Topic
Stochastic programming
About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.
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TL;DR: The L-shaped method leads to a new algorithm for minimizing conditional value-at-risk, which outperformed by at least one order of magnitude all general-purpose solvers, with an accuracy of solution being in the same range as that with the LP solvers.
Abstract: We consider optimization problems for minimizing conditional value-at-risk (CVaR) from a computational point of view, with an emphasis on financial applications. As a general solution approach, we suggest to reformulate these CVaR optimization problems as two-stage recourse problems of stochastic programming. Specializing the L-shaped method leads to a new algorithm for minimizing conditional value-at-risk. We implemented the algorithm as the solver CVaRMin. For illustrating the performance of this algorithm, we present some comparative computational results with two kinds of test problems. Firstly, we consider portfolio optimization problems with 5 random variables. Such problems involving conditional value at risk play an important role in financial risk management. Therefore, besides testing the performance of the proposed algorithm, we also present computational results of interest in finance. Secondly, with the explicit aim of testing algorithm performance, we also present comparative computational results with randomly generated test problems involving 50 random variables. In all our tests, the experimental solver, based on the new approach, outperformed by at least one order of magnitude all general-purpose solvers, with an accuracy of solution being in the same range as that with the LP solvers.
99 citations
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TL;DR: In this article, a stochastic midterm risk-constrained hydrothermal scheduling algorithm in a generation company (GENCO) is presented, where the objective is to maximize payoffs and minimize financial risks when scheduling its midterm generation of thermal, cascaded hydro, and pumped storage units.
Abstract: This paper presents a stochastic midterm risk-constrained hydrothermal scheduling algorithm in a generation company (GENCO). The objective of a GENCO is to maximize payoffs and minimize financial risks when scheduling its midterm generation of thermal, cascaded hydro, and pumped-storage units. The proposed schedule will be used by the GENCO for bidding purposes to the ISO. The optimization model is based on stochastic price-based unit commitment. The proposed GENCO solution may be used to schedule midterm fuel and natural water inflow resources for a few months to a year. The proposed stochastic mixed-integer programming solution considers random market prices for energy and ancillary services, as well as the availability of natural water inflows and generators in Monte Carlo scenarios. Financial risks associated with uncertainties are considered by applying expected downside risks which are incorporated explicitly as constraints. Variable time-steps are adopted to avoid the exponential growth in solution time and memory requirements when considering midterm constraints. A single water-to-power conversion function is used instead of several curves for representing water head and discharge parameters. Piecewise linearized head-dependant water-to-power conversion functions are used for computational efficiency. Illustrative examples examine GENCOs' midterm generation schedules, risk levels, fuel and water usage, and hourly generation dispatches for bidding in energy and ancillary services markets. The paper shows that GENCOs could decrease their financial risks by adjusting expected payoffs.
99 citations
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TL;DR: In this paper, single stage stochastic programs with ambiguous distributions for the involved random variables are considered and equivalent formulations as finite dimensional non-convex, semi definite saddle point problems are proposed.
Abstract: In this paper, single stage stochastic programs with ambiguous distributions for the involved random variables are considered. Though the true distribution is unknown, existence of a reference measure P enables the construction of non-parametric ambiguity sets as Kantorovich balls around P. The original stochastic optimization problems are robustified by a worst case approach with respect to these ambiguity sets. The resulting problems are infinite optimization problems and can therefore not be solved computationally by straightforward methods. To nevertheless solve the robustified problems numerically, equivalent formulations as finite dimensional non-convex, semi definite saddle point problems are proposed. Finally an application from portfolio selection is studied for which methods to solve the robust counterpart problems explicitly are proposed and numerical results for sample problems are computed.
99 citations
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TL;DR: In this paper, an inexact fuzzy-stochastic energy model (IFS-EM) is developed for planning energy and environmental systems (EES) management under multiple uncertainties.
99 citations
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TL;DR: This paper considers the issue of call center scheduling in an environment where arrivals rates are highly variable, aggregate volumes are uncertain, and the call center is subject to a global service level constraint, and finds that the stochastic model provides a significant reduction in the expected cost of operation.
99 citations