THE ECONOMIC MODEL FOR DETERMINING THE OPTIMAL STRUCTURE OF PRODUCTION, PROCESSING AND EXPORT OF AGRICULTURAL PRODUCTS
DOI:10.30825/5.EJPAU.193.2020.23.4

Tatiana Porudeyeva¹, Kateryna Glubochenko², Tetiana Ivanenko^3
1 Mykolaiv State Agricultural Research Station, Institute of Irrigated Agriculture, National Academy of Agrarian Sciences of Ukraine, Mykolaiv, Ukraine
² V.O. Sukhomlynskyi National University of Mykolaiv, Mykolaiv, Ukraine
³ Mykolaiv National Agrarian University, Mykolaiv, Ukraine

ABSTRACT

The paper analyzes the features of agri-food market functioning in Ukraine. Taking into account the importance of the agri-food sector in Ukraine, the authors develop the model for determining the optimal structure of production, processing and export of agricultural products. The purpose of the study was to define the optimal relation of agri-food industries in Ukraine that would provide a balance of production, processing, and export in Odessa, Mykolaiv, and Kherson regions of Ukraine while maintaining the maximum economic productivity of the regional agricultural system. The multi variant model based on the methodology of mathematical modelling in economics was developed to define the optimal structure of production, processing, and export of agricultural products. The model was developed based on the statistical data of Mykolaiv, Odessa, and Kherson regions of Ukraine. Using the model matrix, the authors analyze the statistical information as the input data to forecast the trends for the domestic agri-food market in Ukraine. The authors develop the system of variables and constraints indices that includes the sets of regions; agricultural and processed industries; planted areas in a corresponding region; numbers of cattle in the regions; processing and distribution of agricultural products; production of processed outcomes; agricultural and processed products sales in the domestic market; agricultural and processed products export; general needs in different kinds of resources; additional feed; production capacity; raw materials; general expenses on production and processing of agri-food products; general expenses of labor resources; general cost of final agri-food products in the domestic market; processed products costs in the domestic market; export agri-food products costs. Considering the developed system of 9 structural groups of constrains, the model deals with such coefficients and parameters as planted area, raw materials, production and sales volumes of agri-food products, and export volumes of these products. The paper allows to conclude that optimization of the parameters reflected in the model will allow to increase the productivity and export potential of agri-food industries in Ukraine. Although these industries are influenced by climate and political risks, the model can be used to optimize the relation of important components of Ukrainian agri-food market in order to improve its competitiveness and productivity. Thus, by optimizing the relation of planted area for growing cereals, industrial crops, vegetable crops and melon fields, the raw material base for processing industry and feed, numbers of cattle for regional needs, and the export potential for agricultural and processing industries higher productivity of Ukrainian agri-food industries can be achieved.

Key words: agricultural production; agriculture in Ukraine; agricultural productivity; agri-food industries.

INTRODUCTION

Agriculture is the main economic sector in Ukraine. Standard of living and food depend on the effective functioning of agriculture. Nevertheless, the productivity of Ukrainian agricultural industry is insufficient. At the same time, Ukraine is a leading agricultural exporter to the global agri-food markets, so international collaboration is of utmost importance. International collaboration in agriculture focuses on the growth of effectiveness of the resource usage, the improvement of food provisioning, support and protection of agricultural commodity producers, mutually beneficial sales promotion, and the improvement of standard of living in rural countries. Ukraine is able to get such benefits from international agricultural collaboration by entering new markets, increasing income due to the reinforcement of agricultural products and technology exchange, attracting foreign investment in Ukrainian agriculture, etc. However, the issue of agricultural productivity assessment is still relevant.

The assessment of agricultural productivity is traditionally achieved by the use of multi variant models. In particular, Groot et al. [9] offer a farm design tool, which supports evaluation and design of mixed farming systems. The authors developed a static farm balance model to reveal the correlation between fertilizers use, feed balance, labor balance and economic results on an annual basis. The model employs an algorithm to maximize operating profit and generate sufficient income, optimize allocation of labor resources, improve soil structure, and minimize nitrogen soil loss. The authors conclude that the interactions among farm components need further investigation. By contrast, Dogliotti et al. [8] use a mixed integer linear programming model (MILP) to allocate production activities to a farm with land units differing in soil quality, while maximizing or minimizing socio-economic and environmental objectives, subject to constraints at the farm level. The study suggests that decreasing the area of vegetable crops by introducing long crop rotations with pastures and green manure during the inter-crop periods and integrating beef cattle production into the farm systems can be a better strategy for the agri-food sector. Delmotte et al. [7] also use linear programming, multi agent models, and land-use change models to develop an instrument for assessment of diverse scenarios in agri-food sectors, taking into consideration the sustainability of agricultural systems.

