Review of the economic-mathematical analysis for the management of irrigation water and other crop production parameters

Document Type : Review Article


1 Department of Water Science and Engineering, College of Agricultural Science, Fasa University, Fasa, I. R. Iran

2 Irrigation Department, & Drought Research Center, School of Agriculture, Shiraz University, Shiraz, I. R. Iran

3 Department of Range and Watershed Management (Nature Engineering), College of Agricultural Science, Fasa University, Fasa, I. R. Iran



Plant growth and yield are influenced by many production parameters such as the amount of irrigation water, fertilization, plant density, etc. Due to the limitation of resources and agricultural inputs, increased production costs, food demand, population growth, and environmental problems, the development of scheduling approaches to use production parameters is necessary. In this study, firstly, crop yield and net benefit responses to variation of production parameters and secondly, economic-mathematical analysis of production parameters such as irrigation water were reviewed. Presented analyses in this study were categorized into four cases including 1) constant or variable crop price, 2) single, two, or multiple variables production functions, 3) limited land area and water or not limited, and 4) variable water price. The economic-mathematical analysis presented about deficit irrigation in this study was extended to determine the optimum value of other production parameters such as fertilizer rate, plant density, seed density, corm planting intensity, etc.


Article Title [Persian]

مروری بر تحلیل اقتصادی - ریاضی برای مدیریت آب آبیاری و سایر پارامترهای تولیدمحصول

Authors [Persian]

  • علی شعبانی 1
  • علیرضا سپاسخواه 2
  • محمد مهدی مقیمی 1
  • عبدالرسول زارعی 3
1 بخش علوم و مهندسی آب، دانشکده کشاورزی، دانشگاه فسا، فسا، ج. ا. ایران
2 بخش مهندسی آب و مرکز مطالعات خشکسالی، دانشکده کشاورزی، دانشگاه شیراز، شیراز، ج.ا. ایران
3 بخش مهندسی مرتع و آبخیزداری (مهندسی طبیعت)، دانشکده کشاورزی، دانشگاه فسا، فسا، ج. ا. ایران
Abstract [Persian]

رشد و عملکرد گیاه تحت تأثیر بسیاری از پارامترهای تولید مانند میزان آب آبیاری، کوددهی، تراکم بوته و غیره است. با توجه به محدودیت منابع و نهاده های کشاورزی، افزایش هزینه های تولید، تقاضای غذا، رشد جمعیت و مشکلات زیست محیطی، توسعه رویکردهای زمانبندی برای استفاده از پارامترهای تولید ضروری است. در این مطالعه ابتدا عملکرد محصول و پاسخ سود خالص به تغییرات پارامترهای تولید مورد بحث قرار می گیرد، دوم تحلیل اقتصادی-ریاضی پارامتر های تولید مانند آب آبیاری مورد بررسی ‌قرار گرفت. تحلیل های ارائه شده در این مطالعه در چهار مورد شامل 1) قیمت محصول، ثابت یا متغیر، 2) تابع های تولید تک، دو یا چند متغیره، 3) سطح زمین و آب محدود یا نامحدود و 4) قیمت آب متغییر طبقه بندی شدند. تجزیه و تحلیل اقتصادی-ریاضی ارائه شده در مورد کم آبیاری در این مطالعه برای تعیین مقدار بهینه سایر پارامترهای تولید مانند میزان کود، تراکم بوته، تراکم بذر، شدت کاشت بنه و غیره گسترش یافت.

