CC BY
26
в своей поисковой платформе, и они получат список предлагаемых исследований, в которых они могут принять участие.
Таким образом, в настоящее время фактор высокой конкуренции на рынке фармацевтики и медицинских услуг является движущей силой формирования нового информационно-цифрового дизайна современных медицинских учреждений. Наступил период значительных изменений, инициируемых растущим глобальным рынком, что означает для российских акторов постоянную необходимость поддерживать высокую конкурентоспособность и соответствовать стандартам регуляторов.
Источники:
1. Аналитический портал Tadviser: http://www.tadviser.ru.
2. Гусев А.В. Автоматизация здравоохранения: потребности, реалии, перспективы // Врач и информационные технологии. 2012. № 4.- С. 15-21.
3. Концепция долгосрочного социально-экономического развития Российской Федерации на период до 2020 года (утв. распоряжением Правительства РФ от 17 ноября 2008 г. N 1662-р)//ГАРАНТ: http://base.garant.ru/194365/#ixzz3MlbpqWuK.
4. Концепция создания Федеральной системы «Онкология» (вертикально-интегрированной медицинской информационной системы по профилю «Онкология») 00083925.ФС ОНКО ВИМИС.001.Б3.01. Версия 2.4. Москва, 2019.
5. Мурашко М.А. Минздрав разрабатывает электронные системы по нескольким направлениям медицины// https://tass.ru/nacionalnye-proekty/8767499.
6. Федеральная служба государственной статистики: http://www.gks.ru. References:
1. Analytical portal Tadviser: http://www.tadviser.ru.
2. Gusev A.V. Automation of healthcare: needs, realities, prospects//Doctor and information technology. 2012. NO. 4.- S. 15-21.
3. Concept of long-term socio-economic development of the Russian Federation for the period up to 2020 (utv. by order of the Government of the Russian Federation dated November 17, 2008 N 1662-r )//GUARANTOR: http://base.gar-ant.ru/194365/#ixzz3MlbpqWuK.
4. The concept of creation of the Federal Oncology system (the vertically integrated medical information system on the Oncology profile) 00083925.FS OHKO VIMIS.001.B3.01. Version 2.4. Moscow, 2019.
5. Murashko M.A. Ministry of Health develops electronic systems in several areas of medicine//https ://tass.ru/nacionalnye-proekty/8767499.
6. Federal State Statistics Service: http://www.gks.ru.
DOI: 10.24412/2309-4788-2020-10542
L.G. Matveeva - Dr.sc.oec., professor, Southern Federal University, Russia, principal research worker, Russian Information-Analytic and Research Water Economy Centre [email protected];
O. A. Chernova - Dr.sc.oec., professor, Southern Federal University, Russia, chief research worker, Russian Information-Analytic and Research Water Economy Centre [email protected];
N. A. Kosolapova - Dr.sc.oec., professor, Southern Federal University, Russia, chief research worker, Russian Information-Analytic and Research Water Economy Centre [email protected];
E. A. Likhatskaya - lecturer, Southern Federal University, Russia, [email protected].
THE OPTIMIZATION MODEL OF THE USE OF WATER RESOURCES IN THE AGRICULTURE OF A REGION TAKING INTO ACCOUNT ITS SPECIALIZATION
Abstract. The article provides the conceptual aspects of forming efficient policy of rational water consumption in the agriculture production of regions, specializing mainly in agriculture and for which the problem of sufficient water supply is a priority. We developed and verified an economic and mathematical model of optimization of the use of water resources in the agriculture of a region, taking into account of the hydroeconomic balance in the basin, the existing scheme of irrigation of lands under cultivation, availability of additional irrigation fund, the farming system recommended as the optimal one for this region, the technical state of irrigation network and the ameliorative state of the irrigated lands. Key words: region, water resources, agriculture, optimization model of water consumption.
