Network planning under uncertainty with an application to hydropower generation

Alvarez, Manuel; Cuevas, C. M.; Escudero, Laureano F.; Escudero, J. L.; García, Cristina; Prieto, Francisco J.

doi:10.1007/bf02574759

Cited by 8 publications

(8 citation statements)

References 13 publications

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“…In this case, the system Ax = b can be written as There exists a broad range of application fields for stage programs of this form, such as electricity water gas distribution, financial planning, exchange rate management with currency arbitrage, production planning, input-output tables in macroeconomic analysis, design and operation of communications networks, road networks, etc. See [1,2,6,13,17,18,21,22,24,27,33,34,36,42,[47][48][49][50], among others. In many…”

Section: Model Descriptionmentioning

confidence: 99%

“…One way to deal with the uncertainty is to obtain the solution x that best tracks each of the scenarios, while attempting to satisfy the constraints for each scenario. This can be achieved by obtaining a solution that minimizes the weighted sum or the largest of the upper differences between the proposed solution value and the optimal solution value for each scenario, see [1,2,13,26,32]. The resulting model does not increase the number of variables of the original formulation, but now there are m|S| constraints.…”

Section: Uncertaintymentioning

confidence: 99%

“…The resulting model does not increase the number of variables of the original formulation, but now there are m|S| constraints. Unfortunately, this representation of the model does not preserve the structure of the deterministic model (1) (for example, in the case of network models we have two nonzero constraint entries for each variable, at most, and one of them is +1), and the objective function is no longer linear; see [1,2] for some procedures to overcome this difficulty. Models of this form are known as scenario immunization models, see [13,32], or SI models for short.…”

Section: Uncertaintymentioning

confidence: 99%

“…The results of these studies do not all go in the same direction, but none of them analyze decomposition procedures. A Dantzig-Wolfe decomposition scheme, and (its dual) a Benders approach to the solution of ( 7) have been presented in [2], but no computational results are reported; the authors claim they are not good enough.…”

Section: The Modelmentioning

confidence: 99%

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Untitled

Escudero¹,

Fuente²,

García³

et al. 1999

Annals of Operations Research

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This paper presents a parallel computation approach for the efficient solution of very large multistage linear and nonlinear network problems with random parameters. These problems result from particular instances of models for the robust optimization of network problems with uncertainty in the values of the right-hand side and the objective function coefficients. The methodology considered here models the uncertainty using scenarios to characterize the random parameters. A scenario tree is generated and, through the use of full-recourse techniques, an implementable solution is obtained for each group of scenarios at each stage along the planning horizon.As a consequence of the size of the resulting problems, and the special structure of their constraints, these models are particularly well-suited for the application of decomposition techniques, and the solution of the corresponding subproblems in a parallel computation environment. An augmented Lagrangian decomposition algorithm has been implemented on a distributed computation environment, and a static load balancing approach has been chosen for the parallelization scheme, given the subproblem structure of the model. Large problems -9000 scenarios and 14 stages with a deterministic equivalent nonlinear model having 166000 constraints and 230000 variables -are solved in 45 minutes on a cluster of four small (11 Mflops) workstations. An extensive set of computational experiments is reported; the numerical results and running times obtained for our test set, composed of large-scale real-life problems, confirm the efficiency of this procedure.

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Section: Model Descriptionmentioning

confidence: 99%

Section: Uncertaintymentioning

confidence: 99%

Section: Uncertaintymentioning

confidence: 99%

Section: The Modelmentioning

confidence: 99%

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Untitled

Escudero¹,

Fuente²,

García³

et al. 1999

Annals of Operations Research

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“…This is being applied in many others fields involving optimization under uncertainty.Álvarez et al [2] use a scenario framework to characterize the uncertainty on the right-hand side (rhs), minimizing the regret of wrong decisions and forming implementable policies. Also, Berman, Ganz, and Wagner [4] introduce a scenario-modeling approach for capacity-expansion planning in the service industry.…”

Section: Introductionmentioning

confidence: 99%

A risk function for the stochastic modeling of electric capacity expansion

Marı́n

Salmerón

2001

Naval Research Logistics

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Abstract:We present a stochastic optimization model for planning capacity expansion under capacity deterioration and demand uncertainty. The paper focuses on the electric sector, although the methodology can be used in other applications. The goals of the model are deciding which energy types must be installed, and when. Another goal is providing an initial generation plan for short periods of the planning horizon that might be adequately modified in real time assuming penalties in the operation cost. Uncertainty is modeled under the assumption that the demand is a random vector. The cost of the risk associated with decisions that may need some tuning in the future is included in the objective function. The proposed scheme to solve the nonlinear stochastic optimization model is Generalized Benders' decomposition. We also exploit the Benders' subproblem structure to solve it efficiently. Computational results for moderate-size problems are presented along with comparison to a general-purpose nonlinear optimization package.

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