Waste load allocation in rivers under uncertainty: application of social choice procedures

A novel integration of regret-based methodology and bankruptcy theory for waste load allocation

Developing a suitable index for Waste Load Allocation (WLA) is essential for both industrial polluters and environmental organizations. Identifying the index that best describes the quality conditions of the river is the main concern of this study. To achieve this purpose, a novel framework incorporating a regret-based index and a bankruptcy-based approach to address the impacts of low water quality and pollutant locations within the WLA are introduced. The framework includes a simulation-optimization model to minimize river quality regret for environmental organizations and total treatment cost for industrial polluters, employing Nash bargaining theory for conflict resolution. Additionally, a new bankruptcy approach, the Namin's rule, is proposed for redistributing the River Quality Regret Index among industrial polluters. Applying this methodology to data from the KhoramAbad River, a sensitivity analysis reveals that while there is no significant difference between the methodology and fuzzy risk when polluters are close, the methodology provides more accurate results as the distance between polluters increases. When the distance between two pollutants was 20 km, the sum of WLA was evaluated to be 300 kg per day higher than that in the compared method, potentially enhancing environmental justice.

River water quality management using an integrated multi-objective optimization-simulation approach based on bankruptcy rules

The aim of this research is to allocate the river's self-purification (acceptance capacity of pollution) fairly between the beneficiaries (pollutant sources) using bankruptcy theory. For this purpose, four bankruptcy rules (CAE, CEL, P, and TAL) were called using the link of the water quality simulation model (QULA2Kw) to an evolutionary optimization algorithm (multi-objective imperialist competition algorithm (MOICA)). The objective functions were reducing polluters' wastewater treatment costs and preventing biochemical oxygen demand (BOD) violations of the standard level along the river. The applicability of the approach is demonstrated by the case study that was carried out on the Dez River in Iran. According to the results, the CEL scenario is the most effective method for the Dez River when taking into account the most optimal state for both objective functions (selecting the best compromise solution from the Pareto front). This is because it has the lowest violation value of the standard level for BOD along the river when compared to other scenarios. Alternatively, when considering Solution 20, which focuses on the maximum cost of treating the polluters while staying within the acceptable level of pollution in the river, the results indicated that the CEA rule emerged as the most favorable option. This is due to its lower treatment cost (156.9 (1000$)) and higher pollution discharge to the river (681.91 g/s).

Optimal waste load allocation in river systems based on a new multi-objective cuckoo optimization algorithm

Water pollution escalates with rising waste discharge in river systems, as the rivers' limited pollution tolerance and constrained self-cleaning capacity compel the release of treated pollutants. Although several studies have shown that the non-dominated sorting genetic algorithm-II (NSGA-II) is an effective algorithm regarding the management of river water quality to reach water quality standards, to our knowledge, the literature lacks using a new optimization model, namely, the multi-objective cuckoo optimization algorithm (MOCOA). Therefore, this research introduces a new optimization framework, including non-dominated sorting and ranking selection using the comparison operator densely populated towards the best Pareto front and a trade-off estimation between the goals of discharges and environmental protection authorities. The suggested algorithm is implemented for a waste load allocation issue in Jajrood River, located in the North of Iran. The limitation of this research is that discharges are point sources. To analyze the performance of the new optimization algorithm, the simulation model is linked with a hybrid optimization model using a cuckoo optimization algorithm and non-dominated sorting genetic algorithms to convert a single-objective algorithm to a multi-objective algorithm. The findings indicate that, in terms of violation index and inequity values, MOCOA's Pareto front is superior to NSGA-II, which highlights the MOCOA's effectiveness in waste load allocation. For instance, with identical population sizes and violation indexes for both algorithms, the optimal Pareto front ranges from 1.31 to 2.36 for NSGA-II and 0.379 to 2.28 for MOCOA. This suggests that MOCOA achieves a superior Pareto front in a more efficient timeframe. Additionally, MOCOA can attain optimal equity in the smaller population size.

