An inexact optimization model associated with two robust programming approaches for water resources management

Abstract

In this study, an interval fuzzy-robust two-stage stochastic-robust programming (IFRTSRP) model is developed for water resources management under uncertainty. The developed IFRTSRP model incorporates two-stage stochastic programming (TSP), fuzzy robust programming (FRP), interval linear programming (ILP), and stochastic robust optimization (SRO) within a general optimization framework. The IFRTSRP model can not only deal with uncertainties presented as probability distributions, fuzzy membership functions, discrete interval numbers, and their combinations, but also provide an effective linkage between the pre-regulated water resources management policies and the associated economic implications. The IFRTSRP model can also enhance the robustness for the optimization process by delimiting the uncertain decision space through dimensional enlargement of the original fuzzy constraints. Moreover, the IFRTSRP model can evaluate the trade-offs between system economy and stability by incorporating the variability measures on penalty costs into the objective function. The IFRTSRP model is applied to a hypothetical case study of water resources management. The results indicate that reasonable solutions would be generated under different levels of k and/or x (non-negative weight coefficients); moreover, a higher net system benefit would correspond to lower system stability and higher system failure risk. Thus, the modeling results can be used for generating decision alternatives and thus help the managers to identify desired water allocation policies based on the reasonable consideration of system economy, system stability, and system failure risk.

Construction project planning under fuzzy time constraint

“…Worth mentioning is the work of Afsordegan et al (2016) which takes into account linguistic data provided by the decision makers without any previous aggregation. Li et al (2015) suggest an interval fuzzy-robust two-stage stochastic-robust programming model for management in conditions of uncertainty. The model can enhance the robustness for the optimization process under fuzzy constraints.…”

A Risk-Based Interval Two-Stage Programming Model for Agricultural System Management under Uncertainty

“…Step 7. Solve two submodels and generate final solutions of [8,13], [10,15], [12,17], and [14,19] × 10 6 $, respectively; those under the low-medium condition are [10,17], [12,19], [14,21], and [16, 23] × 10 6 $, respectively; those under the medium condition are [12,19], [14,21], [16,23], and [18, 25] × 10 6 $, respectively; those under the high condition are [14,21], [16,23], [18,25], and [20, 27] × 10 6 $, respectively. Since RBITSP was developed through incorporating financial risk measure into ITSP model, the solutions show characteristics of both methods.…”

“…As demonstrated in previous studies [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], uncertain optimization techniques are suitable in tackling water quality management problems, which included stochastic mathematical programming (SMP), fuzzy mathematical programming (FMP), and interval linear programming (ILP), as well as their integrations. Among above optimization approaches, inexact two-stage stochastic programming (ITSP) model proposed by Huang and Loucks [18] was frequently applied in water management fields [15,[19][20][21][22][23].…”