Waste Load Allocation (WLA) in rivers refers to the determination of required pollutant fractional removal levels at a set of point sources of pollution to ensure that water quality standards are maintained throughout the system. Optimal waste load allocation implies that the selected pollution treatment vector not only maintains the water quality standards, but also results in the best value for the objective function defined for the management problem. Waste load allocation problems are characterized by uncertainties due to the randomness and imprecision. Uncertainty due to randomness arises mainly due to the random nature of the variables influencing the water quality. Uncertainty due to imprecision or fuzziness is associated with setting up the water quality standards and goals of the Pollution Control Agencies (PCA), and the dischargers (e.g., industries and municipal dischargers). Many decision problems in water resources applications are dominated by natural, extreme, rarely occurring, uncertain events. However usually such events will be absent or be rarely present in the historical records. Due to the scarcity of information of these uncertain events, a realistic decision-making becomes difficult. Furthermore, water resources planners often deal with imprecision, mostly due to imperfect knowledge and insufficient or inadequate data. Therefore missing data is very common in most water resources decision problems. Missing data introduces inaccuracy in analysis and evaluation. For instance, the sample mean of the available data can be an inaccurate estimate of the mean of the complete data. Use of sample statistics estimated from inadequate samples in WLA models would lead to incorrect decisions. Therefore there is a necessity to incorporate the uncertainty due to missing data also in WLA models in addition to the uncertainties due to randomness and imprecision. The uncertainty in the input parameters due to missing or inadequate data renders the input parameters (such as mean and variance) as interval grey parameters in water quality decision-making. In a Fuzzy Waste Load Allocation Model (FWLAM), randomness and imprecision both can be addressed simultaneously by using the concept of fuzzy risk of low water quality (Mujumdar and Sasikumar, 2002). In the present work, an attempt is made to also address uncertainty due to partial ignorance due to missing data or inadequate data in the samples of input variables in FWLAM, considering the fuzzy risk approach proposed by Mujumdar and Sasikumar (2002). To address the uncertainty due to missing data or inadequate data, the input parameters (such as mean and variance) are considered as interval grey numbers. The resulting output water quality indicator (such as DO) will also, consequently, be an interval grey number. The fuzzy risk will also be interval grey number when output water quality indicator is an interval grey number. A methodology is developed for the computation of grey fuzzy risk of low water quality, when the input variables are characterized by uncertainty due to partial ignorance resulting from missing or inadequate data in the samples of input variables. To achieve this, an Imprecise Fuzzy Waste Load Allocation Model (IFWLAM) is developed for water quality management of a river system to address uncertainties due to randomness, fuzziness and also due to missing data or inadequate data. Monte Carlo Simulation (MCS) incorporating a water quality simulation model is performed two times for each set of randomly generated input variables: once for obtaining the upper bound of DO and once for the lower bound of DO, by using appropriate upper or lower bounds of interval grey input variables. These two bounds of DO are used in the estimation of grey fuzzy risk by substituting the upper and lower values of fuzzy membership functions of low water quality. A backward finite difference scheme (Chapra, 1997) is used to solve the water quality simulation model. The goal of PCA is to minimize the bounds of grey fuzzy risk, whereas the goal of dischargers is to minimize the fractional removal levels. The two sets of goals are conflicting with each other. Fuzzy multiobjective optimization technique is used to formulate the multiobjective model to provide best compromise solutions. Probabilistic Global Search Lausanne (PGSL) method is