Introduction
In the system of economic strategizing determined by a fundamental influence of negative factors of external environment, in the context of providing food supply security the priority is given to the task of rational usage of natural resources (including water) of agricultural areas of Russia, their optimal allocation in the process of growing certain crops. Due to its specifics this type of regional resources plays a backbone part not only within agricultural areas, but in economy as a whole because together with oil, gas, electric and heat energy it is one of basic factors which determine the level of social and economic development of a state. Thus the problems of creating economic and mathematical tools, adapted for the specifics of a region and used to support the decision making in the processes of rational usage of water resources with the purpose of maximizing the profits of agricultural producers, become of a significant importance.
These tools represented by a comprehensive system of methods and models will let us provide the development and choice of optimal variants of the allocation of limited water resources between the concerned parties within the
borders of agricultural areas. The solution of this problem must be oriented towards, first, reaching the strategic goals of the development the economy of a region, consisting of an array of economic sectors which jointly use the resources of the same water reservoir, second -the concord of divergent interests of consumers of water resources concerning the restrictions of hydroeconomic balance of a region. Such twofold nature of the problem determines the specific character and the particularities of the tool basis of the research of prospects of development of hydroeconomic complexes of agricultural areas which provides rational allocation of water resources between the parties of irrigated agriculture. In addition, the measurement of existing resource (including water) potential must be carried out taking into consideration the strategic objectives of the development of a region.
Thus, the goal of this article is to develop an economic and mathematical model of creating optimal variants of water supply of agricultural businesses of a region without increasing the volumes of withdrawal of water resources.
Theoretical and methodological basis of the study
For many regions of Russia specialized mainly in agriculture irrigated agriculture is one of the main sources of social and economic growth. In light of this the question of quantitative evaluation of the volumes of allocation of water resources between agricultural producers in the context of competitive usage of water attracts the interest of many scientists. In many recent researches a particular attention is paid to the problems of rational usage of water resources due to a high level of water intensity of agricultural production, tested by actual practice, and prominent inefficient losses. [1-4].According to Russian Statistics Agency in 2016 7141 m3of fresh water [5] were used for irrigation, at the same time the water intensity of agriculture in Russian regions was much higher than in other countries, and the losses of water were 30-40%.
This problem is of particular importance in the South of Russia, where most agricultural areas of the country are located. The irrigated lands are situated in different agro-climatic zones with different natural settings which influence the measurement of irrigation norms, crop yield level and other factors, determining the level of efficiency of irrigation agriculture and water resources used for these purposes. According to Russian Statistics Agency in 2016 the volume of fresh water used in Russia was 54693 mln m3,of circulated and successively used water - 137893 mlnm3 [5]. At the same time the amount of lands under cultivation increases both in Russia and in Southern Federal District (table 1) and it influences the need for water resources.
Table 1 - Dynamics of lands under cultivation of agricultural crops in the Russian Federation
(in businesses of all categories, thousands of hectares) [6]
2005 2010 2012 2013 2014 2015 2016
The Russian Federation 75837 75187,9 76325,4 78057,1 78525 79319 79993
Southern Federal District 11220,2 11315,2 11265,6 11453,5 12220,3 12423,6 12614,7
Republic of Adygeya 184,1 228,9 223,6 234,7 235,7 236,7 240,2
Republic of Kalmykia 275,1 298,8 229,3 264,2 236,8 263,1 253
Republic of Crimea 731,8 711 774,1
Krasnodar Territory 3531,7 3634,4 3600,2 3657,1 3657,7 3679 3693,3
Astrakhan region 70 75,5 79,1 71,9 73,5 76,7 76,1
Volgograd region 2979,3 2726,2 2843,2 2838,4 2917,8 2988 3039,3
Rostov region 4180,1 4351,4 4290,3 4387,4 4365,6 4467,8 4537,6
Sebastopol 1,4 1,3 1,1
Understanding the problem of usage of water resources which is not rational enough next to negative factors of human impact leading to their quick depletion, led to the creation of numerous fundamental and applied studies devoted to the development of models and mechanisms of managing the processes of water usage including agriculture, and revealing the factors which have both limiting and stimulating impact on these processes [1- 4, 7 etc.].
