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Journal ArticleDOI

Mixed-Integer Programming Model for Reservoir Performance Optimization

01 Sep 1999-Journal of Water Resources Planning and Management (American Society of Civil Engineers)-Vol. 125, Iss: 5, pp 298-301
Abstract: Failures in operation of water supply reservoir systems are often unavoidable during critical hydrologic periods. The failure characteristics of such systems can be represented by performance indicators such as reliability, resilience, and vulnerability. A mixed-integer programming model for the operation of a water supply reservoir during critical periods has been presented in the literature that incorporates these performance indicators. An improved formulation of this model that represents resilience more completely is discussed herein. In addition, a set of constraints with binary integer variables are included to account for reservoir spills. The improvements achieved with the modified model is demonstrated using the same example as presented with the original model.
Citations
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Journal ArticleDOI
TL;DR: A behaviour analysis addressing monotonic behaviour, overlap and correlation between the estimators of water resources system reliability, resilience and vulnerability was carried out by routing time series of monthly runoff through a reservoir with a specified storage volume.
Abstract: Definitions and estimators of water resources system reliability (the probability that the system will remain in a non-failure state), resilience (the ability of the system to return to non-failure state after a failure has occurred) and vulnerability (the likely damage of a failure event) have been thoroughly investigated. A behaviour analysis addressing monotonic behaviour, overlap and correlation between the estimators was carried out by routing time series of monthly runoff through a reservoir with a specified storage volume that is operated according to a fixed operation policy. Estimation based on historical time series is shown to be problematic and a procedure encompassing generation of synthetic time series with a length of at least 1000 years is recommended in order to stabilize the estimates. Moreover, the strong correlation between resilience and vulnerability may suggest that resilience should not be explicitly accounted for.

154 citations


Cites background or result from "Mixed-Integer Programming Model for..."

  • ...Srinivasan et al. (1999) highlighted the same urther argued that using the maximum duration might mask resilient...

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  • ...The high negative correlation indicates that reliable systems tend to have a high degree of resilience (keeping in mind that the experiment considers the correlation between reliability and the inverse of resilience), which corresponds to the findings of others, for example, Kundzewicz & Kindler (1995) and Srinivasan et al. (1999). All three methods of estimating resilience gave correlation coefficients of the same order of magnitude....

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  • ...…that reliable systems tend to have a high degree of resilience (keeping in mind that the experiment considers the correlation between reliability and the inverse of resilience), which corresponds to the findings of others, for example, Kundzewicz & Kindler (1995) and Srinivasan et al. (1999)....

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  • ...Srinivasan et al. (1999) highlighted the same urther argued that using the maximum duration might mask resilient Thomas Rodding Kjeldsen & Dan Rosbjerg 758 behaviour in the rest of the series compared to other series with shorter maximum duration but more non-resilient behaviour in the remaining…...

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  • ...…(1982), the use of the additional risk criteria of resilience and vulnerability has been widely discussed; see for example, Moy et al. (1986), Jinno et al. (1995), Kundzewicz & Laski (1995), Vogel & Bolognese (1995), Kundzewicz & Kindler (1995), Srinivasan et al. (1999) and Vogel et al. (1999)....

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Journal ArticleDOI
TL;DR: A mixed integer fuzzy interval-stochastic programming model was developed for supporting the improvement of eco-resilience to floods in wetlands and indicates that the model is helpful for supporting adjustment or justification of allocation patterns of ecological flood-resisting capacities, and analysis of interactions among multiple administrative targets within a wetland.
Abstract: In this study, a mixed integer fuzzy interval-stochastic programming model was developed for supporting the improvement of eco-resilience to floods in wetlands. This method allows uncertainties that are associated with eco-resilience improvement and can be presented as both probability distributions and interval values to be incorporated within a general modeling framework. Also, capacity-expansion plans of eco-resilience can be addressed through introducing binary variables. Moreover, penalties due to ecological damages which are associated with the violation of predefined targets can be effectively incorporated within the modeling and decision process. Thus, complexities associated with flood resistance and eco-resilience planning in wetlands can be systematically reflected, highly enhancing robustness of the modeling process. The developed method was then applied to a case of eco-resilience enhancement planning in three ecologically vulnerable regions of a wetland. Interval solutions under different river flow levels and different ecological damages were generated. They could be used for generating decision alternatives and thus help decision makers identify desired eco-resilience schemes to resist floods without causing too much damages. The application indicates that the model is helpful for supporting: (a) adjustment or justification of allocation patterns of ecological flood-resisting capacities, (b) formulation of local policies regarding eco-resilience enhancement options and policy interventions, and (c) analysis of interactions among multiple administrative targets within a wetland.

103 citations


Additional excerpts

  • ...Moreover, due to its effectiveness n determining capacity-expansion options, mixed integer linear rogramming (MILP) was frequently used for flooding mitigation nd adaptation planning (Day and Weisz, 1976; Windsor, 1981; andall et al., 1997; Srinivasan et al., 1999; Needham et al., 2000; lsen et al., 2000)....

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Book
18 Dec 2008-
Abstract: Thesis (Ph. D.)--Massachusetts Institute of Technology, Engineering Systems Division, 2005.

91 citations


Cites background from "Mixed-Integer Programming Model for..."

