Abstract
Optimal water allocation within a river basin still remains a great modeling challenge for engineers due to various hydrosystem complexities, parameter uncertainties and their interactions. Conventional deterministic optimization approaches have given their place to stochastic, fuzzy and interval-parameter programming approaches and their hybrid combinations for overcoming these difficulties. In many countries, including Mediterranean countries, water resources management is characterized by uncertain, imprecise and limited data because of the absence of permanent measuring systems, inefficient river monitoring and fragmentation of authority responsibilities. A fuzzy-boundary-interval linear programming methodology developed by Li et al. (2010) is selected and applied in the Alfeios river basin (Greece) for optimal water allocation under uncertain system conditions. This methodology combines an ordinary multi-stage stochastic programming with uncertainties expressed as fuzzy-boundary intervals. Upper- and lower-bound solution intervals for optimized water allocation targets and probabilistic water allocations and shortages are estimated under a baseline scenario and four water and agricultural policy future scenarios for an optimistic and a pessimistic attitude of the decision makers. In this work, the uncertainty of the random water inflows is incorporated through the simultaneous generation of stochastic equal-probability hydrologic scenarios at various inflow positions instead of using a scenario-tree approach in the original methodology.
Highlights
Optimal water allocation of a river basin poses great challenges for engineers due to various uncertainties associated with the hydrosystem, its parameters and its impact factors as well as their interactions
These four options for each solution method correspond to lower-min fopt (and in tables and figures written as min (f−)), lower-max fopt (and in tables and figures written as max (f−)), upper-min fopt (and in tables and figures written as min (f+))
The interval solution can be interpreted for generating decision alternatives, where upper-bound system benefits is associated with more advantageous conditions while the lower-bound one corresponds to the demanding conditions [1]
Summary
Optimal water allocation of a river basin poses great challenges for engineers due to various uncertainties associated with the hydrosystem, its parameters and its impact factors as well as their interactions. Reference [6] developed an inexact two-stage stochastic programming method for water resources management, dealing with uncertainties expressed as both probability distributions and intervals and accounting for economic penalties due to infeasibility. Reference [13] developed a two-stage fuzzy-stochastic programming method for planning water resources allocation of agricultural irrigation systems In this case a scenario-based approach sets limitations when the study system is very large and complicated. In reference [14], a method is developed for tackling multiple uncertainties through integration of stochastic dynamic programming, fuzzy-Markov chain, vertex analysis and factorial analysis techniques It may have, though, computational (among others) difficulties to handle many other uncertain parameters (such as interval or dual-probabilities) that exist in large-scale practical problems.
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