used to solve the optimization problem. Finally the results of the model are compared with the results of risk minimization model (Ghosh and Mujumdar, 2006), when the methodology is applied to the case study of the Tunga-Bhadra river system in South India. The model is capable of determining a grey fuzzy risk with the corresponding bounds of DO, at each check point, rather than specifying a single value of fuzzy risk as done in a Fuzzy Waste Load Allocation Model (FWLAM). The IFWLAM developed is based on fuzzy multiobjective optimization problem with ‘max-min’ as the operator, which usually may not result in a unique solution and there exists a possibility of obtaining multiple solutions (Karmakar and Mujumdar, 2006b). Karmakar and Mujumdar (2006b) developed a two-phase Grey Fuzzy Waste Load Allocation Model (two-phase GFWLAM), to determine the widest range of interval-valued optimal decision variables, resulting in the same value of interval-valued optimal goal fulfillment level as obtained from GFWLAM (Karmakar and Mujumdar 2006a). Following Karmakar and Mujumdar (2006b), two optimization models are developed in this study to capture all the decision alternatives or multiple solutions: one to maximize and the other to minimize the summation of membership functions of the dischargers by keeping the maximum goal fulfillment level same as that obtained in IFWLAM to obtain a lower limit and an upper limit of fractional removal levels respectively. The aim of the two optimization models is to obtain a range of fractional removal levels for the dischargers such that the resultant grey fuzzy risk will be within acceptable limits. Specification of a range for fractional removal levels enhances flexibility in decision-making. The models are applied to the case study of Tunga-Bhadra river system. A range of upper and lower limits of fractional removal levels is obtained for each discharger; within this range, the discharger can select the fractional removal level so that the resulting grey fuzzy risk will also be within specified bounds. In IFWLAM, the membership functions are subjective, and lower and upper bounds are arbitrarily fixed. Karmakar and Mujumdar (2006a) developed a Grey Fuzzy Waste Load Allocation Model (GFWLAM), in which uncertainty in the values of membership parameters is quantified by treating them as interval grey numbers. Imprecise membership functions are assigned for the goals of PCA and dischargers. Following Karmakar and Mujumdar (2006a), a Grey Optimization Model with Grey Fuzzy Risk is developed in the present study to address the uncertainty in the memebership functions of IFWLAM. The goals of PCA and dischargers are considered as grey fuzzy goals with imprecise membership functions. Imprecise membership functions are assigned to the fuzzy set of low water quality and fuzzy set of low risk. The grey fuzzy risk approach is included to account for the uncertainty due to missing data or inadequate data in the samples of input variables as done in IFWLAM. Randomness and imprecision associated with various water quality influencing variables and parameters of the river system are considered through a Monte-Carlo simulation when input parameters (such as mean and variance) are interval grey numbers. The model application is demonstrated with the case study of Tunga-Bhadra river system in South India. Finally the results of the model are compared with the results of GFWLAM (Karmakar and Mujumdar, 2006a). For the case study of Tunga Bhadra River system, it is observed that the fractional removal levels are higher for Grey Optimization Model with Grey Fuzzy Risk compared to GFWLAM (Karmakar and Mujumdar, 2006a) and therefore the resulting risk values at each check point are reduced to a significant extent. The models give a set of flexible policies (range of fractional removal levels). Corresponding optimal values of goal fulfillment level and the grey fuzzy risk are all in terms of interval grey numbers. The IFWLAM and Grey Fuzzy Optimization Model with Grey Fuzzy Risk, developed in the study do not limit their application to any particular pollutant or water quality indicator in the river system. Given appropriate transfer functions for spatial distribution of the pollutants in water body, the models can be used for water quality management of any general river system.