Mathematical programming models have been used to analyze agri-food markets since 1980’s. For instance, Albezov et al. [3] developed the General Regional Agricultural Model (GRAM) to create a universal methodology for planning in agriculture. The model was developed using the “bottom-up” approach, which consists of orienting the model toward technological interdependencies at the level of the agricultural areas in the region, and including a set of variables and parameters that enable the model to be linked with other aspects of the regional economy. The model deals with such elements as a set of crops subject to rotation constraints, types of agricultural animals, types of livestock products, and feed components, three types of market and three types of land ownership, different crop growing and livestock breeding technologies; and different soil qualities and types of fertilizer, according to the contents of the elements. Econometric methods in agriculture planning were also developed in multi-variants models of Kopec and Nietupski [11]. The authors analyzed the characteristics of natural, economic, external and internal conditions in agriculture, the structure of the organization of crop and livestock industries, which is determined by the economic system, and the results of technical and economic efficiency.

Modern studies continue to use multi variant modeling for agriculture, widening the number of factors and conditions that need to be taken into account. Carpentier et al. [6] reviewing economic modelling of agricultural production, conclude that “the ever-increasing complexity of production models in terms of sectors, technology representation, dynamic and spatial aspects implies a parallel increase in data requirements” (p. 154). The authors argue for a different balance between the theoretical properties of agricultural production models and their empirical tractability. They analyze the pros and cons of the Mathematical Programming models in agriculture, Multicrop Econometric models, Land Use models and Acreage Choice models, highlight their different estimation issues, and conclude that the development of regional type of modelling in the field of agriculture is desirable. By contrast, Ackerberg et al. [1] review a subset of the econometric techniques to assess outcomes of agri-markets such as demand systems, production functions, and dynamic estimation. In addition, AGMEMOD model [2] offers a system of estimated partial equilibrium models for the agricultural, fishery and food sectors. It considers the most important agricultural sectors of European countries, and the interactions between different sectors. The agricultural products modelled by AGMEMOD include all major cereals and oilseeds, sugar, livestock, meat, milk and dairy products. It is really useful for analysis of agricultural market policies, however, it is more convenient for evaluation of agri-food market relations between neighboring countries, not regions of a particular country.

The most relevant challenges related to the use of multi variant models for agriculture are the climate and political issues that should be taken into account in the model design. For instance, Burke and Emerick [4] model reflects how potential impacts of climate change influence the economic outcome. The authors analyzelarge variations in recent temperature and precipitation trends to identify adaptation to climate change in US agriculture, and use this information to generate new estimates of the potential impact of future changes on agricultural outcomes. The climate issue is relevant for Ukraine as well. Khokhlov et al. [10] research reveals the number of summers which were abnormally dry increased in some Ukrainian regions, including Mykolaiv, Kherson, and Odessa. As a result, climate fluctuations make the agri-food markets less predictable.

The political issues of agri-food market influence Ukrainian agriculture significantly as well. For instance, Rechka [12] highlights the complicated relationships between grain elevators, processing enterprises, wholesale markets, and agricultural firms. The author points out that “in selling products to processing enterprises in Ukraine, it is important to establish long-lasting and mutually beneficial relationships between agrarians and processors and compensate socially necessary expenses to agricultural enterprises in order to obtain mutual maximum benefits by each of the participants” (p. 251). Sarna [14] also highlights that current priorities of Ukrainian agricultural policy have led to quantitative changes rather than to qualitative transformation in the field, reinforcing the model of production within large-scale agricultural holdings. Ukrainian agri-food sector attracts the most significant amount of capital investments in comparison with other Ukrainian industries – 44,7% [15]. Thus, the capital for Ukrainian agri-food sector is quite accessible. However, there are still limitations related to legal restriction to buy land that decrease the investment attractiveness of Ukrainian agri-food industries.

PURPOSE

The models mentioned mainly consider a particular product or industry in order to determine sales or export optimization within the agri-food industries and define the best export opportunities for a particular product. At the same time, the purpose of this research is to develop a model able to plan the parameters of agricultural development of several agri-food products and industries, including grain processing, sunflower processing, and milk processing, and taking into account the optimization of export potential of these industries.

