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: In this paper, a mixed interval-fuzzy two-stage integer programming (IFTIP) method is developed for flood diversion planning under uncertainty by allowing uncertainties expressed as probability distributions, fuzzy sets, and discrete intervals to be directly incorporated within the optimization framework.
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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TL;DR: In this paper, an integrated procedure for design combinations of drought properties, such as duration, severity, and peak, involving the truncation of drought events, the goodness-of-fit of joint and marginal distributions, the determination of combinations of these properties for a given Kendall return period, and the evaluation of uncertainty of the combinations, was developed.
65 citations
TL;DR: In this article, Monte Carlo simulations were carried using data of the Dharoi Reservoir (India) and the inflows to the reservoir were generated by following two approaches: long-memory models and short memory models.
Abstract: The behaviour of statistical performance indices, namely, reliability, resilience and vulnerability for a multipurpose storage reservoir is examined. Monte Carlo simulations were carried using data of the Dharoi Reservoir (India) and the inflows to the reservoir were generated by following two approaches: long-memory models and short-memory models. Statistical behaviour of three indices were examined for two cases: (i) municipal and industrial water supply; and (ii) irrigation, thus making a total of six indices for the analysis. To interpret the behaviour of these indices, a probabilistic approach was followed. It was noted that when inflows generated using long-memory models were input in simulation, there were large variations in reliability, resilience and vulnerability among the runs. In contrast, when data from short-memory models were used, the indices were confined to a narrow band. Average values of reliabilities and their variance for both the demands were much higher when the data gene...
63 citations
Cites background from "Mixed-Integer Programming Model for..."
...The use of the last two performance criteria, resilience and vulnerability, has been discussed in many works, 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 multistage scenario-based interval-stochastic programming (MSISP) method is developed for water-resources allocation under uncertainty and sensitivity analyses demonstrate that the violation of the environmental constraint has a significant effect on the system benefit.
Abstract: In this study, a multistage scenario-based interval-stochastic programming (MSISP) method is developed for water-resources allocation under uncertainty. MSISP improves upon the existing multistage optimization methods with advantages in uncertainty reflection, dynamics facilitation, and risk analysis. It can directly handle uncertainties presented as both interval numbers and probability distributions, and can support the assessment of the reliability of satisfying (or the risk of violating) system constraints within a multistage context. It can also reflect the dynamics of system uncertainties and decision processes under a representative set of scenarios. The developed MSISP method is then applied to a case of water resources management planning within a multi-reservoir system associated with joint probabilities. A range of violation levels for capacity and environment constraints are analyzed under uncertainty. Solutions associated different risk levels of constraint violation have been obtained. They can be used for generating decision alternatives and thus help water managers to identify desired policies under various economic, environmental and system-reliability conditions. Besides, sensitivity analyses demonstrate that the violation of the environmental constraint has a significant effect on the system benefit.
63 citations
Additional excerpts
...Previously, a large number of optimization methods were undertaken for allocating and managing water resources in efficient and environmentally benign ways (Bazaare and Bouzaher 1981; Jacovkis et al. 1989; Paudyal and Manguerra 1990; Basağaoğlu et al. 1999; Srinivasan et al. 1999; Sethi et al. 2002; Gang et al. 2003)....
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01 Jan 2007
TL;DR: In this article, the authors proposed a method for the integration of multiple objectives and criteria, and the incorporation of uncertainty, risk and reliability considerations in the water supply systems analysis, in order to help to implement these objectives in everyday planning, design and operation of Wasserversorgung systems.
Abstract: The ongoing changes in the society’s perception of the role and function of infrastructure systems as well as degradation of the state of natural resources, increasingly appoint new challenges to the management of water supply systems. Out of many, the main the main research objectives of this research are: the integration of multiple objectives and criteria, and the incorporation of uncertainty, risk and reliability considerations in the water supply systems analysis. In order to help to implement these objectives in everyday planning, design and operation of water supply systems, an unique optimisation methodology has been developed and implemented into corresponding computer models.
The methodology uses the network approach for conceptual and structural representation of water supply systems and define planning, design and operation management problems as Network Minimum Cost Flow problems with multiple objectives. Different impacts of water supply projects or actions such as economic costs, environmental consequence or social disapproval are add together according to the utilities (preferences) of decision makers by implementing theMulti Objective Simulated Annealing (MOSA) method. In order to improve the performance of the algorithm for complex combinatorial problems and reduce questioning of non-optimal alternatives, the MOSA algorithm is embedded into the Branch and Bound method. For optimisation problems defined on networks, the combination of the previous two algorithms provide for robust and efficient identification of Pareto-solutions.
The inclusion of uncertainty, risk and reliability considerations in the analysis is based on the Stochastic design approach. It provides for the inclusion of decision makers’s risk perception in evaluation of the satisfactory system’s performance. The accepted risk for some system configuration is obtained as a statistical expectation of the costs of expected failures. A deterministically defined failure of an individual system component is considered with an advanced Path Restoration method, while a probabilistically defined performance failure is addressed with stochastical simulation of system’s performances. An advanced sampling method (i.e. Latin Hypercube) is used for the creation of representative samples of uncertain and variable parameters. The system’s reliability is obtained form the statistical analysis of calculated system’s performances evaluated with predefined risk tolerance levels. Finally, a demonstration at a) a multi-objective planning problem of a system expansion, b) a NP-hard design problem of pipe diameters selection and c) a complex operation problem of pump scheduling is done on the basis of well known test studies from the literature.