Para implantação de diversas funções de controle e operação em tempo real em Sistemas de Distribuição (SDs), como, por exemplo, restabelecimento de energia, é necessário um procedimento para representar a carga em tempo real. Ou seja, uma metodologia que possibilite a estimação em tempo real das demandas dos transformadores de distribuição que em geral não são monitoradas de forma direta. Para esse fim propõe-se, neste trabalho, um Estimador de Demanda em Tempo Real (EDTR) baseado em: informações off-line (consumo mensal dos consumidores e curvas de carga típicas); um algoritmo computacionalmente eficiente para cálculo de fluxo de potência baseado na estrutura de dados denominada Representação Nó-Profundidade (RNP); e nas poucas medidas disponíveis em tempo real nos SDs. O EDTR proposto opera em dois estágios: (1) Estimação Off-line das Demandas; e (2) Refinamento em Tempo Real das Demandas, executados em instantes diferentes (um de maneira off-line e outro em tempo real), de forma a prover uma estimativa das demandas dos transformadores de distribuição. Considerando somente as informações off-line, o EDTR proposto permite a estimação das demandas dos transformadores de distribuição com uma medida da incerteza da estimativa. Através do processamento das medidas disponíveis em tempo real, via um algoritmo eficiente para cálculo de fluxo de potência, o EDTR proposto permite o refinamento das estimativas off-line. Neste trabalho serão apresentados resultados de diversas simulações computacionais demonstrando a eficiência do EDTR proposto. Alguns parâmetros são avaliados quanto à influência nas estimativas do EDTR proposto, como a presença de erros grosseiros nas medidas disponíveis em tempo real e alimentadores somente com medidas de magnitude de corrente. Além disto, destaca-se a influência da qualidade das estimativas iniciais obtidas pelo Estágio (1), e a importância das hipóteses estatísticas utilizadas nesse estágio para o processo de estimação. Apresenta-se, ainda, a aplicação do EDTR proposto em um SD real brasileiro. Um teste de validação foi realizado através de uma campanha de medição em um alimentador real, que consistiu na instalação de medidores de demanda em três transformadores de distribuição para aferir a qualidade das estimativas obtidas pelo EDTR proposto. Finalmente, o EDTR proposto é aplicado em um SD real de larga escala, para aferir o desempenho computacional da metodologia implantada e as dificuldades de implantação. Vale ressaltar que sua implantação é condizente com ferramentas consolidadas nos Centros de Operação da Distribuição, como o uso do processo de agregação de cargas e o cálculo de fluxo de potência, e poucas rotinas precisam ser adicionadas para integração do EDTR. / Several real time control and operation applications for Distribution Systems (DS), such as, service restoration, require a procedure for real time load modeling. That is, a methodology for real time estimation of the distribution transformers loading which are generally not monitored. For this purpose, in this dissertation, a Real Time Load Estimator (RTLE) is proposed based on: off-line information (monthly consumption and typical load curves); a computationally efficient algorithm for power flow calculation based on the data structure called Node-Depth Encoding; and on the few available real time measurements on the distribution system. The proposed RTLE operates in two stages: (1) Off-line Load Estimation and (2) Real Time Load Refinement, performed in different moments (one off-line and the other in real time), providing the distribution transformers load estimates. Using only the offline information, the proposed RTLE allows the estimation of the loads of the distribution transformers with a measure of uncertainty. By processing the available real time measurements, using an efficient power flow calculation algorithm, the proposed RTLE refines these off-line estimates. This dissertation presents several simulations showing the efficiency of the proposed RTLE. Some parameters are evaluated and their influence on the RTLE load estimates, such as gross errors in the available real time measurements and feeders with only current magnitude measurements. Besides, it is emphasized the influence of the initial load estimates obtained from Stage (1), and the importance of the statistical hypothesis used in this stage in the load estimation process. Also, this work presents the application of the proposed RTLE in a real Brazilian DS. A validation test was performed through in-field verification in a real distribution feeder, which was executed via load meters installation in three distribution transformers to evaluate the quality of the load estimates provided by the RTLE. Finally, the proposed RTLE was tested in a real large scale DS to evaluate its computational performance and the difficult level of its implementation. It is noteworthy that its implementation is straightforward with other Distribution Operation Center tools, such as load aggregation and load flow calculation, and few routines must be added for integrating the RTLE.

