Multistage scenario-based interval-stochastic programming for planning water resources allocation

Abstract

In this study, a multistage scenario-based interval-stochastic programming (MSISP) method is developed for water-resources allocation under uncertainty. MSISP improves upon the existing multistage optimization methods with advantages in uncertainty reflection, dynamics facilitation, and risk analysis. It can directly handle uncertainties presented as both interval numbers and probability distributions, and can support the assessment of the reliability of satisfying (or the risk of violating) system constraints within a multistage context. It can also reflect the dynamics of system uncertainties and decision processes under a representative set of scenarios. The developed MSISP method is then applied to a case of water resources management planning within a multi-reservoir system associated with joint probabilities. A range of violation levels for capacity and environment constraints are analyzed under uncertainty. Solutions associated different risk levels of constraint violation have been obtained. They can be used for generating decision alternatives and thus help water managers to identify desired policies under various economic, environmental and system-reliability conditions. Besides, sensitivity analyses demonstrate that the violation of the environmental constraint has a significant effect on the system benefit.

Uncertain Production Scheduling Based on Fuzzy Theory Considering Utility and Production Rate

“…Coefficient c ui and maximum supply amount of utility U max ui are fuzzy numbers, as given by constraints (25) and (26). The two fuzzy numbers are described by triangular possibility distributions.…”

“…Constraint (25) can be converted into inequality constraints. All the fuzzy numbers are on one side of inequality constraints, so fuzzy numbers ranking problem is not involved.…”

“…Chance constraint programming needs a large amount of historical data to analyze the distribution function of uncertainty [24]. The scenario trees method adds many constraints, enables a large programming model scale, and has a computation time too long to meet requirements [25]. If the historical data of uncertainty is insufficient or difficult to acquire, then fuzzy theory is an effective means.…”

Inexact Mathematical Modeling for the Identification of Water Trading Policy under Uncertainty

“…However, the uncertainties existing in practical water trading programs are often related to errors in the acquired data, variations in spatial and temporal units and the incompleteness or impreciseness of the observed information, which leads to difficulties in planning water trading scientifically [9]. Consequently, the effective planning of water resource management under such uncertainties and complexities is important for facilitating sustainable socio-economic development for watershed systems [10].…”

“…IPP is an alternative for handling uncertainties in the model's left-and/or right-hand sides, as well as those that cannot be quantified as membership or distribution functions, since interval numbers are acceptable as its uncertain inputs. Moreover, in practical water resource management problems, uncertainties may be related to errors in the acquired data, variations in spatial and temporal units and the incompleteness or impreciseness of the observed information in water resource management [10,20]. Fuzzy programming (FP) is effective in handling ambiguous coefficients of objective functions and constraints caused by imprecision and vagueness, when the quality and quantity of uncertain information is often not satisfactory enough to be presented as a probabilistic distribution.…”