توسعه مدل چندهدفی خطی تخصیص بهینه آب بر اساس چهار قاعده ورشکستگی و حل آن با رویکرد سازش فازی

نوع مقاله : پژوهشی

نویسندگان

1 استادیار، گروه مهندسی منابع طبیعی، دانشگاه هرمزگان، بندرعباس

2 دانشیار، هسته پژوهشی آب و محیط‌زیست، دانشگاه هرمزگان، بندرعباس

3 دانشیار، بخش مهندسی عمران و محیط زیست، دانشگاه شیراز، شیراز

4 استاد، دانشکده محیط زیست، دانشگاه تهران، تهران

چکیده

در این پژوهش مدلی برای بهینه‌سازی خطی چندهدفی تهیه شد که برای تخصیص‌دادن آب و سطح کشت در دو شبکه‌ی آبیاری و زه‌کشی درودزن و کربال (دربرگیرنده‌ی پنج ناحیه‌ی زراعی) به‌کار رفت. این مدل براساس چهار قاعده‌ی ورشکستگی کم‌کردن نسبی (PC)، دریافتی­های برابر محدودشده (CEA)، ضررهای برابر محدودشده (CEL) و تناسب تعدیل­شده (APR) با لحاظ‌کردن قطعیت و عدم‌قطعیت در موجودی آب تدوین شد. مدل توسعه‌یافته چهار تابع هدف برای انعکاس دادن مطلوبیت‌های مختلف بخش کشاورزی و محیط زیست دارد، که برای دو وضعیت خشک و غیرخشک با روی‌کرد سازش فازی حل شد. به‌طور کلی خروجی مدل نشان داد که ناحیه‌های با سهم آب بیش‌تر، در شرایط خشک و غیرخشک به‌ترتیب براساس قواعد ورشکستگی PC و CEL مجموع آب تخصیص‌یافته‌ی بیش‌تری را دریافت می‌کنند. از طرفی، بیش‌ترین آب تخصیص‌یافته برای ناحیه‌های با سهم آب کم‌تر، در هر دو حالت آبی-اقلیمی براساس قاعده‌ی ورشکستگی CEA اتفاق می‌افتد. برون‌داد فرایند ارزیابی پایداری با شاخص پایداری ورشکستگی (BASI) نشان داد که این معیار نمی‌تواند برای ارزیابی پایداری در تمام حالت‌های ورشکستگی به‌کار رود. بنابراین، تصمیم‌گیری بر اساس خروجی آن باید با احتیاط باشد.

کلیدواژه‌ها


عنوان مقاله [English]

Developing a Multi-Objective Linear Model for an Optimal Water Allocation Based on Four Bankruptcy Rules and Solve it Through the Fuzzy Compromise Approach

نویسندگان [English]

  • Ali Reza Nafarzadegan 1
  • Hassan Vagharfard 2
  • Mohammad Reza Nikoo 3
  • Ahmad Nohegar 4
1 Assistant Professor, Department of Natural Resources Engineering, University of Hormozgan, Bandar-Abbas, Iran
2 Associate Professor, Water and Environmental Research Group, University of Hormozgan, Bandar-Abbas, Iran
3 Associate Professor, Department of Civil and Environmental Engineering, Shiraz University, Shiraz, Iran
4 Professor, Faculty of Environment, University of Tehran, Tehran, Iran
چکیده [English]

A multi-objective linear optimization model has been formulated, which is used for water and crop area allocation in two irrigation and drainage networks of Dorudzan and Karbal, including five farming regions. The developed model is based on four bankruptcy rules of proportional cutback (PC), constrained equal awards (CEL), constrained equal losses (CEL), and adjusted proportional (APR) in terms of the certainty and uncertainty in the water availability. The developed model has four objective functions to reflect the various agricultural and environmental consumptions and is solved for two dry and non-dry conditions using a fuzzy compromise approach. The outputs of the model showed that the regions with higher shares of water receives the most allocated water through the bankruptcy rules of the PC and CEL in dry and non-dry condition, respectively. On the other hand, the most allocated water for the regions with lower shares of water occurs through the bankruptcy rule of the CEA in both hydro-climatic conditions. The outcome of the stability evaluation using the bankruptcy stability index (BASI) indicated that this criterion could not be used to evaluate stability under all bankruptcy situations; thus, one should take the necessary precaution for making a decision according to its output.