Among the factors determining the volumes of possible usage of water most authors empathize irrigation fund, changing weather and climatic conditions, which influence soil humidity [8, 9], possibility of complex usage of underground and surface waters [10, 11]. In many releases authors develop economic and mathematical models of optimal management of water resources, in which we can see a review of climatic and social and economic scenarios [4, 12-14 etc.].
Generalizing and systematizing of existing approaches and model projects in this sphere let us classify them within the following groups.
Oriented towards the realization of resource-saving technologies. These models reach the compromise between the participants of hydroeconomic complexes thanks to price control, and the balance of interests is achieved due to maximizing their profits on the basis of stimulation to apply water-saving technologies [15 -19]. Using these models, we can carry out factor analysis of the sources of development of agricultural areas, for example, trace the connection between the growth of national economy and the price policy for water resources. At the same time the problems of strategic structural changes in agricultural economics on the basis of rational allocation of water resources between the main parties of irrigated agriculture are not solved in these models. For instance, using leading water-saving technologies an agricultural enterprise can produce a product not corresponding to the strategic priorities of regional development. Moreover,
agricultural crops have statutory indicators of water usage, and their cut leads to shrinkage of crop yield and carries a threat to for agriculture sector and food supply security, so we can say that such models can not be widely applied to solve strategic problems.
Oriented towards maximizing the economic benefit of agricultural producers. Opposed to the models, which prioritize the use of water-saving technologies by agricultural producers to gain economic benefit, this group of models allow to achieve benefits in other ways.
For instance, due to sowing agricultural structures with a lower need for water resources and a higher level of yield or due to cutting operational costs. In this case the model of management of water resources in a region shown in study [20] is of practical interest. The model includes the evaluation of risks caused by a lack of irrigation water in some territories of a region, which lets us distribute in an optimal way the land resources for these or those agricultural crops in a way which provides the biggest cost advantage possible
Oriented towards achieving the strategic aim of social and economic development of an area. This type of models is based on the idea, that rationality of water consumption can be achieved only in case if programs and plans of the allocation and use of water resources are in correlation with the strategies of economic and social development of an area. The supporters of this approach think, that the optimal allocation of water resources must be based not only on consumers' demand determined by their economic interests, but also on target indicators of social and economic development of a region and its agriculture [3, 4].
Thus, though there are many researches devoted to theoretical and conceptual validation and methodology of building the mathematical models of rational use of water resources in agricultural production, up to the present day there are gaps concerning tool support of processes of optimal allocation of water resources in order to provide a rational structure of land under cultivation.
Given the fact that the problems of a rational allocation of water resources between consumers are connected with setting a limit of withdrawal of water from a water body, which limits the possibilities to expand their economic activity, one of important aspects of some studies is the problem of reconciling the interests of different groups of agricultural producers (which differ in the type of crops produced, range of activity, territorial attribute etc.). Nearly all scientists agree that rationality of water consumption is achieved due to reaching the balance of interests of consumers of water resources [2, 3, 4, 7 etc.] At the same time there are different points of view on what consumers' interests are prioritized, and it is reflected in the choice of approaches, mechanisms and tools of managing the agriculture of a region.
Thus, the problem of evaluating the efficiency of water supply of agricultural enterprises on irrigated lands is complex and multiobjective, because it requires to solve the problems not only of sufficient water supply of agricultural production, but also of taking into account the interests of other water consumers in the basin of a water body. From the point of view of regional and basinal approach we can treat a water body as a territory of operation of certain economic sectors and activity of the participants of water industry. Traditionally a multisectoral water industry includes:
- water supply of all categories of consumers (industrial, including heat and atomic power plants, non-production sphere, households (including municipal), administration, agricultural water supply, flooding of pastures and minor rivers);
- fish industry (reproduction of fish stock, salable pond production);
- irrigated agriculture;
- water transport;
- water power engineering and others.