A new fuzzy approach and bankruptcy theory in risk estimation in Waste Load Allocation

In this paper, we developed a simulator-optimizer model based on risk analysis to determine Waste Load Allocation (WLA). A new Fuzzy index as Fuzzy Risk Index (FRI) was linked with multi-objective optimization to minimize FRI for the environmental stakeholder and the total cost of sewage treatment for the polluting industries as the other collective stakeholder. Afterwards, the conflict was resolved with the help of Nash bargaining and bankruptcy approach (Constrained Equal Awards Rule). The model was run using quantitative/qualitative data for the KhoramAbad River. To check the efficiency of FRI, the process followed for WLA was reimplemented by the Monte Carlo simulation (MCS). A comparison between the two approaches revealed that the outcomes derived from Fuzzy arithmetic across all aspects, encompassing river qualitative simulation, nondominated curve, Nash bargaining's agreed point, and bankruptcy output, closely mirrored the results of MCS. The notable distinction lies in the drastic reduction of the model's execution time by a factor of 450.

A fuzzy multi-stakeholder socio-optimal model for water and waste load allocation

This study proposes a fuzzy multi-stakeholder socio-optimal methodology for joint water and waste load allocation (WWLA) in river systems while addressing upstream flow uncertainty and different social choice rules (SCRs). QUAL2Kw, as the numerical river water quality model, is executed for various scenarios of water and waste loads to construct a comprehensive dataset of plausible settings, which is in turn used to train a meta-model in the form of multivariate linear regressions. The river upstream flow as the main uncertain parameter is assessed by fuzzy transformation method (FTM). Then, for different confidence levels of fuzzy uncertain input, the meta-model is linked with the non-dominated sorting genetic algorithm (NSGA-II) multi-objective optimization model to generate trade-off curves among the stakeholders' utility functions. Subsequently, five SCRs are utilized at each confidence level to determine the fuzzy interval solutions for each objective. Next, the possibility degree method is applied to rank the fuzzy interval solutions in each α-cut level. Finally, considering the priorities of all stakeholders, the fallback bargaining method is used to specify the most appropriate SCR in each confidence level. Application of the proposed methodology in Kor River, Iran, shows its efficacy to realize the socio-optimal WWLA scenario(s) among different stakeholders.

Planning for agricultural return flow allocation: application of info-gap decision theory and a nonlinear CVaR-based optimization model

A new methodology is proposed for sizing the required infrastructures for water and waste load allocation in river systems receiving return flow from agricultural networks. A nonlinear optimization model with a constraint based on conditional value at risk (CVaR) is developed to provide water and waste load allocation policies. The CVaR-based constraint limits the probabilistic losses due to existing uncertainties in available surface water. The deep uncertainties of return flow simulation model parameters, which have significant impacts on the simulated quantity and quality of agricultural return flows, are handled by using the info-gap theory. Total dissolved solid (TDS) is selected as water quality indicator and diverting a fraction of return flows to evaporation ponds is considered to control the TDS load of agricultural waste load dischargers. Quantity and TDS load of agricultural return flows over a 1-year cultivation period are simulated by using a calibrated SWAP agro-hydrological model. The results of many runs of SWAP model for different combinations of important uncertain parameters in their ranges of variations provide some response (impact) matrixes which are used in optimization model. The applicability of the proposed methodology is illustrated by applying it to the PayePol region in the Karkheh River catchment, southwest Iran. The selected strategy for water and waste load allocation in the study area is expected to provide total annual benefit of 48.64 million US dollars, while 7.84 million m³ of total return flow should be diverted to evaporation ponds. The results support the effectiveness of the methodology in incorporating existing deep uncertainties associated with agricultural water and waste load allocation problems.