These proved that network system representation, multi-objective problem formulation and inclusion of decision makers’ preferences and risk perception in the development of optimal alternatives improve the creation of Pareto-optimal solutions, increase the efficiency of optimisation procedure and add to the transparency of the system analyse.
Die verstarkte Nutzung der naturlichen Wasserressourcen und die weltweite Verunreinigung dieses kostbaren Schatzes im 20. Jahrhundert fuhrte zur Erschopfung und Verschmutzung vieler natuurlicher Wasserkorper. Die wachsende Spannung zwischen intensiver Wassernutzung und der naturlichen Funktion von Okosystemen, veranderte unsere Vorstellung uber die Aufgabe der Wasserversorgungssysteme. Die integrierte Betrachtung von gesellschaftlichen, okonomischen und okologischen Aspekten von Wasserversorgungssystemen und die Einbeziehung der Unsicherheiten und der Veranderlichkeit der Eingangsparameter wurden als Hauptbeweggrunde dieser Studie festgelegt. Um diese Herausforderungen in der alltaglichen Planung, beim Entwurf und im Betrieb der Wasserversorgungssysteme einzusetzen, wurde hier eine Methodologie fur die modellbasierte Analyse und Optimierung dieser Systeme entwickelt.
Die Methodologie verwendet den Netzwerkansatz fur die konzeptionelle und strukturelle Darstellung der Wasserversorgungssysteme und definiert damit ein Network Minimum Cost Flow Problem mit mehrfachen Zielsetzungen, um Planungs-, Entwurfs- und Betriebsmanagementprobleme mathematisch zu formulieren. Unterschiedliche Aspekte von Wasserversorgungsprojekten und -aufgaben, wie Minimierung von okonomischen Kosten, Umweltauswirkungen oder negativen soziale Folgerungen, werden den Praferenzen von Entscheidungstragern entsprechend, mit der Multi-objective Simulated Annealing (MOSA) Methode (Ulungu et al., 1995; Kirkpatrick et al., 1983; Cerny, 1985) zusammengefuhrt. Um die Leistungsfahigkeit des Algorithmus fur komplizierte kombinatorische Probleme zu verbessern und das Abfragen der nicht-optimalen Alternativen zu verringern, wird der MOSA Algorithmus in die Branch and Bound Methode (Land 1960) eingebettet. Fur gut strukturierte Netzwerk-Optimierungsprobleme gewahrleistet die Kombination der beiden genannten Algorithmen eine robuste und leistungsfahige Ermitllung der Pareto-optimalen Losungen.
Eine methodische Einbeziehung der Unsicherheiten und der Veranderlichkeit der Eingangsparameter wird erreicht, indem man unterschiedliche mogliche Systemalternativen mit Hilfe der stochastischen Simulationsverfahren evaluiert. Die dafur notigen reprasentativen Stichproben der Eingangsparameter wurden mit der Latin Hypercube Sampling Technik (Iman and Shortencarier 1984) generiert. Eine statistische Analyse der berechneten Systemsleistungen fur diese Stichproben wird dann fur die Einschatzung der Systemzuverlassigkeit verwendet. Zusammen mit der Ausfallanalyse, welche durch das Pat Restoration Verfahren (Iraschko et al. 1998) eingefuhrt worden ist, wird die Kompromissfindung zwischen der Systemzuverlassigkeit und Kriterien wie okonomische Kosten ermoglicht.
Die beschriebene Methodologie wurde in drei entsprechenden Computermodellen umgesetzt. Sie sind an die spezifischen Aspekte der Wasserversorgungsplanung, des Entwurfes und des Betriebsmanagements angepasst und ermoglichen im Verbund eine volle Entscheidungsunterstutzung im Management von Wasserversorgungssystemen. Die Teilmodelle wurden anhand von folgenden Fallstudien erlautert: a) Planung der Entwicklung der Wasserversorgungsstruktur, b) Bestimmung der Kapazitat des Wasserversorgungsnetzes und c) Identifizierung des optimalen Pumpbetriebs desWasserversorgungssystems.
51 citations
References
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TL;DR: In this paper, three criteria for evaluating the performance of water resource systems are discussed, i.e., reliability, resilience, and vulnerability, which describe how likely a system is to fail, how quickly it recovers from failure, and how severe the consequences of failure may be.
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.
1,458 citations
TL;DR: In this paper, a linear decision rule is proposed to specify 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.
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.
290 citations
TL;DR: In this article, the tradeoffs between reliability, vulnerability, and resilience were examined using multiobjective mixed-integer, linear programming, and it was 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.
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.
267 citations
TL;DR: In this article, 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.
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.
145 citations
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.
113 citations