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
TL;DR: In this paper, a mixed-integer programming model for the operation of a water supply reservoir during critical periods has been presented in the literature that incorporates reliability, resilience, and vulnerability, and an improved formulation of this model that represents resilience more completely is discussed.
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.
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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.
172 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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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.
112 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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TL;DR: In this paper, the authors proposed a multivariate approach as a measure of socioeconomic drought, termed Multivariate Standardized Reliability and Resilience Index (MSRRI), which combines information on the inflow and reservoir storage relative to the demand.
Abstract: Socioeconomic drought broadly refers to conditions whereby the water supply cannot satisfy the demand. Most previous studies describe droughts based on large scale meteorological/hydrologic conditions, ignoring the demand and local resilience to cope with climate variability. Reservoirs provide resilience against climatic extremes and play a key role in water supply and demand management. Here, we outline a unique multivariate approach as a measure of socioeconomic drought, termed Multivariate Standardized Reliability and Resilience Index (MSRRI). The model combines information on the inflow and reservoir storage relative to the demand. MSRRI combines: (I) a “top-down” approach that focuses on processes/phenomena that cannot be simply controlled or altered by decision makers, such as climate change and variability, and (II) a “bottom-up” methodology that represents the local resilience and societal capacity to respond or adapt to droughts. MSRRI is based on a nonparametric multivariate distribution function that links Inflow-Demand Reliability (IDR) indicator to Water Storage Resilience (WSR) indicator. These indicators are used to assess socioeconomic drought during the Australian Millennium Drought (1998–2010) and the 2011–2014 California Drought. The results show that MSRRI is superior to univariate indices because it captures both early onset and persistence of water stress over time. The suggested framework can be applied to both individual reservoirs and a group of reservoirs in a region, and it is consistent with the currently available standardized drought indicators. MSRRI provides complementary information on socioeconomic drought development and recovery based on reservoir storage and demand that cannot be achieved from the commonly used drought indicators.
110 citations
TL;DR: In this article, 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.
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...
98 citations
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18 Dec 2008
TL;DR: In this article, the authors present an approach to improve the performance of a single-input-single-output (SISO) system using a set of tools from the Massachusetts Institute of Technology, Engineering Systems Division.
Abstract: Thesis (Ph. D.)--Massachusetts Institute of Technology, Engineering Systems Division, 2005.
92 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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References
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TL;DR: Several linear decision rules used in chance-constrained models for estimating efficient reservoir capacities and operating policies are compared and evaluated.
Abstract: Several linear decision rules used in chance-constrained models for estimating efficient reservoir capacities and operating policies are compared and evaluated. A chance-constrained model that includes known or unknown reservoir release targets, or storage volume targets, permits this comparison, since regardless of the linear decision rule chosen, release or storage volume commitments can be made, and their maximum probabilities of failure estimated, well in advance of any period in which they apply. Optimization and simulation techniques are used to evaluate the performance of each decision rule.
105 citations
TL;DR: In this paper, the concept of resilience of a water resource system is explored, and a few definitions are suggested and compared These are based on the time required to pass from one system state to another and involve the passage to or from a state defined as failure.
Abstract: The concept of resilience of a water resource system is explored, and a few definitions are suggested and compared These are based on the time required to pass from one system state to another and involve the passage to or from a state defined as failure Some of the definitions involve probability of recovery from failure to some acceptable state within a specified time interval; thus the system's dynamics and standards are explicitly included
100 citations
TL;DR: In this paper, the effects of operating a water supply reservoir with a policy of hedging on various reservoir performance criteria are investigated, including reliability, resiliency, and mean and maximum deficit.
Abstract: The effects of operating a water supply reservoir with a policy of hedging on various reservoir performance criteria are investigated. The results of simulations where policies with different degrees of hedging are adopted are used to determine how reliability, resiliency, and mean and maximum deficit vary as functions of hedging parameters and to derive the relationships between these criteria. It is found that the standard operating policy is the best in relation to reliability and resiliency and is satisfactory with regard to deficits. Hedging improves the performance with respect to mean deficit if it is started with sufficient water in storage. If hedging is applied when there is little water in storage, it reduces the risk of very large future deficits, although the mean deficit will be increased. If hedging is continued even when the demand can be supplied, the performance of the reservoir will be more stable and the mean deficit will be decreased, but these will be achieved at a cost of increasing the rate of failure.
85 citations
TL;DR: In this paper, a series of synthetic short-term forecasted values (which satisfy a specified distribution of forecast errors) is used to examine operation of a single reservoir, and the performance of an operation policy based on a model that uses predicted streamflows as deterministic inputs cannot be correlated directly with the shape of the assumed loss function.
Abstract: Short-term operation policy for multipurpose reservoirs can be derived from an optimization model with the objective of minimizing short-term losses (opportunity costs). Construction of such loss functions requires the definition of target values for the decision variables, assessment of reliabilities with which inflows can be predicted, and an explicit statement of operational objectives. Formulation and evaluation of a model is complicated by the uncertainties inherent in the prediction of future streamflows and by controversies about the criteria of evaluation. We discuss these issues and illustrate some of our arguments with simple numerical experiments. A series of synthetic short-term forecasted values (which satisfy a specified distribution of forecast errors) is used to examine operation of a single reservoir. The quality of forecasted values is represented by the mean and variance of these errors or the coefficient of prediction (Cp). The objective function of the operation model is assumed to be the best possible tradeoff between probable deviations from two operation targets: release and storage volume. Reservoir release was effected according to the solution of the optimization model conditioned upon the forecasted streamflow volumes for a given time increment. The storage volume was then corrected to reflect actual streamflow for the forecasted period. This became the initial storage for the next forecast period. Actual losses, deviations between actual and forecasted losses, the variance of storage and release volumes, and operational performance measures, including reliability, resiliency, and vulnerability, were found to be sensitive to the relative importance given to deviations from release or storage targets and the quality of forecasts. The performance of an operation policy based on a model that uses predicted streamflows as deterministic inputs cannot be correlated directly with the shape of the assumed loss function.
78 citations
TL;DR: In this article, an improved linear decision rule is derived for reservoirs suffering evaporation losses and several reservoir performance measures are formulated as objective functions that can be optimized by linear programing, including expected and reliable values of storages and releases, deviations from targets, and reliabilities of achieving stated goals.
Abstract: The application of linear decision rules to reservoir management and design is extended in two directions. First, an improved linear decision rule is derived for reservoirs suffering evaporation losses. Release commitments generated by this rule are based on the storage at the beginning of the period, the predicted evaporation depth in the period, and the linearized storage area curve of the reservoir. A clearer and more rigorous derivation of the chance constraints, including the effects of both evaporation losses and possible failures to meet previous commitments, is presented. Second, several reservoir performance measures are formulated as objective functions that can be optimized by linear programing. These performance measures include expected and reliable values of storages and releases, deviations from targets, and reliabilities of achieving stated goals.
61 citations