کلیدواژه‌ها [English]

  • Agricultural water management
  • environmental water need
  • multi-objective optimization
  • uncertainty
  • water bankruptcy
Ansink E, Weikard HP. 2012. Sequential sharing rules for river sharing problems. Social Choice and Welfare. 38(2): 187–210.
Aumann RJ, Maschler M. 1985. Game theoretic analysis of a bankruptcy problem from the Talmud. Journal of Economic Theory. 36(2): 195–213.
Chen H-K, Chou H-W. 1996. Solving multiobjective linear programming problems- a generic approach. Fuzzy Sets and Systems. 82(1): 35–38.
Choubin B, Khalighi-Sigaroodi S, Malekian A, Kişi Ö. 2016. Multiple linear regression, multi-layer perceptron network and adaptive neuro-fuzzy inference system for forecasting precipitation based on large-scale climate signals. Hydrological Sciences Journal. 61(6): 1001–1009.
Curiel IJ, Maschler M, Tijs SH. 1987. Bankruptcy games. Zeitschrift für Operations Research. 31(5): A143–A159
Dagan N, Volij O. 1993. The bankruptcy problem: a cooperative bargaining approach. Mathematical Social Sciences. 26(3): 287–297.
Degefu DM, He W. 2016. Allocating water under bankruptcy scenario. Water Resources Management. 30(11): 3949–3964.
Dinar A, Howitt RE. 1997. Mechanisms for allocation of environmental control cost: empirical tests of acceptability and stability. Journal of Environmental Management. 49(2): 183–203.
Herrero C, Villar A. 2001. The three musketeers: four classical solutions to bankruptcy problems. Mathematical Social Sciences. 42(3): 307–328.
Li S, He Y, Chen X, Zheng Y. 2019. The improved bankruptcy method and its application in regional water resource allocation. Journal of Hydro-environment Research. In Press.
Li X-q, Zhang B, Li H. 2006. Computing efficient solutions to fuzzy multiple objective linear programming problems. Fuzzy Sets and Systems. 157(10): 1328–1332.
Loehman E, Orlando J, Tschirhart J, Whinston A. 1979. Cost allocation for a regional wastewater treatment system. Water Resources Research. 15(2): 193–202.
Madani K, Dinar A. 2013. Exogenous regulatory institutions for sustainable common pool resource management: Application to groundwater. Water Resources and Economics. 2-3: 57–76.
Madani K, Lund JR. 2011. A Monte-Carlo game theoretic approach for multi-criteria decision making under uncertainty. Advances in Water Resources, 34(5): 607–616.
Madani K, Zarezadeh M, Morid S. 2014. A new framework for resolving conflicts over transboundary rivers using bankruptcy methods. Hydrology and Earth System Sciences. 18(8): 3055–3068.
Mahab Ghods Consulting Engineers. 2012. Report on water resources planning; From studies for the project of performance evaluation, monitoring of operation and maintenance management, restoration, and improvement of Dorudzan irrigation and drainage network. Regional Water Company of Fars. (In Persian).
Mianabadi H, Mostert E, Zarghami M, van de Giesen N. 2015. A new bankruptcy method for conflict resolution in water resources allocation. Journal of Environmental Management. 144: 152–159.
Moridi A. 2019. A bankruptcy method for pollution load reallocation in river systems. Journal of Hydroinformatics. 21(1): 45–55.
Nafarzadegan AR. 2018. Developing a stochastic optimization model for water allocation based on the virtual water concept using game theory and bankruptcy approaches. Ph.D. Dissertation. Faculty of Agriculture and Natural Resources. University of Hormozgan. 174 p. (In Persian).
Nafarzadegan AR, Vagharfard H, Nikoo MR, Nohegar A. 2018a. Socially-Optimal and Nash Pareto-Based Alternatives for Water Allocation under Uncertainty: an Approach and Application. Water Resources Management. 32(9): 2985–3000.
Nafarzadegan AR, Vagharfard H, Nikoo MR, Nohegar A. 2018b. Resolving conflict on the trade-off curve generated by a multi-purpose sustainability model for the natural environment and farming under water bankruptcy. Journal of Environmental Studies. 43(4): 699-713. (In Persian).
O'Neill B. 1982. A problem of rights arbitration from the Talmud. Mathematical Social Sciences. 2(4): 345–371.
Read L, Madani K, Inanloo B. 2014. Optimality versus stability in water resource allocation. Journal of Environmental Management. 133: 343–354.
Sechi GM, Zucca R. 2015. Water resource allocation in critical scarcity conditions: a bankruptcy game approach. Water Resources Management. 29(2): 541–555.