ON ONE SCIENTIFICALLY BASED SOWING MANAGEMENT FOR GETTING PARETO-OPTIMAL CROPS HARVEST
DOI:
https://doi.org/10.17770/etr2021vol1.6647Keywords:
Optimization problem, Pareto-optimal decision-making, guaranteed harvest, cereal cropsAbstract
In the present work, we construct and study a mathematical model for one important agrarian problem of grain production, in which it is necessary to obtain such a guaranteed harvest of crops, the yield of which depends on soil-climatic conditions, so that the gross income from the sale of the grown crop is maximum. The constructed mathematical model is a multi-criteria optimization problem (with five criteria), and it can be attributed to optimal control, in which the controlled parameters are the kind and proportion of crops to be sown. Based on the results obtained, a concrete example is implemented using the application package Mathcad, version 14.0.0.163.
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References
Latvian Environment, Geology and Meteorology Centre, "Latvijas klimats." [Online]. Available: https://www.meteo.lv/lapas/laiks/latvijas-klimats/latvijas-klimats?id=1199&nid=562 [Accessed: March 14, 2021]
Ch. Gienapp, D. Dreger, A. Zaharenko, etc., Cereal Crops: Growing, Harvesting, Reworking and Using. Moscow: "DLV AgroDelo" Publishing, 2008.
D. Spaar, H. Kleinhempel, and R. Fritzsche, Getreide, Mais und Futtergräser. Berlin, Germany: Springer-Verlag, 2013.
R. J. Henry and P. S. Kettlewell, Cereal Grain Quality. London: Chapman & Hall, 1996.
V. M. Vazhov, Buckwheat in the fields of Altai. Moscow: Academy of Natural Sciences Press, 2013.
A. Nurbekov, A. Kassam, D. Sydyk, Z. Ziyadullaev, I. Jumshudov, H. Muminjanov, D. Feindel, and J. Turok, Practice of conservation agriculture in Azerbaijan, Kazakhstan and Uzbekistan. Ankara, Turkey: Food and Agriculture Organization of the United Nations Publishing, 2016.
A. Nurbekov, A. Musaev, D. Sydyk, Z. Ziyadullaev, and J. Turok. Conservation Agriculture in Irrigated Areas of Azerbaijan, Kazakhstan and Uzbekistan. Beirut: International Centre for Agricultural Research in the Dry Areas, 2015.
"European Commission. EU prices for selected representative products. Monthly prices for vegetal products." [Online]. Available: https://ec.europa.eu/info/sites/info/files/food-farming-fisheries/farming/documents/market-prices-vegetal-products_en.pdf [Accessed: March 14, 2021]
Ministry of Agriculture of the Republic of Latvia, "Agriculture Annual Reports. Agricultural Report 2019 for 2018." [Online]. Available: https://www.zm.gov.lv/public/files/CMS_Static_Page_Doc/00/00/01/62/36/2019_lauks_gada_zinojums.pdf [Accessed: March 14, 2021]
Latvian Rural Advisory and Training Centre. [Online]. Available: http://new.llkc.lv/ [Accessed: March 14, 2021]
Food and Agriculture Organization of the United Nation, "FAOSTAT: Crops." [Online]. Available: http://www.fao.org/faostat/en/#data/QC [Accessed: March 14, 2021]
R. Aleksejevs, R. Guseinovs, A. N. Medvedev, and Sh. E. Guseynov, "On a Multi-criterion Problem of Planning Maritime Cargo Transportation," Journal of Traffic and Transportation Engineering, vol. 5, no. 3, pp. 124-146, 2017.
S. A. Ashmanov and A. V. Timokhov, Theory of optimization in in tasks and exercises. Moscow: Nauka Publishing, 1991.
A. Chinchuluun, P. M. Pardalos, A. Migdalas, and L. Pitsoulis, Eds., Pareto Optimality, Game Theory and Equilibria. New York: Springer, 2008.
R. L. Keeney and H. Raiffa, Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Cambridge: Cambridge University Press, 1993.
R. E. Steuer, Multiple Criteria Optimization: Theory, Computation, and Application. New York: John Wiley & Sons, 1986.
F. W. Gembicki, "Vector Optimization for Control with Performance and Parameter Sensitivity Indices," Ph.D. thesis, Department of System Engineering, Case Western Reserve University, Cleveland, USA, 1973.
C. A. Coello Coello and G. B. Lamont, Applications of Multi-Objective Evolutionary Algorithms: Advances in Natural Computation. New Jersey: World Scientific Press, 2004.
K. Deb, Multi-objective Optimization Using Evolutionary Algorithms. New York: John Wiley & Sons, 2001.
T. L. Saaty, The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation. New York: McGraw-Hill, 1980.
P. J. Fleming, "Computer-aided control system design of regulators using a multiobjective optimization," Annual Review in Automatic Programming, vol. 13, part 2, pp. 47-52, 1985.
Sh. E. Guseynov, R. Aleksejevs, J. V. Aleksejeva, and Y. S. Gasimov, "Evaluating attractiveness of the Central and the Eastern European countries by using index approach for the strategic decision making process related to expansion of the financial service markets," Advanced Mathematical Models & Applications, vol. 2, no. 3, pp.167-214, 2017.
Y. Y. Haimes, "Integrated System Identification and Optimization," Control and Dynamic Systems, vol. 10, pp. 435-518, 1973.
P. J. Fleming and A. P. Pashkevich, "Application of Multiobjective Optimization to Compensator Design for SISO Control Systems," Electronics Letters, vol. 22, no. 5, pp. 258-259, 1986.
F. W. Gembicki and Y. Y. Haimes, "Approach to Performance and Sensitivity Multiobjective Optimization: The Goal Attainment Method," IEEE Transactions on Automatic Control, vol. 29, no 6, pp. 769-771, 1975.
A. N. Tikhonov and V. Ya. Arsenin, Solutions of Ill-Posed Problems. Washington: Winston and Sons, 1977.
V. A. Morozov, Methods for Solving Incorrectly Posed Problems. New York: Springer-Verlag, 1984.
S. A. Andreyev and Sh. E. Guseynov, Regularizing Algorithms for Diagnosing: Applied to Gas Turbine Engines in Operation. Saarbrucken: LAP Publishing, 2013.
K. Schittkowski, NLQPL. "A FORTRAN subroutine solving constrained nonlinear programming problems," Annals of Operations Research, vol. 5, no. 6, pp. 485-500, 1985.
R. K. Brayton, S. W. Director, G. Hachtel, and L. Vidigal, "A new algorithm for statistical circuit design based on quasi-Newton methods and function splitting," IEEE Transactions on Circuits and Systems, vol. 26, no. 9, pp. 784-794, 1979.