Keywords [Persian]

  • قیمت محصول
  • محدودیت زمین
  • تابع تولید
  • محدودیت آب
Amiri, M. J., Hamidifar, H., Bahrami, M., & Eslamian, S. (2016). Optimisation of deficit-irrigation under variable seasonal rainfall and planning scenarios for rice in a semi-arid region of Iran. International Journal of Hydrology Science and Technology, 6(4), 331-343.
Azizian, A., & Sepaskhah, A. R. (2014). Maize response to different water, salinity and nitrogen levels: Agronomic behavior. International Journal of Plant Production, 8(1), 107-130.
Artyszak, A., Klarzyńska, E., Litwińczuk-Bis, M., & Siuda, A. (2019). Profitability of sugar beet foliar nutrition with silicon. Annals of the Polish Association of Agricultural and Agrobusiness Economists, 21(1), 7-13.
doi: 10.5604/01.3001.0013.0539
Assefa, Y., Vara Prasad, P. V., Carter, P., Hinds, M., Bhalla, G., Schon, R., Jeschke, M., Paszkiewicz, S., & Ciampitti, I. A. (2016). Yield responses to planting density for US modern corn hybrids: A synthesis-analysis. Crop Science, 56(5), 2802-2817. 
Baeza, P., Junquera, P., Peiro, E., Lissarrague, J. R., Uriarte, D., & Vilanova, M. (2019). Effects of vine water status on yield components, vegetative response and must and wine composition. Advances in Grape and Wine Biotechnology, 1, 73-94.
Banda, M. M., Heeren, D. M., Martin, D. L., Munoz-Arriola, F., & Hayde, L. G. (2019). Economic analysis of deficit irrigation in sugarcane farming: Nchalo Estate, Chikwawa District, Malawi. Boston, Massachusetts: American Society of Agricultural and Biological Engineers.
Barzegari, M., Sepaskhah, A. R., & Ahmadi, S. H. (2017). Irrigation and nitrogen managements affect nitrogen leaching and root yield of sugar beet. Nutrient Cycling in Agroecosystems, 108(2), 211-230.
Berg, W. K., Cunningham, S. M., Brouder, S. M., Joern, B. C., Johnson, K. D., Santini, J., & Volenec, J. J. (2005). Influence of phosphorus and potassium on alfalfa yield and yield components. Crop Science, 45(1), 297-304.
Bronson, K. F., Hunsaker, D. J., & Thorp, K. R. (2019). Nitrogen fertilizer and irrigation effects on seed yield and oil in camelina. Agronomy Journal, 111(4), 1712-1719.
Burke, E., Kendall, G., Newall, J., Hart, E., Ross, P., & Schulenburg, S. (2003). Hyper-heuristics: An emerging direction in modern search technology. In Glover, F., Kochenberger, G.A. (eds). Handbook of metaheuristics (pp 457–474). International series in operations research & management science, vol 57. Boston, MA, USA: Springer.
Carciochi, W. D., Schwalbert, R., Andrade, F. H., Corassa, G. M., Carter, P., Gaspar, A. P., Schmidt, J., & Ciampitti, I. A. (2019). Soybean seed yield response to plant density by yield environment in north America. Agronomy Journal, 111(4), 1923-1932.
Cetin, O., & Bilgel, L. (2002). Effects of different irrigation methods on shedding and yield of cotton. Agricultural Water Management, 54(1), 1-15. doi: 10.1016/S0378-3774(01)00138-X
Chartzoulakis, K., & Bertaki, M. (2015). Sustainable water management in agriculture under climate change. Agriculture and Agricultural Science Procedia, 4, 88-98.
Chatterjee, A., Subedi, K., Franzen, D. W., Mickelson, H., & Cattanach, N. (2018). Nitrogen fertilizer optimization for sugarbeet in the Red River Valley of North Dakota and Minnesota. Agronomy Journal, 110(4), 1554-1560.
Chauhan, B. S., Singh, V. P., Kumar, A., & Johnson, D. E. (2011). Relations of rice seeding rates to crop and weed growth in aerobic rice. Field Crops Research, 121(1), 105-115.
Cui, G., Lu, Y., Zheng, C., Liu, Z., & Sai, J. (2019). Relationship between soil salinization and groundwater hydration in Yaoba Oasis, Northwest China. Water, 11(1), 175.