In accordance with the existing multisectoral system of water consumption in a basin and taking into account the above mentioned groups of consumers of water resources, the task of forming an ideal structure of agricultural production via rational allocation of limited water resources must be dealt with the help of a system of economic and mathematical models.
At the first stage we can apply balance models, which let us adjust the volumes of water resources for every participant of water industry; on the second stage we can use optimized models of the use of the water resources of a basin, which help to determine the best (from the point of view of the water users) options, considering restrictions to water resources, which exist in every water industry. Thus, this is about using a model complex which lets us optimize the use of water resources on lands under cultivation in a water reservoir.
The model below suggests that we use multi-criteria optimization: reaching the maximum effect from the production of certain agricultural crops or their groups (in natural or value terms) and minimum expenses of water resources, necessary for fulfilling the program of output of products of crop farming in the regions of a water basin.
Thus the scheme of optimization calculations given below lets us choose the best variant of allocation of water resources and use of irrigated lands, second, the research of the chosen variant in the context of changing aims of producing main agricultural crops and changing limits on water resources for irrigated agriculture and the growth of efficiency coefficient of irrigation systems (pic. 1).
Performance potential of production of farm produce Variants of specialization of crop-raising
V V Variants of using the irrigated land in a region
Demand for water resources from agricultural producers Production level and size of irrigated area Influence of the efficiency coefficient of irrigation systems on the production of agricultural crops Evaluation of water resources saving when using different variants of production of farm produce
Picture 1 - Conceptual scheme of scenario calculations following the The setting and the modeling of this problem are as follows.
On the basis of a simulation model of hydroeconomic balance, formally represented by the following equation: B = Wwr + Wint + Wpgw + Wrw + Wrwf ±AV±W, + Wew + Wf + Wdr + Wtw + Wcon + Wrsw
we calculated the amount of water resources, potentially available to use by the participants of a river-basin
scheme.
Balance(B) includes receipt and expense sides. The receipt side if formed by the following components:
Wwr - afflux from parts of a basin situated above;
Wint - the volume of resources formed in this section,
Wrw return waters in this section;
Wrwf- territorial redistribution of water runoff;
±A V- evacuation or filling of ponds and water storage reservoirs situated in the water-resource region. Expense side which includes the losses of water:
±Wj - when ice settles on the shores and/or water return as a result of ice melting in spring; Wew - from evaporation; Wf - as a result of filtration;
Wdr - as a result of the decrease of runoff, connected with water withdrawal from water bodies, fluidly connected with a river;
Wtw - water transfer outside the sector. Also the model includes following showings:
Wcon- total number of claims from water consumers of the given hydroeconomic section; Wr w - total sanitary and economic flash;
Wpgw- regulatory confirmed volume of water withdrawal from underground sources.
At the second stage of modeling in order to determine the potentially possible volumes of production of main agricultural crops the problem was solved iteratively with a criterion of the maximum of production of different kinds of produce crop-raising in the context of irrigated agriculture in the areas virtually used by agricultural producers. Restrictions for resources (including land and water) in the model were put together into blocks, shown in table 2.
