A Generalized Interval Fuzzy Chance-Constrained Programming Method for Domestic Wastewater Management Under Uncertainty – A Case Study of Kunming, China

Abstract

In this study, interval mathematical programming (IMP), m λ -measure, and fuzzy chance-constrained programming are incorporated into a general optimization framework, leading to a generalized interval fuzzy chance-constrained programming (GIFCP) method. GIFCP can be used to address not only interval uncertainties in the objective function, variables and left-hand side parameters but also fuzzy uncertainties on the right-hand side. Also, it can reflect the aspiration preference of optimistic and pessimistic decision makers due to the integration of m λ -measure. The developed method is applied to the long-term planning of a domestic wastewater management system in the city of Kunming, China, with consideration of the eco-environmental protection of downstream water body. The solution results of the GIFCP method can generate a series of optimal wastewater allocation patterns and WTPs capacity expansion schemes under different risk levels, provide in-depth insights into the Water Resour Manage (2015) 29:3015-3036 effects of uncertainties, and consider the proper balance between system cost and risk of constraint violation.

A Stochastic Multi-Objective Chance-Constrained Programming Model for Water Supply Management in Xiaoqing River Watershed

“…For example, as shown in Table 4, at q i levels of 0.01, 0.05 and 0.1, the water amounts transferred to tributary 2 in the first period are 240. 15,197.44 and 177.88 × 10 3 m 3 , respectively; similarly, the water amounts allocated to tributary 7 in the second period are 156.46, 135.88 and 126.05 × 10 3 m 3 , respectively. The reason behind such a difference is that the water demand constraint is involved in the stochastic variables, where the required water amounts of the tributaries were expressed as random variables with log-normal distributions.…”

“…Previously, many uncertain analysis approaches were developed for dealing with watershed-scale water resource management issues, including stochastic mathematical programming (SMP) [3][4][5][6][7], fuzzy mathematical programming (FMP) [8][9][10][11] and interval mathematical programming (IMP) [12,13], as well as their combinations [14][15][16][17][18]. Among them, stochastic chance-constrained programming (SCCP) was extensively applied in water resource management due to its capacity in evaluating the trade-offs between realization of system objectives and satisfaction degrees of model constraints [19][20][21][22].…”

Environmentally sustainable stochastic procurement model

“…In addition, there are other few works which considers stochastic parameters in modeling the procurement problem. Some of these works are Gallien and Wein, (2001), He et al (2009), Ma et al , (2010), Goel and Gutierrez (2012), Xu and Huang (2013), Dong et al (2014), Wang et al (2015), Tan et al (2016) and Dai et al (2015, 2016). Table I tabulates the summary of past work on the stochastic procurement problem and its associated stochastic parameters.…”

Development of a constructed wetland network for mitigating nonpoint source pollution through a GIS-based watershed-scale inexact optimization approach

“…Sub-basin (i) 1, 3, 5, 14, 15, 17, 24, 25, 27, 31-33 2, 4, 6, 7-13, 16, 19 18, 20-23, 26, 28, 35 29, 36, 37 30, 34, 38-40 Level ( watershed belongs to a water source conservation region whose outlet is the Songhuaba reservoir, which is the source of fresh water for the 3.2 million people living in Kunming City (Dai et al, 2015). The regional climate is subtropical (humid monsoon climate), with an annual mean temperature of 12-26 C and an average precipitation of more than 1030 mm.…”

“…Moreover, because of the incompleteness and/or unavailability of required information, a number of factors and parameters (e.g., the watershed's self-purification capacity for nutrients) may be expressed as fuzzy membership functions. Recently, a number of research efforts were undertaken to deal with uncertainties C. Dai et al / Ecological Engineering xxx (2015) xxx-xxx through inexact optimization methods, such as stochastic and fuzzy mathematical programming (Cai et al, 2011a,b;Dai et al, 2015;Dong et al, 2013;Ganji et al, 2008;Han et al, 2013;Housh et al, 2012;Tan et al, 2011;Uddameri et al, 2014;Zarghami and Szidarovszky, 2009;Zeng et al, 2011;Zhang and Huang, 2011). Among them, two-stage stochastic programming (TSP), a typical stochastic mathematical programming method, is effective for tackling optimization problems where an analysis of policy scenarios is desired and the model's coefficients are random with known probability distributions (Dai et al, 2014).…”