MATERIALS AND METHODS

In order to define the directions for Ukrainian agri-food industries development, the offered economic model was developed. It defines the optimal structure of production, processing, and export of agricultural products based on the data of Mykolaiv, Odessa, and Kherson regions of Ukraine. The main benefit of the model is the opportunity to increase income from agri-food export, taking into account Ukrainian consumer needs. It should be noted that the model fits the Ukrainian conditions because it reflects the realities of its domestic agri-food market.

As a result of the industrial structure assessment based on mathematical modelling in economics, different variants of the optimal production and processing structure are defined, whereas resource endowment, technologies and industrial organization remain unchanged. The model unifies different directions of the economic production and processing export oriented system. The consistent product movement based on the technological vertical is manifested in the corresponding parts of the model matrix (matrix size is 146 ? 168).

The input data for the model design is due to the information of agri-food industries from all enterprises of the defined regions [16].

The initial information of all agricultural industries in the regions contains:

• land use according to the type of lands;
• number of cattle;
• predicted product outcomes per a hectare or per a head of cattle in each region;
• dairy cow feeding rates and approximate feed rations;
• additional feed costs;
• product distribution based on the types of consumption;
• labor and material costs per unit production costs.

The information of food processing industries contains:

• raw material expenses per unit production costs;
• constraints of production capacity;
• labor and material expenses per unit production costs;
• production volumes of particular processed products.

The information of product sales contains:

• sales volumes in the domestic market;
• export volumes of vegetable and livestock products;
• forecast sales prices in the domestic and global market.

The model assumes that the industrial development is limited by available resources. At the same time, the opportunity to purchase additional feed for livestock and the increase in production capacity in processing subsystem are assumed. In should be noted that purchased additional feeds have surplus in slaughtered animals and also in processed food (domestic retail prices and export prices). In Ukraine, the majority of all types of livestock is kept by household farms, and regarding production output, households have produced 80% of total milk production in Ukraine, whereas 55% of all meat has been produced by agricultural enterprises [17]. The purpose of the model was to define the optimal relation of agri-food industries that would provide a balance of production, processing, and export functioning in the defined regions and the maximum economic productivity of the agricultural system, taking into account the following:

1. The forecasting of the agri-food market development is due to the concept of partial self-sufficiency with the opportunity to sell transportable products in the world market.
2. Agricultural products are divided into:
   • the products to satisfy own needs;
   • the products to be processed;
   • the products to feed livestock;
   • the products to be bought by Ukrainian customers in the domestic market;
   • the products for export.
3. Modelling considers the volumes of export of agricultural and processed products from Ukraine to other countries. The data are gathered and analyzed separately, considering the directions of agricultural and processing subindustries.

RESULTS AND DISCUSSION

The model deals with such variables as planted area, the structure of raw material base (milk industry), the volumes of production and sales of agricultural and processed products, and the export volumes of agricultural and processed products.

The system of variables includes the following:

• j, k – variable indices;
• i – constraints indices.

The constraints are grouped, so there are the following sets of variables and constraints:

• D – a set of regions (D = {1, 2, 3});
• L – a set of agricultural and processed industries;
• J₁ – a set of variables that indicates agricultural areas in a corresponding region;
• J₂ – a set of variables that defines the number of cattle in the regions;
• K₁ –a set of variables that defines processing and distribution of agricultural products;
• K₂ – a set of variables that defines the production of processed products;
• K₃ – a set of variables that defines indices of agricultural and processed products sales in the domestic market;
• K₄ – a set of variables that defines indices of agricultural and processed products export;
• R – a set of variables that indicates general needs in different types of resources, additional feed, production capacity, and raw materials;
• M₁ – a set of variables that indicates general expenses on production and processing of agri-food products;
• M₂ – a variable that indicates general expenses of labor resources;
• C₁ – a variable that indicates general cost of final agri-food products in the domestic market;
• C₂ – a variable that indicates the cost of processed products in the domestic market;
• C₃ – a variable that indicates the cost of export agri-food products.

The model constraints create the system of 9 structural groups, which are determined as follows:

• I₁ – a set of constraints defined by the structure of planted area;
• I₂ – a set of constraints defined by the balance of industry and feed needs;
• I₃ – a set of constraints defined by the number of cattle;
• I₄ – a set of constraints defined by production and distribution of agri-food products;
• P₁ – a set of constraints that reflects the balance of raw materials for agri-food products processing;
• P₂ – a set of production capacity constraints;
• U₁ – a set of constraints that reflects the sales volumes of agricultural and processed products in the domestic market;
• U₂ – the constraints that reflect the volumes of agricultural and processed products export;
• W – a set of constraints that creates a balance of production resources.