Dong, H., Kong, X., Li, W., Tang, W., & Zhang, D. (2010). Effects of plant density and nitrogen and potassium fertilization on cotton yield and uptake of major nutrients in two fields with varying fertility. Field Crops Research, 119(1), 106-113.
Du, Y. D., Cao, H. X., Liu, S. Q., Gu, X. B., & Cao, Y. X. (2017). Response of yield, quality, water and nitrogen use efficiency of tomato to different levels of water and nitrogen under drip irrigation in Northwestern China. Journal of Integrative Agriculture, 16(5), 1153-1161.
Dusserre, J., Raveloson, H., Michellon, R., Gozé, E., Auzoux, S., & Sester, M. (2017). Conservation agriculture cropping systems reduce blast disease in upland rice by affecting plant nitrogen nutrition. Field Crops Research, 204, 208-221.
English, M. (1990). Deficit irrigation. I: Analytical framework. Journal of Irrigation and Drainage Engineering, 116(3), 399-412.
English, M., & Raja, S. N. (1996). Perspectives on deficit irrigation. Agricultural Water Management, 32(1), 1-14.
English, M. J. (1981). The uncertainty of crop models in irrigation optimization. Transactions of the ASAE. 24, 917–921.
French, R. J. (2016). Lupin: Agronomy. In Reference module in food science. Elsevier. doi:10.1016/b978-0-08-100596-5.00194-3.
Geerts, S., & Raes, D. (2009). Deficit irrigation as an on-farm strategy to maximize crop water productivity in dry areas. Agricultural Water Management, 96(9), 1275-1284.
Haj-Amor, Z., Tóth, T., Ibrahimi, M. K., & Bouri, S. (2017). Effects of excessive irrigation of date palm on soil salinization, shallow groundwater properties, and water use in a Saharan oasis. Environmental Earth Sciences, 76(17), 590
Han, J., Shi, J., Zeng, L., Xu, J., & Wu, L. (2017). Impacts of continuous excessive fertilization on soil potential nitrification activity and nitrifying microbial community dynamics in greenhouse system. Journal of Soils and Sediments, 17(2), 471-480.
Hazra, G. (2016). Different types of eco-friendly fertilizers: An overview. Sustainability in Environment, 1(1), 54-70.
Herzog, M., Striker, G. G., Colmer, T. D., & Pedersen, O. (2016). Mechanisms of waterlogging tolerance in wheat–a review of root and shoot physiology. Plant, Cell and Environment, 39(5), 1068-1086.
Hoffmann, C. M. (2010). Root quality of sugarbeet. Sugar Tech, 12(3-4), 276-287.
Hong-xing, X. U., Ya-jun, Y., Yan-hui, L. U., Xu-song, Z., Jun-ce, T., Feng-xiang, L., Qiang, F. U., & Zhong-xian, L. (2017). Sustainable management of rice insect pests by non-chemical-insecticide technologies in China. Rice Science, 24(2), 61-72.
Hosseini, S. A., Réthoré, E., Pluchon, S., Ali, N., Billiot, B., & Yvin, J. C. (2019). Calcium application enhances drought stress tolerance in sugar beet and promotes plant biomass and beetroot sucrose concentration. International Journal of Molecular Sciences, 20(15), 3777.
Imtiyaz, M., Mgadla, N. P., Chepete, B., & Manase, S. K. (2000). Response of six vegetable crops to irrigation schedules. Agricultural Water Management, 45(3), 331-342.
Johnson, C. R., Reiling, B. A., Mislevy, P., & Hall, M. B. (2001). Effects of nitrogen fertilization and harvest date on yield, digestibility, fiber, and protein fractions of tropical grasses. Journal of Animal Science, 79(9), 2439-2448.
Kang, S., Zhang, L., Liang, Y., Hu, X., Cai, H., & Gu, B. (2002). Effects of limited irrigation on yield and water use efficiency of winter wheat in the Loess Plateau of China. Agricultural Water Management, 55(3), 203-216.