Para implantação de diversas funções de controle e operação em tempo real em Sistemas de Distribuição (SDs), como, por exemplo, restabelecimento de energia, é necessário um procedimento para representar a carga em tempo real. Ou seja, uma metodologia que possibilite a estimação em tempo real das demandas dos transformadores de distribuição que em geral não são monitoradas de forma direta. Para esse fim propõe-se, neste trabalho, um Estimador de Demanda em Tempo Real (EDTR) baseado em: informações off-line (consumo mensal dos consumidores e curvas de carga típicas); um algoritmo computacionalmente eficiente para cálculo de fluxo de potência baseado na estrutura de dados denominada Representação Nó-Profundidade (RNP); e nas poucas medidas disponíveis em tempo real nos SDs. O EDTR proposto opera em dois estágios: (1) Estimação Off-line das Demandas; e (2) Refinamento em Tempo Real das Demandas, executados em instantes diferentes (um de maneira off-line e outro em tempo real), de forma a prover uma estimativa das demandas dos transformadores de distribuição. Considerando somente as informações off-line, o EDTR proposto permite a estimação das demandas dos transformadores de distribuição com uma medida da incerteza da estimativa. Através do processamento das medidas disponíveis em tempo real, via um algoritmo eficiente para cálculo de fluxo de potência, o EDTR proposto permite o refinamento das estimativas off-line. Neste trabalho serão apresentados resultados de diversas simulações computacionais demonstrando a eficiência do EDTR proposto. Alguns parâmetros são avaliados quanto à influência nas estimativas do EDTR proposto, como a presença de erros grosseiros nas medidas disponíveis em tempo real e alimentadores somente com medidas de magnitude de corrente. Além disto, destaca-se a influência da qualidade das estimativas iniciais obtidas pelo Estágio (1), e a importância das hipóteses estatísticas utilizadas nesse estágio para o processo de estimação. Apresenta-se, ainda, a aplicação do EDTR proposto em um SD real brasileiro. Um teste de validação foi realizado através de uma campanha de medição em um alimentador real, que consistiu na instalação de medidores de demanda em três transformadores de distribuição para aferir a qualidade das estimativas obtidas pelo EDTR proposto. Finalmente, o EDTR proposto é aplicado em um SD real de larga escala, para aferir o desempenho computacional da metodologia implantada e as dificuldades de implantação. Vale ressaltar que sua implantação é condizente com ferramentas consolidadas nos Centros de Operação da Distribuição, como o uso do processo de agregação de cargas e o cálculo de fluxo de potência, e poucas rotinas precisam ser adicionadas para integração do EDTR. / Several real time control and operation applications for Distribution Systems (DS), such as, service restoration, require a procedure for real time load modeling. That is, a methodology for real time estimation of the distribution transformers loading which are generally not monitored. For this purpose, in this dissertation, a Real Time Load Estimator (RTLE) is proposed based on: off-line information (monthly consumption and typical load curves); a computationally efficient algorithm for power flow calculation based on the data structure called Node-Depth Encoding; and on the few available real time measurements on the distribution system. The proposed RTLE operates in two stages: (1) Off-line Load Estimation and (2) Real Time Load Refinement, performed in different moments (one off-line and the other in real time), providing the distribution transformers load estimates. Using only the offline information, the proposed RTLE allows the estimation of the loads of the distribution transformers with a measure of uncertainty. By processing the available real time measurements, using an efficient power flow calculation algorithm, the proposed RTLE refines these off-line estimates. This dissertation presents several simulations showing the efficiency of the proposed RTLE. Some parameters are evaluated and their influence on the RTLE load estimates, such as gross errors in the available real time measurements and feeders with only current magnitude measurements. Besides, it is emphasized the influence of the initial load estimates obtained from Stage (1), and the importance of the statistical hypothesis used in this stage in the load estimation process. Also, this work presents the application of the proposed RTLE in a real Brazilian DS. A validation test was performed through in-field verification in a real distribution feeder, which was executed via load meters installation in three distribution transformers to evaluate the quality of the load estimates provided by the RTLE. Finally, the proposed RTLE was tested in a real large scale DS to evaluate its computational performance and the difficult level of its implementation. It is noteworthy that its implementation is straightforward with other Distribution Operation Center tools, such as load aggregation and load flow calculation, and few routines must be added for integrating the RTLE.