The coefficients and parameters of the model are the following:

• a_ijl – outcome of ? kind of product per unit of j field of plant growing in l region;
• o_ij – outcome of ? kind of forage per unit of j field of crop growing;
• v_il – a need in ? kind of forage per 1 head of cattle in l region;
• Tn_l – minimum number of cattle in l region;
• Th_l – maximum number of cattle in l region;
• S_il – planted area i kind of crop in l region;
• Sn_i – minimum planted area of definite crops;
• Sh_i – maximum planted area of definite crops;
• d_l – productivity per 1 a head of cattle in l region;
• f_i – a share of the product manufactured to be used for the particular purposes (feed, processing, sales, etc.);
• b_pjl – cost standards for p type of raw per unit of j type of products in l processing field;
• V_p – capacity of p type of processing enterprises;
• q_ij – resource expenses of i type per unit of j crop planted area or a head of cattle;
• y_rjl – resource expenses of r type per unit of j type of processed products l field;
• r_i – a share of the agricultural and processed products for sales in the domestic and global market;
• g_j – forage cost of j type of additional feed;
• csv_j – cost of an agricultural product of j type in the domestic market;
• cpv_jl – cost of a processed product of j type of l processing industry in the domestic market;
• cse_j – cost per unit of agricultural products of j type for export;
• cpe_jl – cost per unit of processed products of j type of l processing industry for export.

The purpose of the model is to reveal the optimal correlation of variables at which

	(1)

and the following conditions are satisfied:

1. The use of planted area

a. general area of planted land and by the types of particular purposes (pastures, hayfields, forage fields, etc.).

	(2)

b. minimum planted area

	(3)

c. maximum planted area

	(4)

2) The balance of production and feed use:

	(5)

3) The constraints of cattle numbers:

a. general minimum number of cattle

	(6)

b. maximum number of cattle

	(7)

4) Production and processing of agri-food products:

a. gross production of crop production products

	(8)

b. gross milk production

	(9)

c. agricultural product distribution for different purposes (feed, processing, sales, etc.).

	(10)

d. raw materials and processed products distribution on assortment groups (flour, cereals, dairy products, etc.)

	(11)

5) The equation of the raw balance for processing industry in each field:

	(12)

6) The capacity constraints of processing industry in each field

	(13)

7) The balance constraints of final agricultural and processed products sales

a. domestic market sales

	(14)

b. export sales

	(15)

8) The balance of production resources (labor, material assets, etc.):

a. for products of the agricultural industry

	(16)

b. for products of the processing industry

	(17)

9) The price product constrains

a. agricultural product sales in the domestic market

	(18)

b. processed product sales in the domestic market

	(19)

c. export sales of agricultural and processed products

	(20)

10) The constraints of additional feed costs

	(21)

11) The condition of non-negative variables:

	(22)

The goal has been accomplished via Solver.dll the functional library in the system of MS Excel tools. The Solver is a MS Excel tool that allows to find optimal solutions for a problem. Taking into account the decisions to be made, the constrains of the decisions, and the overall measure of performance (parameters) for these decisions, the allows us to formulate the linear programming model.

As a result, in the crop production industry, there were defined optimal planted area for growing cereals, industrial crops and products, vegetable crops and melon fields, that compose agricultural production for the domestic market and export, the raw material base for processing industry and forage, the number of cattle for regional needs, but considering the export potential of agricultural and processing industries (Table 1). The data were summarized based on the statistical data of State Statistic Service of Ukraine [16]. Analyzing the chart data and comparing the data from the model, the authors have concluded that the adjustment of the planted area structure is needed, in particular, a decrease in area for cereals and rapeseed and increase in area for feed crops (Table 2). The table also demonstrates the amount of resources used that reveals how the target function would change when resource use per unit, wherein the value of resource growth maintains the optimal set of variables. The normalized value reveals how the increase in a variable per unit would influence on export profit.