  • ...Besides the literature mentioned in the section for water resources planning, Srinivasan, Neelakantan, Narayan, and Nagarajukumar (1999) presented a mixed-integer programming model for the operation of a water supply reservoir during critical periods that incorporates important performance…...

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  • ...Besides the literature mentioned in the section for water resources planning, Srinivasan, Neelakantan, Narayan, and Nagarajukumar (1999) presented a mixed-integer programming model for the operation of a water supply reservoir during critical periods that incorporates important performance indicators, such as reliability, resilience, and vulnerability....

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Journal ArticleDOI
Abstract: Innovative prevention, adaptation, and mitigation approaches as well as policies for sustainable flood management continue to be challenges faced by decision-makers. In this study, a mixed interval–fuzzy two-stage integer programming (IFTIP) method is developed for flood-diversion planning under uncertainty. This method improves upon the existing interval, fuzzy, and two-stage programming approaches by allowing uncertainties expressed as probability distributions, fuzzy sets, and discrete intervals to be directly incorporated within the optimization framework. In its modelling formulation, economic penalties as corrective measures against any infeasibilities arising because of a particular realization of the uncertainties are taken into account. The method can also be used for analysing a variety of policy scenarios that are associated with different levels of economic penalties. A management problem in terms of flood control is studied to illustrate the applicability of the proposed approach. The results...

90 citations


Cites background from "Mixed-Integer Programming Model for..."

  • ...A number of linear and mixed integer-linear programming methods have been developed to support flood management decisions (Day and Weisz 1976, Windsor 1981, Randall et al. 1997, Correia et al. 1998, Srinivasan et al. 1999, Needham et al. 2000, Olsen et al. 2000,Wang and Du 2003, Wang et al. 2003)....

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Journal ArticleDOI
Abstract: This paper reviews existing approaches to system resilience, and proposes a scheme to quantify the resilience of water resource systems. In general, three aspects of resilience are considered in water resource systems: (1) that against crossing a performance threshold; (2) that for response and recovery after disturbances; and (3) that of adaptive capacity. Conventionally these aspects are treated separately without considering possible functional relationships or interdependencies. We argue that the adaptive capacity of the system is better treated as an input variable of the other two aspects of resilience, and that response/recovery may be considered only when the performance threshold is not crossed. Because of the dynamic and evolving nature of water resource systems, proper consideration of uncertainty and associated information, whether obtained from well-defined numerical data or vague linguistic articulation, is essential for better understanding and proper management of their resilience. Constan...

85 citations


References
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Journal ArticleDOI
Abstract: Three criteria for evaluating the possible performance of water resource systems are discussed. These measures describe how likely a system is to fail (reliability), how quickly it recovers from failure (resiliency), and how severe the consequences of failure may be (vulnerability). These criteria can be used to assist in the evaluation and selection of alternative design and operating policies for a wide variety of water resource projects. The performance of a water supply reservoir with a variety of operating policies illustrates their use.

1,286 citations


Journal ArticleDOI
Abstract: With the aid of a linear decision rule, reservoir management and design problems often can be formulated as easily solved linear programing problems. The linear decision rule specifies the release during any period of reservoir operation as the difference between the storage at the beginning of the period and a decision parameter for the period. The decision parameters for the entire study horizon are determined by solving the linear programing problem. Problems may be formulated in either the deterministic or the stochastic environment.

284 citations


Journal ArticleDOI
Abstract: Reliability in water supply reservoir operation is commonly thought of as the probability of failing to achieve some target release. Here we explore two additional proposed descriptions of reservoir performance: the maximum shortfall from the target (system vulnerability) and the maximum number of consecutive periods of deficit during a record (system resilience). The larger the maximum shortfall, the greater the vulnerability. The shorter the maximum length of deficits, the more resilient the system. Using multiobjective mixed-integer, linear programming, the tradeoffs between reliability, vulnerability, and resilience are examined. It is found that as reliability is increased or as the maximum length of consecutive shortfalls decreases (resilience increases), the vulnerability of the water system to larger deficits increases.

242 citations


Journal ArticleDOI
Abstract: Demand-management policy rules are sought during drought and impending drought for a water system consisting of a reservoir dedicated only to water supply. The creation of such rules requires solution of a nonlinear, nonseparable mathematical programming problem. A polytope search algorithm using a combination of simulation and optimization is compared to an iterative mixed integer programming method to determine the parameters of continuous demand management rules. The signal used for calling rationing is a trigger volume given in terms of months of demand (as a volume) that are needed in storage. When the sum of actual storage plus anticipated inflow is less than the trigger volume, rationing is initiated. The extent of rationing or demand reduction that is required is determined by the ration of the sum of storage plus inflow to the trigger volume. The two methodologies for parameter determination are compared using as a criteria the maximum shortage that occurs over some planning period.

129 citations


Journal ArticleDOI
TL;DR: A mixed integer programming model is constructed for the operation of a single water supply reservoir during drought and impending drought and determines trigger volumes of storage plus anticipated inflow which signal the need for each of the several phases of rationing.
Abstract: A mixed integer programming model is constructed for the operation of a single water supply reservoir during drought and impending drought. Operating on a critical sequence of low flows, the model determines trigger volumes of storage plus anticipated inflow which signal the need for each of the several phases of rationing. The trigger volumes are examined as the allowed frequency of the various phases of rationing are varied.

102 citations