Kapur, B., Celiktopuz, E., Saridas, M. A., & Kargi, S. P. (2017). Effects of different irrigation levels with bio-stimulant applications on plant growth in ‘Kabarla’ Strawberry variety. American Journal of Plant Biology, 2(4), 120-124.
Kaveh, A., & Talatahari, S. (2010). A novel heuristic optimization method: Charged system search. Acta Mechanica, 213(3-4), 267-289.
Khozaie, M., & Sepaskhah, A. R. (2018). Economic analysis of the optimal level of supplemental irrigation for rain-fed figs. Iran Agricultural Research, 37(2), 17-26.
Leghari, S. J., Wahocho, N. A., Laghari, G. M., HafeezLaghari, A., MustafaBhabhan, G., HussainTalpur, K., Bhutto, T.A., Wahocho, S.A. & Lashari, A. A. (2016). Role of nitrogen for plant growth and development: A review. Advances in Environmental Biology, 10(9), 209-219.
Li, F., Zhu, L., Xie, Y., Jiang, L., Chen, X., Deng, Z., & Pan, B. (2015). Colonization by fragments of the submerged macrophyte Myriophyllum spicatum under different sediment type and density conditions. Scientific Reports, 5, 11821. doi:10.1038/srep11821
Li, Y., Li, J., Gao, L., & Tian, Y. (2018). Irrigation has more influence than fertilization on leaching water quality and the potential environmental risk in excessively fertilized vegetable soils. PloS one, 13(9), e0204570.
Liu, Y., Li, C., Fang, B., Fang, Y., Chen, K., Zhang, Y., & Zhang, H. (2019). Potential for high yield with increased seedling density and decreased N fertilizer application under seedling-throwing rice cultivation. Scientific Reports, 9(1), 731.
Loel, J., Kenter, C., Märländer, B., & Hoffmann, C. M. (2014). Assessment of breeding progress in sugar beet by testing old and new varieties under greenhouse and field conditions. European Journal of Agronomy, 52, 146-156.
Mahmoud, E. S. A., Hassanin, M. A., Borham, T. I., & Emara, E. I. (2018). Tolerance of some sugar beet varieties to water stress. Agricultural Water Management, 201, 144-151.
Muñoz, M. A., Sun, Y., Kirley, M., & Halgamuge, S. K. (2015). Algorithm selection for black-box continuous optimization problems: A survey on methods and challenges. Information Science, 317, 224-245.
Pulido-Bosch, A., Rigol-Sanchez, J. P., Vallejos, A., Andreu, J. M., Ceron, J. C., Molina-Sanchez, L., & Sola, F. (2018). Impacts of agricultural irrigation on groundwater salinity. Environmental Earth Sciences, 77(5), 197.
Rahman, M. M., Hossain, M. M., Anwar, M. P., & Juraimi, A. S. (2011). Plant density influence on yield and nutritional quality of soybean seed. Asian Journal of Plant Sciences, 10(2), 125-132. doi: 10.3923/ajps.2011.125.132
Ren, B., Liu, W., Zhang, J., Dong, S., Liu, P., & Zhao, B. (2017). Effects of plant density on the photosynthetic and chloroplast characteristics of maize under high-yielding conditions. The Science of Nature, 104(3-4), 12. 
Sadeghi-Shoae, M., Taleghani, D. F., & Paknejad, F. (2015). Meta-analysis the effect of nitrogen fertilizer on quantitative and qualitative characteristics of sugar beet. Biological Forum 7, 65-71.
Sangoi, L. (2001). Understanding plant density effects on maize growth and development: An important issue to maximize grain yield. Ciência Rural, 31(1), 159-168.
Schlegel, A. J., Havlin, J. L. (2017). Corn yield and grain nutrient uptake from 50 years of nitrogen and phosphorus fertilization. Agronomy Journal, 109(1), 335-342.
Sepaskhah, A. R., Azizian, A., & Tavakoli, A. R. (2006). Optimal applied water and nitrogen for winter wheat under variable seasonal rainfall and planning scenarios for consequent crops in a semi-arid region. Agricultural Water Management, 84(1-2), 113-122.
Sepaskhah, A. R., Dehbozorgi, F., & Kamgar-Haghighi, A. A. (2008). Optimal irrigation water and saffron corm planting intensity under two cultivation practices in a semi-arid region. Biosystems Engineering, 101(4), 452-462.