Table 2 - Economic and mathematical model of determining potential volumes of production of main
agricultural crops in a region
The objective function of the model Minimal possible water resource spend to complete the production program: X X ^^(hjir/Vij) taw ^ min i J r lr Maximum volume of output of different types of farm produce : ХХУ1'1гХщГ ^ max i- the number of a hydroeconomic sector, j- the number of an irrigating system, Xiji - target values - irrigated area for crop l for crop rotation r, Цщ - irrigation norm of crop l in crop rotation r, jy- efficiency coefficient of irrigation system j, Ущг- yield of l
Water resource restrictions considering a reservoir as a whole XiX jXrXir(4ijir/Jij)xljlr < M
considering an irrigation system^Xir(4iiir/Jii)Xijir < ти
M- limit of the use of water resources according to the Scheme of a complex use of a water body, mil- water limit for irrigation system j
Land resource restrictions XrXlrXijlr < Sib
Sij- irrigation fund available in irrigation system j
Production restrictions XrXlryijlrXijlr < Gi,
Gt - the aim for the production of crop l
Labor force restrictions XXkrxljlr<Ti r lr
tir -production costs for crop l, Tj- labor force in the area ofirrigation system j
Financial restrictions XlrPlrXijlr < Ch
Pir- specific cost ratio to produce crop l, Cj- financial capacity of businesses situated in the area of irrigation system j
Technological restrictions Crop rotation restrictions within farmlands Xir Xijir < arSij
по отдельным культурам в севообороте^ Xlr Xijlr < XWr < @lr Xlr XWr
ar-the proportion of crop rotation r according to the regional farming system, Pirandyir- the maximum and minimum of crop participation in crop rotation r.
To prove the efficiency of the model as a tool of such type of tool sets of decision support we carried out its conditional and factual approbation. All the calculations were made through the example of the Don hydroeconomic system, which is one of the biggest in the South of Russia.
On the basis of multiple-option calculations with the use of information base, which describes the functioning of the irrigation agriculture system in the basin of lower Don, we searched for an efficient solution considering the use of the water resources of the region.
Scenario calculations were made in accordance with the task of determining potentialities of production of different agricultural crops depending on a variety of conditions connected with real volumes of water resources available and regulatory and technological requirements to the production of agricultural produce.
The results of information analysis concerning the state of resources of irrigating systems of lower Don prove that it is possible to carry out calculations in order to find an effective solution for the problem of allocation and use of irrigated lands and water resources of this water basin. This being said, the search for an optimal variant of the use of water resources and irrigated lands is performed taking into account the hydroeconomic balance in the basin, the existing scheme of irrigation of lands under cultivation, availability of additional irrigation fund, the farming system recommended as the optimal one for this region, the technical state of irrigation network and the ameliorative state of the irrigated lands.
Using the results of solving the specific task of finding the maximum possible overall output of certain types of farm produce(which, in this study, are viewed as input parameters of the model of optimal use of the water resources of a basin), we chose a compromise variant, which ensures a complete use of all irrigation fund and corresponds to the best long-range use of irrigated lands. The search for such compromise variant was performed as a result of sequential solution of the task shown in table 2, with different combinations of volumes of production of main types of farm produce.
On this basis, in the strategic aspect the task of an optimal use of irrigated lands of Lower Don is based on the condition that only after sufficient water supply of the production of all main types of farm produce, the water resources left after the allocation are used for the production of grain, and this fact corresponds to the objective function - the criterion of the maximum of production of crops in the region. The search for the solution for the optimization problem of finding the additional demand for water resources and their rational allocation was performed taking into account different levels of production objectives of main types of farm produce with given data concerning the optimal variant found before, but with a 2% decrease of production objectives after every step of calculating. (table 3).
Table 3 - The results of optimization calculations of determining the need for water resources
when decreasing the production objectives for farm produce
The number of the variant Overall production, % Irrigated area Need for water
Thousands of hectares % Millions of cubic meters %
1 100 235 100 1960 100
2 99 225 96 1724 88
3 98 223 95 1702 87
4 96 218 93 1663 85
5 94 213 91 1623 83
6 92 207 88 1586 81
7 90 203 86 1549 79
8 88 199 85 1514 77
9 86 195 83 1481 75
10 85 193 82 1464 75
To study the impact of decreasing the assigned limit of water resources on the level of production of farm produce and the size of irrigated lands we solved (on the phase basis) the optimization task given in table 2 with the given data concerning the optimal variant, but with gradual continually decreased the volume of assigned water resources. The results of the calculations for the main types of farm produce are shown in table 4.