Table 1. Actual and Forecast Planted Area in Mykolaiv, Kherson, and Odessa Regions of Ukraine

Crops	Average for 2010–2015		Forecast
	Planted area [ha]	Structure [%]	Planted area [ha]	Structure [%]
Cereals and legumes	2806354.0	65.62	2498500.0	58.41
including winter wheat	1073652.5	25.10	832000.0	19.45
winter barley	784493.5	18.34	651000.0	15.22
winter rye	53896.5	1.26	3500.0	0.08
spring cereals	831973.8	19.45	991000.0	23.17
legumes	62337.7	1.47	21000.0	0.49
Industrial crops	959700.0	22.43	1069400.0	25.00
including sugar beet	166.7	0.00	400.0	0.01
sunflower	477949.3	11.17	820000.0	19.17
rapeseed	377754.0	8.83	198000.0	4.63
soybeans	103830.0	2.43	51000.0	1.19
Potato	26400.0	0.61	78000.0	1.82
Vegetables and melons	186800.0	4.37	245780.9	5.75
Forage crops	75850.0	1.78	155619.1	3.64
including roots	10693.8	0.25	26904.3	0.63
corn and silage	427.8	0.01	1100.0	0.03
maize	18821.0	0.44	30900.0	0.72
annual herbs for green forage	4705.3	0.11	11000.0	0.26
annual herbs for hay	8982.8	0.21	16000.0	0.37
perennial herbs for green forage	17110.0	0.40	35900.0	0.84
perennial herbs for hay	15109.3	0.35	33814.8	0.79
Fallow	222396.0	5.20	230200.0	5.38
Total	4277500.0	100.00	4277500.0	100.00

Table 2. Actual and Forecast Volumes of Export Products in Mykolaiv, Kherson, and Odessa Regions of Ukraine

Type of products	Average for 2010–2015		Forecast
	Export volume [thousand, Euro]	Structure [%]	Export volume [thousand, Euro]	Structure [%]
Plant products	254334.9	77.1	281037.8	82.8
including cereals	119392.2	36.2	141398.5	41.7
rapeseed	40566.9	12.3	28412.9	8.4
flour	26.3	0.0	612.5	0.2
groats	26.4	0.0	301.9	0.1
sunflower	17146.9	5.2	18355.9	5.4
sunflower oil	77176.2	23.4	91956.1	27.1
Animal products	75545.3	22.9	58280.3	17.2
including hard cheese	63983.7	19.4	56837.2	13.7
casein	1319.2	0.4	171.5	0.4
powdered milk	1337.5	0.4	307.1	0.7
butter	8904.9	2.7	964.5	2.3
Total	329880.2	100.0	339318.1	100

Considering the sets K1-K3, it should be noted that the processing quantity is based on the economic efficiency and also real production output, taking into account the processed products due to the fact that any additional processing or processing of raw materials brings added value, including profit. In addition, agri-food products price-making process in Ukraine is affected by many factors, including production costs, which are lower in Ukraine than in Europe that provides export price benefits. The relations between producer prices, customer purchase prices and export process are also influenced by lower logistics costs. Due to its geographical location, Ukraine has an advantage over Western Europe in exports to the Middle East, East Africa and Southeast Asia. However, there are some price product limitations of Ukrainian competitiveness in markets due to the government guaranteed quotas for export of agricultural products to protect the interests of Ukrainian customers [5].

CONCLUSIONS

These findings illustrate that the increase in agricultural productivity in Ukraine is able to improve its competitiveness in markets abroad and investment attractiveness. Optimization of the parameters reflected in the model (planted area, raw materials, production and sales volumes of agri-food products, and export volumes of agri-food products) allows to increase productivity of agri-food industries. Although agri-food industries in Ukraine are influenced by significant climate and political risks, the model offered allows to increase the predictability of the industries. We show that the productivity of the crop production industry can be increased by defining the optimal planted area for growing cereals, industrial crops and products, vegetable crops and melon fields, creating the raw material base for processing industry and feed, defining the number of cattle for regional needs, and considering the export potential for agricultural and processing industries. The results and their interpretation showed the complexity of the agri-food industries interrelations in Ukraine.

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Received: 1.09.2020
Reviewed: 15.10.2020
Accepted: 16.11.2020

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Tatiana Porudeyeva
Mykolaiv State Agricultural Research Station, Institute of Irrigated Agriculture, National Academy of Agrarian Sciences of Ukraine, Mykolaiv, Ukraine
The leading researcher
email: tanyapor@ukr.net

Kateryna Glubochenko
V.O. Sukhomlynskyi National University of Mykolaiv, Mykolaiv, Ukraine

email: e.glubochenko@gmail.com

Tetiana Ivanenko
Mykolaiv National Agrarian University, Mykolaiv, Ukraine

email: ivanenkotetiana84@gmail.com

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Responses to this article, comments are invited and should be submitted within three months of the publication of the article. If accepted for publication, they will be published in the chapter headed 'Discussions' and hyperlinked to the article.

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