of the volume of proceeds Q on the volume of products V for different values of parameters A and B. Increasing of number of curves corresponds to increasing of value of parameter A (Fig. 1a) and B (Fig. 1b). The dependences of the volume of proceeds on the volume of output for various values of the parameters R, T, S are similar to those shown in Fig. 1a.
These figures show that the dependences of the amount of proceeds on the volume of product for various values of parameters could be both monotonic and non- monotonic with an explicit extreme (in this case, maximal) value. The extreme value could be determined by relation (3). Figs. 2 show dependences of the volume of proceeds on the parameters R, T, S, A and B. All dependencies are straight lines with different angular coefficients. Depending on the values of the parameters, the predicted profit could be either positive or negative, which corresponds to the loss of the enterprise.
Figs. 3-5 show dependences of the maximum volume of manufactured products on values of considered parameters for different means of other parameters. These dependences obtained are usually as linear. Some of them are hyperbolic.
Fig. 1a. Dependences of proceeds Q on volume of products V for different values of parameters R, T, S, A (all dependencies are qualitatively similar to each other). Increasing of number of curves corresponds to increasing of parameter B
Fig. 1b. Dependences of proceeds Q on volume of products V for different values of parameters R, T, S, B (all dependences are qualitatively similar to each other). Increasing of number of curves corresponds to increasing of parameter A
Fig. 2a. Dependences of proceeds Q on value of parameter A for different values of parameters R, T, S, B (all dependences are qualitatively similar to each other). Increasing of number of curves corresponds to increasing of parameter V
Fig. 2b. Dependence of proceeds Q on value of parameter B for different values of parameters R, T, S, A (all dependencies are qualitatively similar to each other). Increasing of number of curves corresponds to increasing of value of parameter V
Fig. 3a. Dependencies of the maximum volume of manufactured products on the values of parameter A. Increasing of number of curves corresponds to increasing of value of parameter B
Fig. 3b. Dependencies of maximum volume of products on values of parameters A. Increasing of number of curves corresponds to increasing of parameters A
Fig. 4a. Dependences of maximum volume of product on value of parameter B. Increasing of number of curves corresponds to increasing of parameter A
Fig. 4b. Dependencies of maximum volume of product on value of parameter B. Increasing of number of curves corresponds to increasing of parameters R, T, S
Fig. 5a. Dependences of maximum volume of products on values of parameters R, T, S. Increasing of number of curves corresponds to increasing of parameter A
Fig. 5b. Dependences of maximum volume of products on values of parameters R, T, S. Increasing of number of curves corresponds to increasing of parameter B
It should be noted, that an alternative approach to solve main aim of the present paper is analysis [11,12]. The approach based on handling of empirical data. However empirical data are usually discrete data. Framework this paper we introduce an approach to analyze date with smaller step, which gives a possibility to consider approximately continuous empirical data. The approach, which considered in this paper, gives a possibility to analyze empirical data and make prognosis with arbitrarily small step between concrete values of these data.
Conclusion
In this paper we introduce a model for prognosis of proceeds of industrial enterprises. The model gives a possibility to make prognosis of the proceeds with account changing of quantity of manufactured products and various expenses (raw materials, transportation costs, ...). An analytical approach for analyzing the influence of various parameters on the proceeds has been also introduced. Based on the approach we analyzed dependences of proceeds of industrial enterprises on different parameters.
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