Using the data from table 4, we can see that, with a gradual decrease of water resources limit the irrigated area remains the same, until the limit of water reaches 1360 million m3, and the decrease of the production of grain starts, when the limit of water consumption reaches 1560 million m3. We shall notice that the calculation matrix can be expanded due to adding the showings describing production of other types of farm produce in irrigated areas (feeding-stuff, vegetables, fruit etc.).
We believe, that a significant reduction of water consumption or increase of levels of production of farm produce in the same irrigated territory without additional withdrawal of water can be achieved through reconstruction of irrigating system, which is a factor of intensification and more efficient use of the limited water resources of the basin.
Table 4 - Changes in the production of the main types of farm produce and sizes of irrigated areas
in dependence to the reduction of the limit of water resources assigned
Number of the variant Objective function Value of the objective function Irrigated area (thousands of hectares) Water consumption (millions of) Output of products (thousands of tons)
The optimal variant Max of grain and rice 511 234,8 1960 Grain 511, of which rice 100
1 Max of grain and rice 512 234,8 1760 Grain511, of which rice78
2 Max of grain and rice 510 234,8 1560 Grain 510, of which rice 54
2 Max of grain and rice 508 234,8 1360 Grain 508of which rice 32
4 Max of grain and rice 483 229 1310 Grain 483, of which rice 32
5 Max of grain and rice 448 218 1260 Grain 448, of which rice 32
6 Max of grain and rice 265 198 1160 Grain 365, of which rice 32
We must notice that the results obtained using this economic and mathematical model can be treated as a preliminary stage for further decision making (based on existing economic and mathematical models) in the sphere of congruence of oppositely directed interests of the water consumers from the regions of the same water basin taking into account their sector profiles and the particularities of the territory.
In other words, the model suggested in this article can be viewed as an important element of the system of support of making efficient managerial decisions in the context of the river-basin scheme.
Conclusions
As distinguished from existing models, which study the aggregate of multifold tasks of efficient management of water resources on theoretical and conceptual levels and give a sense of regularities of interdependent development of the water industry of the region and agriculture, including in the context of global climatic changes, the authors of the article offer an optimization model which makes it possible to solve the problems of rational allocation of limited water resources of the region for agricultural production on the empiric level. Such methodological approach towards the development of
optimal solutions lets us orient the prioritizing when distributing water resources towards the economic viability of the structure of seeds.
The Novelty of the approach is in the fact that the authors offer a simulative set of tools which not only gives a possibility of choosing the optimal variant of using irrigated lands based on the existing potential of water industry, natural and climatic conditions and the demand for water resources, but also to determine the planting structure of agricultural production, basing on the priorities of strategic regional development. At the same time the allocation of limited water resources is performed through using a mixed mechanism, which combines the features of the priority and decentralized ones, which lets us solve the given problem on the basis of stimulating the regional subject towards economic growth. Also we must notice that the universality of the created simulative set of tools, which permits to apply it to project the development of agricultural areas in regional strategies of different areas.
References:
1. Belyaev S. D., Merzlikina Yu. b., Prokhorova N. B. Proposals for the transition to a basin-based water resources management system // Water management in Russia. -2014. - No. 5. - Pp. 10-14.
2. Danilov-Danilyan V. I., Pryazhinskaya V. G. Economic and territorial aspects of water management in Russia. - Moscow: RASKHN, 2013. - 311 p.
3. Kosolapov A. E., Matveeva L. G. Water supply efficiency Management of the regional system // Regional economy and management. -2018. - No. 4. - Pp. 170-181.
4. Kosolapov A. E., Kosolapova N. A., Matveeva L. G., Chernova O. A. Rational use of water resources in the economy of mountain territories of the North Caucasus Federal district // Sustainable development of mountain territories. - 2018. -No.2.- Pp. 48-62.