A fuzzy multi-stakeholder multi-criteria methodology for water allocation and reuse in metropolitan areas

In this paper, a fuzzy decision making methodology is proposed to find a socially optimal scenario for allocating effluent of wastewater treatment plants and urban and suburban runoffs to agricultural regions and recharging aquifers. The presented methodology named modified fuzzy social choice (MFSC) considers multi-stakeholder multi-criteria problems under uncertainties inherent in a decision making process utilizing a fuzzy ranking method and the fuzzy social choice (FSC) theory. A set of water and wastewater allocation scenarios are proposed for water quantity and quality management of the study area, while six main stakeholders with conflicting utilities and different negotiation powers are involved. The proposed methodology is applied to Tehran metropolitan area, the capital city of Iran with the population of about 8 million people, to examine its applicability and effectiveness. The results shows that using fuzzy multi-stakeholder multi-criteria decision making method considering equal and different negotiation powers can lead to different outcomes. Based on the results, the MFSC method, which considers a number of decision makers having different negotiation powers, degrees of importance of decision making criteria, and some important uncertainties, performs more promising in real water resources management problems.

Integrated waste load allocation for river water pollution control under uncertainty: a case study of Tuojiang River, China

This paper presents a bi-level optimization waste load allocation programming model under a fuzzy random environment to assist integrated river pollution control. Taking account of the leader-follower decision-making in the water function zones framework, the proposed approach examines the decision making feedback relationships and conflict coordination between the river basin authority and the regional Environmental Protection Agency (EPA) based on the Stackelberg-Nash equilibrium strategy. In the pollution control system, the river basin authority, as the leader, allocates equitable emissions rights to different subareas, and the then subarea EPA, as the followers, reallocates the limited resources to various functional zones to minimize pollution costs. This research also considers the uncertainty in the water pollution management, and the uncertain input information is expressed as fuzzy random variables. The proposed methodological approach is then applied to Tuojiang River in China and the bi-level linear programming model solutions are achieved using the Karush-Kuhn-Tucker condition. Based on the waste load allocation scheme results and various scenario analyses and discussion, some operational policies are proposed to assist decision makers (DMs) cope with waste load allocation problem for integrated river pollution control for the overall benefits.

A decision-making framework for river water quality management under uncertainty: Application of social choice rules

An important issue in river water quality management is taking into account the role played by wastewater dischargers in the decision-making process and in the implementation of any proposed waste load allocation program in a given region. In this study, a new decision-making methodology, called 'stochastic social choice rules' (SSCR), was developed for modeling the bargaining process among different wastewater dischargers into shared environments. For this purpose, the costs associated with each treatment strategy were initially calculated as the sum of treatment cost and the fines incurred due to violation of water quality standards. The qualitative simulation model (QUAL2Kw) was then used to determine the penalty function. The uncertainty associated with the implementation of strategies under the economic costs (i.e., the sum of treatment and penalty costs) was dealt with by a Monte-Carlo selection method. This method was coupled with different social choice methods to identify the best solution for the waste load allocation problem. Finally, using the extended trading-ratio system (ETRS), the most preferred treatment strategy was exchanged among dischargers as the initial set of discharge permits aimed at reducing the costs and encouraging dischargers to participate in the river water quality protection scheme. The proposed model was finally applied to the Zarjoub River in Gilan Province, northern Iran, as a case study. Results showed the efficiency of the proposed model in developing waste load allocation strategies for rivers.

Waste load equilibrium allocation: a soft path for coping with deteriorating water systems

Waste load allocation is always regarded as another efficient approach comparing with the technology-based approach to improve the water quality. This paper proposes a bi-level multi-objective optimization model for optimally allocating the waste load of a river basin incorporating some concerns (i) the allocation equity from the regional authority, (ii) maximal benefits from the subareas along the river, and (iii) the Stackelberg-Nash-Cournot equilibrium strategy between the upper and lower decision makers. Especially, a novel Gini coefficient for measuring the load allocation equity is defined by considering the economic level and waste water quantity. The applicability and effectiveness of the proposed model is demonstrated through a practical case based on the Tuojiang River, which is a typical basin with diversified industrial waste discharges in western China. Some operational suggestions are developed to assist the decision makers' cope with deteriorating water systems.