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: Generic models are presented for single and multiple allocation versions of the hub location problems under uncertainty and changes in the solutions driven by the different sources of uncertainty considered isolated and combined are analyzed.
Abstract: Hub location problems are network design problems which are solved as part of a strategic decision making process. In strategic planning, decisions may have a long lasting effect and the implementation may take considerable time. Moreover, input data is not precisely known in advance. Hence, decisions have to be made anticipating uncertainty. In this paper, we address several aspects concerning hub location problems under uncertainty. Two sources of uncertainty are considered: the set-up costs for the hubs and the demands to be transported between the nodes. Generic models are presented for single and multiple allocation versions of the problems. Firstly, the two sources of uncertainty are analyzed separately and afterwards a more comprehensive model is proposed considering all sources of uncertainty. Using a set of computational tests performed, we analyze the changes in the solutions driven by the different sources of uncertainty considered isolated and combined.
172 citations
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TL;DR: This article introduces the first implementation of general purpose methods for finding good solutions to multistage, stochastic mixed-integer (0, 1) programming problems and introduces the notion of integer convergence for progressive hedging.
Abstract: Many problems faced by decision makers are characterized by a multistage decision process with uncertainty about the future and some decisions constrained to take on values of either zero or one (for example, either open a facility at a location or do not open it). Although some mathematical theory exists concerning such problems, no general-purpose algorithms have been available to address them. In this article, we introduce the first implementation of general purpose methods for finding good solutions to multistage, stochastic mixed-integer (0, 1) programming problems. The solution method makes use of Rockafellar and Wets' progressive hedging algorithm that averages solutions rather than data. Solutions to the induced quadratic (0,1) mixed-integer subproblems are obtained using a tabu search algorithm. We introduce the notion of integer convergence for progressive hedging. Computational experiments verify that the method is effective. The software that we have developed reads standard (SMPS) data files.
171 citations
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TL;DR: This paper extends the applicability of optimization models to situations where both fuzzy and random data are in the state of affairs, and provides some possible avenues for further fruitful developments.
171 citations
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TL;DR: In this paper, a dynamic programming (DP) model was used to improve the operation and efficient management of available water for the Aliyar Dam in Tamil Nadu, India, using a neural network procedure (DPN) and using a multiple linear regression procedure (DPR) model.
Abstract: Reservoir operating policies are derived to improve the operation and efficient management of available water for the Aliyar Dam in Tamil Nadu, India, using a dynamic programming (DP) model, a stochastic dynamic programming (SDP) model, and a standard operating policy (SOP). The objective function for this case study is to minimize the squared deficit of the release from the irrigation demand. From the DP algorithm, general operating policies are derived using a neural network procedure (DPN model), and using a multiple linear regression procedure (DPR model). The DP functional equation is solved for 20 years of fortnightly historic data. The field irrigation demand is computed for this study by the modified Penman method with daily meteorological data. The performance of the DPR, DPN, SDP, and SOP models are compared for three years of historic data, using the proposed objective function. The neural network procedure based on the dynamic programming algorithm provided better performance than the other mo...
171 citations
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TL;DR: In this paper, drivability restrictions are included in a shortest path stochastic dynamic programming (SP-SDP) formulation of the real-time energy management problem for a prototype vehicle, where the drive cycle is modeled as a stationary, finite-state Markov chain.
Abstract: Hybrid vehicle fuel economy performance is highly sensitive to the energy management strategy used to regulate power flow among the various energy sources and sinks. Optimal non-causal solutions are easy to determine if the drive cycle is known a priori. It is very challenging to design causal controllers that yield good fuel economy for a range of possible driver behavior. Additional challenges come in the form of constraints on powertrain activity, such as shifting and starting the engine, which are commonly called “drivability” metrics and can adversely affect fuel economy. In this paper, drivability restrictions are included in a shortest path stochastic dynamic programming (SP-SDP) formulation of the real-time energy management problem for a prototype vehicle, where the drive cycle is modeled as a stationary, finite-state Markov chain. When the SP-SDP controllers are evaluated with a high-fidelity vehicle simulator over standard government drive cycles, and compared to a baseline industrial controller, they are shown to improve fuel economy more than 11% for equivalent levels of drivability. In addition, the explicit tradeoff between fuel economy and drivability is quantified for the SP-SDP controllers.
171 citations