[pt] Em sistemas de distribuição de energia elétrica, um dos maiores desafios para as distribuidoras é a estimação das perdas técnicas. De acordo com a bibliografia, as perdas elétricas nas redes de distribuição em diferentes países podem variar aproximadamente de 3 porcento e 25 porcento da energia fornecida à rede, o que pode significar grandes impactos nos custos do sistema. Especificamente no Brasil, a adequada avaliação das perdas elétricas fornece informação importante para que o regulador estabeleça as tarifas de distribuição de energia elétrica. Na literatura há diversos métodos para a estimação das perdas técnicas de energia, mas devido à dificuldade na modelagem dos equipamentos do sistema, assim como a falta de informação da energia consumida pelas cargas, as estimações podem acarretar em grandes erros. Para tratar este problema, esta dissertação propõe um novo método baseado em um modelo de carga polinomial modificado para estimar as perdas elétricas, considerando medições de tensão e potência na subestação e, quando disponíveis, medições de tensão e potência demandadas pelas cargas. A contribuição principal do método proposto é o uso da informação da topologia da rede e a correlação entre a potência consumida pelas cargas e as grandezas medidas na subestação. Para detalhar e analisar o desempenho do método proposto são utilizados três sistemas elétricos. Os resultados das estimações são comparados com os resultados obtidos por outros métodos de referência encontradas na literatura e em aplicações práticas. / [en] In electrical distribution systems, one of the greatest challenges for utilities is the estimation of technical losses. According to the literature, energy losses throughout the world s electric distribution networks may vary from country to country approximately between 3 percent and 25 percent of the electricity provided, which may cause great impacts on the electrical system costs. Specifically in Brazil, the appropriate evaluation of the energy losses provides valuable information for the regulator to establish the energy distribution tariffs. In literature, there are different ways for estimating energy losses, but due to the difficulty for modeling precisely the equipment of the system, as well as the lack of information regarding the energy consumed of each load, the energy losses estimation may lead to huge errors. To deal with this problem, it is proposed a new method based on a modified load model, taking into account the measurements of voltages and power at the substation and, when available, the measurements of voltages and power demanded by loads with meters installed. The main contribution of the proposed method is the use of the network information and the correlation between the power consumed by the loads and the voltage and power supplied by the substation. In order to detail and analyze the performance of the proposed method, three electric systems are used. The results of the estimations given by the proposed method are compared to those obtained with other methods found in literature and in practical applications.

Este trabalho propõe estudos de casos em sistemas de energia elétrica por meio do Fluxo de Potência Ótimo (FPO) e da Análise de Sensibilidade em diferentes cenários de operação. Para isso, foram obtidos dados teóricos, a partir de levantamento bibliográfico, que explicitaram os conceitos de otimização aplicados ao sistema estático de energia elétrica. A pesquisa fundamentou-se metodologicamente no método primal-dual barreira logarítmica e nas condições necessárias de primeira-ordem de Karush-Kuhn-Tucker (KKT) para o problema de FPO, e no teorema proposto por Fiacco (1976) para a Análise de Sensibilidade. Os sistemas de equações resultantes das condições de estacionaridade, da função Lagrangiana, foram resolvidos pelo método de Newton. Na implementação computacional foram usadas técnicas de esparsidade. Estudos de casos foram realizados nos sistemas 3, IEEE 14, 30, 118, 300 barras e no equivalente CESP 440 kV com 53 barras, em que foi verificada a eficiência das técnicas apresentadas. / This work proposes a study of cases in power systems by Optimal Power Flow (OPF) and Sensitivity Analysis in different operation scenarios. For this purpose, theoretical data were obtained, starting from a bibliographical review, which enlightened the optimization concepts applied to the static system of electrical energy. The research was methodologically based on the primal-dual logarithmic barrier method and in the first-order necessary Karush-Kuhn-Tucker conditions to the OPF problem and in the theorem proposed by Fiacco (1976) to the Sensitivity Analysis. The equation sets generated by the first-order necessary conditions of the Lagrangian function, were solved by Newton\'s method. In the computational implementation, sparsity techniques were used. Studies of cases were carried out in the 3, IEEE 14, 30, 118, 300 buses and in the equivalent CESP 440 kV 53 bus, where the efficiency of the presented techniques was verified.