Sepaskhah, A. R., & Akbari, D., (2005). Deficit irrigation planning under variable seasonal rainfall. Biosystems Engineering, 92(1), 97-106.
Shabani, A. (2019). Determining the optimum applied water for sugar beet in the case of crop price as a function of applied irrigation water. Journal of Water and Soil Science, 23(2), 349-359. (In Persian with English abstract)
Shabani, A., & Sepaskhah, A. R. (2019). Optimal amounts of water and nitrogen applied to sugar beet when crop price depends on its sugar content. Spanish Journal of Agricultural Research, 17(3), 1202. doi:
Shabani, A., Sepaskhah, A. R., & Khorramian, M. (2018). Mathematical-economic analysis to determine optimal applied water in case of crop price depends on its quality. International Journal of Plant Production, 12(3), 191-202.
Shamshiri, Gh., Shabani, A., Sepasian, A. R., Azizian, A., & Sepaskhah, A. R. (2020). Optimizing water consumption of sugar beet in conditions of the irrigation water salinity and dependency of the yield price to quality. Iranian Journal of Irrigation and Drainage, 13(6), 1762-1733. (In Persian with English abstract)
Tarkalson, D. D., King, B. A., & Bjorneberg, D. L. (2018). Yield production functions of irrigated sugarbeet in an arid climate. Agricultural Water Management, 200, 1-9.
Woli, P., Hoogenboom, G., & Alva, A. (2016). Simulation of potato yield, nitrate leaching, and profit margins as influenced by irrigation and nitrogen management in different soils and production regions. Agricultural Water Management, 171, 120-130.
Wu, G. Q., Feng, R. J., & Shui, Q. Z. (2016). Effect of osmotic stress on growth and osmolytes accumulation in sugar beet (Beta vulgaris L.) plants. Plant, Soil and Environment, 62(4), 189-194.
Yang, X. S. (2010). Engineering optimization: an introduction with metaheuristic applications. New Jersey:John Wiley & Sons.
Yoo, D. G. & Kim, J. H. (2014). Meta-heuristic algorithms as tools for hydrological science. Geoscience Letter, 1(1),1-7.
Zanakis, S. H., & Evans, J. R. (1981). Heuristic “optimization”: Why, when, and how to use it. Interfaces, 11(5), 84-91.
Zand-Parsa, S., & Sepaskhah, A. R. (2001). Optimal applied water and nitrogen for corn. Agricultural Water Management, 52(1), 73-85.
Zhang, H., & Oweis, T. (1999). Water–yield relations and optimal irrigation scheduling of wheat in the Mediterranean region. Agricultural Water Management, 38(3), 195-211.
Zhang, T., Zhan, X., Kang, Y., Wan, S., & Feng, H. (2017). Improvements of soil salt characteristics and nutrient status in an impermeable saline–sodic soil reclaimed with an improved drip irrigation while ridge planting Lycium barbarum L. Journal of Soils and Sediments, 17(4), 1126-1139.
Zhang, W., Wu, L., Wu, X., Ding, Y., Li, G., Li, J., Weng, F., Liu, Z., Tang, S., Ding, C., & Wang, S. (2016). Lodging resistance of japonica rice (Oryza Sativa L.): Morphological and anatomical traits due to top-dressing nitrogen application rates. Rice, 9(1), 31.
Zheng, H., Ying, H., Yin, Y., Wang, Y., He, G., Bian, Q., Cui, Z., & Yang, Q. (2019). Irrigation leads to greater maize yield at higher water productivity and lower environmental costs: A global meta-analysis. Agriculture, Ecosystems and Environment, 273, 62-69.
Zhihui, W., Jianbo, S.., Blackwell, M., Haigang, L., Bingqiang, Z., & Huimin, Y. (2016). Combined applications of nitrogen and phosphorus fertilizers with manure increase maize yield and nutrient uptake via stimulating root growth in a long-term experiment. Pedosphere, 26(1), 62-73.