5. Agriculture, hunting and hunting, forestry in Russia. 2017: Stat. sat. / Rosstat - M., 2017 - 201 p.
6. The Regions Of Russia. Socio-economic indicators. 2017: Stat. sat. / Rosstat. -M., 2017. - p. 529.
7. Economic strategizing in new realities: mechanisms, tools, technologies. Monograph. - Taganrog: publishing house of the southern Federal University, 2016. - 463 p.
8. Maneta M.P., Torres M., Wallender W.W., Vosti S., Kirby M., Baissoi L.H., Rodrigues L.N. Water demand and flows in the Sâo Francisco River Basin (Brazil) with increased irrigation // Agricultural Water Management. - 2009. - Volume 96. -Issue 8. - Pp. 1191-1200. https://doi.org/10.10167j.agwat.2009.03.008
9. Souza J., Saad Joâo C., Sánchez-Román R., Rodríguez-Sinobas L. No-till and direct seeding agriculture in irrigated bean: Effect of incorporating crop residues on soil water availability and retention, and yield // Agricultural Water Management. -2016. - Volume 170, -Pp. 158-166. https://doi.org/10.10167j.agwat.2016.01.002
10. Zhang D., Guo P. Integrated agriculture water management optimization model for water saving potential analysis // Agricultural Water Management. - 2016. - Volume 170 - Pp. 5-19.
11. Amisigo B. A., McCluskey A., Swanson R. Modeling Impact of Climate Change on Water Resources and Agriculture Demand in the Volta Basin and other Basin Systems in Ghana // Sustainability. - 2015. - Volume 7. - Pp. 1-19.
12. Ponce R., Blanco M., Giupponi C. Climate Change, Water Scarcity in Agriculture and the Country-Level Economic Impacts. A Multimarket Analysis // Serie Working Paper. - 2014. - No 2. - 30 p. http://repositorio.udd.cl/bitstream/han-dle/11447/20/wp02.pdf
13. Ponce R., Parrado R. Climate Change, Water Scarcity on Agriculture and the Economy-Wide: impacts in the LAC Region // Serie Working Paper. 2015. - No. 16/ - 25 p. http://repositorio.udd.cl/bitstream/handle/11447/110/wp16.pdf?sequence=1
14. Barthel R., Reichenau T., Krimly T., Dabbert S., Schneider K., Mauser W. Integrated Modeling of Global Change Impacts on Agriculture and Groundwater Resources // Water Resources Management. - 2012. - Volume 26. - Issue 7. - Pp. 1929-1951.
15. Danilov-Danilyan V. I., Ivankov S. A., Khranovichi N. L. Coordination of strategies for the use of transboundary water resources // Economics and mathematical methods. - 2010. - Vol. 26. - No. 2. - Pp. 49-59.
16. Habibi Davijani M., Banihabib M.E., Nadjafzadeh Anvar A. et al. Multi-Objective Optimization Model for the Allocation of Water Resources in Arid Regions Based on the Maximization of Socioeconomic Efficiency // Water Resources Management. 2016. - Vol. 30. - No. 927. doi:10.1007/s11269-015-1200-y
17. Chen, Z., Wang, H. & Qi, X. Pricing and Water Resource Allocation Scheme for the South-to-North Water Diversion Project in China // Water Resources Management. - 2013. Vol. 27. - No 5. - Pp. 1457-1472. doi:10.1007/s11269-012-0248-1
18. Esmaeili, A. &Vazirzadeh, S. Water Pricing for Agricultural Production in the South of Iran // Water Resources Management. - 2009. - No. 23. - 957-964. doi:10.1007/s11269-008-9308.
19. Aidam P. The impact of water-pricing policy on the demand for water resources by farmers in Ghana // Agricultural Water Management. - 2015. - No. 158. - Pp. 10-16. https://doi.org/10.1016Zj.agwat.2015.04.007
20. Mo Li, Ping Guo, Singh V., Yang G. An uncertainty-based framework for agricultural water-land resources allocation and risk evaluation // Agricultural Water Management. - 2016. - No. - 177. - Pp. 10-23.