Este trabalho propõe estudos de casos em sistemas de energia elétrica por meio do Fluxo de Potência Ótimo (FPO) e da Análise de Sensibilidade em diferentes cenários de operação. Para isso, foram obtidos dados teóricos, a partir de levantamento bibliográfico, que explicitaram os conceitos de otimização aplicados ao sistema estático de energia elétrica. A pesquisa fundamentou-se metodologicamente no método primal-dual barreira logarítmica e nas condições necessárias de primeira-ordem de Karush-Kuhn-Tucker (KKT) para o problema de FPO, e no teorema proposto por Fiacco (1976) para a Análise de Sensibilidade. Os sistemas de equações resultantes das condições de estacionaridade, da função Lagrangiana, foram resolvidos pelo método de Newton. Na implementação computacional foram usadas técnicas de esparsidade. Estudos de casos foram realizados nos sistemas 3, IEEE 14, 30, 118, 300 barras e no equivalente CESP 440 kV com 53 barras, em que foi verificada a eficiência das técnicas apresentadas. / This work proposes a study of cases in power systems by Optimal Power Flow (OPF) and Sensitivity Analysis in different operation scenarios. For this purpose, theoretical data were obtained, starting from a bibliographical review, which enlightened the optimization concepts applied to the static system of electrical energy. The research was methodologically based on the primal-dual logarithmic barrier method and in the first-order necessary Karush-Kuhn-Tucker conditions to the OPF problem and in the theorem proposed by Fiacco (1976) to the Sensitivity Analysis. The equation sets generated by the first-order necessary conditions of the Lagrangian function, were solved by Newton\'s method. In the computational implementation, sparsity techniques were used. Studies of cases were carried out in the 3, IEEE 14, 30, 118, 300 buses and in the equivalent CESP 440 kV 53 bus, where the efficiency of the presented techniques was verified.

Este artículo tiene como objetivo solucionar el problema de ineficiencia, representado por el bajo nivel de servicio en el sistema de distribución de la planta de combustible, ya que se han presentado retrasos desde el inicio del proceso hasta el final de este. Por este motivo, se analizó todo el flujo del sistema para determinar en qué parte del proceso estaba la causa principal, lo que ayudaría a reducir considerablemente el problema. Se propuso aplicar un sistema de citas para estandarizar los tiempos de servicio, así como la implementación de un algoritmo y el uso de mecanismos eficientes para derivar la mejor solución robusta que responda a todas las incertidumbres con tiempos de ejecución reducidos. / This article aims to solve the inefficiency problem, represented by the low service level, in the fuel plant distribution system, since there have been delays from the beginning of the process to the end of this. For this reason, the entire flow of the system was analyzed in order to determine where in the process the main cause was, which would help reduce this problem considerably. It was proposed to apply an appointment system to standardize service times as well as the implementation of an algorithm and the use of efficient mechanisms to derive the best robust solution that responds to all uncertainties with reduced execution times. / Trabajo de investigación

In this study, methodologies for modeling grey uncertainty in water resources systems are developed, specifically for the problems in two identified areas in water resources: waste load allocation in streams and floodplain planning. A water resources system is associated with some degree of uncertainty, due to randomness of hydrologic and hydraulic parameters, imprecision and subjectivity in management goals, inappropriateness in model selection, inexactness of different input parameters for inadequacy of data, etc. Uncertainty due to randomness of input parameters could be modeled by the probabilistic models, when probability distributions of the parameters may be estimated. Uncertainties due to imprecision in the management problem may be addressed by the fuzzy decision models. In addition, some parameters in any water resources problems need to be addressed as grey parameters, due to inadequate data for an accurate estimation but with known extreme bounds of the parameter values. Such inexactness or grey uncertainty in the model parameters can be addressed by the inexact or grey optimization models, representing the parameters as interval grey numbers. The research study presented in this thesis deals with the development of grey and fuzzy optimization models, and the combination of the two for water resources systems decision-making. Three grey fuzzy optimization models for waste load allocation, namely (i) Grey Fuzzy Waste Load Allocation Model (GFWLAM), (ii) two-phase GFWLAM and (iii) multiobjective GFWLAM, and a Grey Integer Programming (GIP) model for floodplain planning, are developed in this study. The Grey Fuzzy Waste Load Allocation Model (GFWLAM) for water quality management of river system addresses uncertainty in the membership functions for imprecisely stated management goals of the Pollution Control Agency (PCA) and dischargers. To address the imprecision in fixing the boundaries of membership functions (also known as membership parameters), the membership functions themselves are treated as imprecise in the model and the membership parameters are expressed as interval grey numbers. The conflict between the fuzzy goals of PCA and dischargers is modeled using the concept of fuzzy decision, but because of treating the membership parameters as interval grey numbers, in the present study, the notion of ‘fuzzy decision’ is extended to the notion of ‘grey fuzzy decision’. A terminology ‘grey fuzzy decision’ is used to represent the fuzzy decision resulting from the imprecise membership functions. The model provides flexibility for PCA and dischargers to specify their aspirations independently, as the membership parameters for membership functions are interval grey numbers in place of a deterministic real number. In the solution, optimal fractional removal levels of the pollutants are obtained in the form of interval grey numbers. This enhances the flexibility and applicability in decision-making, as the decision-maker gets a range of optimal solutions for fixing the final decision scheme considering technical and economic feasibility of the pollutant treatment levels. The methodology is demonstrated with the case studies of a hypothetical river system and the Tunga-Bhadra river system in Karnataka, India. Formulation of GFWLAM is based on the approach for solving fuzzy multiple objective optimization problem using max-min as the operator, which usually may not result in a unique solution. The two-phase GFWLAM captures all the alternative optimal solutions of the GFWLAM. The solution technique in the Phase 1 of two-phase GFWLAM is the same as that of GFWLAM. The Phase 2 maximizes upper bounds and minimizes lower bounds of decision variables, keeping the optimal value of goal fulfillment level same as obtained in the Phase 1. The two-phase GFWLAM gives the unique, widest, intervals of the optimal fractional removal levels of pollutant corresponding to the optimal value of goal fulfillment level. The solution increases the widths of interval-valued fractional removal levels of pollutants by capturing all the alternative optimal solutions and thus enhances the flexibility and applicability in decision-making. The model is applied to the case study of Tunga-Bhadra river system, which shows the existence of multiple solutions when the GFWLAM is applied to the same case study. The width of the interval of optimal fractional removal level plays an important role in the GFWLAM, as more width in the fractional removals implies a wider choice to the decision-makers and more applicability in decision-making. The multiobjective GFWLAM maximizes the width of the interval-valued fractional removal levels for providing a latitude in decision-making and minimizes the width of goal fulfillment level for reducing the system uncertainty. The multiobjective GFWLAM gives a new methodology to get a satisfactory deterministic equivalent of a grey fuzzy optimization problem, using the concept of acceptability index for a meaningful ranking between two partially or fully overlapping intervals. The resulting multiobjective optimization model is solved by fuzzy multiobjective optimization technique. The consistency of the solution is verified by solving the problem with fuzzy goal programming technique. The multiobjective GFWLAM avoids intermediate submodels unlike GFWLAM, so that the solution from a single deterministic equivalent of the GFWLAM adequately covers all possible situations. Although the solutions obtained from multiobjective GFWLAM provide more flexibility than those of the GFWLAM, its application is limited to grey fuzzy goals expressed by linear imprecise membership functions only, whereas GFWLAM has the capability to solve the model with any monotonic nonlinear imprecise membership functions also. The methodology is demonstrated with the case studies of a hypothetical river system and the Tunga-Bhadra river system in Karnataka, India. The Grey Integer Programming (GIP) model for floodplain planning is based on the floodplain planning model developed by Lund (2002), to identify an optimal mix of flood damage reduction options with probabilistic flood descriptions. The model demonstrates how the uncertainty of various input parameters in a floodplain planning problem can be modeled using interval grey numbers in the optimization model. The GIP model for floodplain planning does not replace a post-optimality analysis (e.g., sensitivity analysis, dual theory, parametric programming, etc.), but it provides additional information for interpretation of the optimal solutions. The results obtained from GIP model confirm that the GIP is a useful technique for interpretation of the solutions particularly when a number of potential feasible measures are available in a large scale floodplain planning problem. Though the present study does not directly compare the GIP technique with sensitivity analysis, the results indicate that the rigor and extent of post-optimality analyses may be reduced with the use of GIP for a large scale floodplain planning problem. Application of the GIP model is demonstrated with the hypothetical example as presented in Lund (2002).