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stochastic optimization of a hydroelectric reservoir using piecewise polynomial approximations

INFOR 2003年第1期41卷 51-69页

作者： Lamond, BF Univ Laval Fac Sci Adm Dept Operat & Syst Decis Quebec City PQ G1K 7P4 Canada

We propose a method for optimizing a single hydro-electric reservoir using a piecewise polynomial approximation of the future value functions. Unlike previous methods based on splines, we avoid discretizing the inflow distribution. Instead, we carry out the expectation step of dynamic programming using an exact, easy-to-evaluate formula for the integral of a piecewise polynomial function. We then apply our method to solving a model which assumes a piecewise linear reward function of the energy produced, and takes into account the turbine head effects.

关键词： Markov decision processes stochastic dynamic programming piecewise polynomial approximation optimal reservoir management energy planning

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Dual sourcing in managing operational and disruption risks in contract manufacturing

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2015年第1期53卷 291-306页

作者： Su, Ping Liu, Shuguang Hofstra Univ Frank G Zarb Sch Business Hempstead NY 11550 USA SUNY Coll New Paltz Sch Business New Paltz NY 12561 USA

We study a US OEM that outsources its production to two contract manufacturers, a local manufacturer (e.g. in the US or Mexico) and a foreign manufacturer (e.g. in China). The local manufacturer is relatively reliable, but low margin. The foreign manufacturer offers high margin, but is subject to disruption risks. Both manufacturers experience some level of operational uncertainties, and the operational risks can be positively or negatively correlated. Disruption risks are modelled as a Poisson jump process at a random magnitude, and operational risks are modelled as correlated stochastic diffusion processes. We develop a stochastic dynamic programming formulation to characterise the OEM's optimal capital allocation decision to contract manufacturers, and provide the necessary and sufficient conditions for each optimal decision. The objective of our study is to investigate how dual sourcing balances the risks and opportunities, when the OEM bears disruption risks and correlated operational risks. We find that the two manufacturers can be substitutes or complements to each other. Risk of disruption renders the unreliable foreign manufacturer less attractive, but has a moderating effect on the allocation to the local manufacturer. We also provide managerial implications of our study.

关键词： contract manufacturing disruption risks correlated operational risks stochastic dynamic programming jump process dual sourcing

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Optimal policy for a dynamic, non-stationary, stochastic inventory problem with capacity commitment

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2009年第2期199卷 400-408页

作者： Xu, Ningxiong Cornell Univ Sch Civil & Environm Engn Ithaca NY 14853 USA

This paper studies a single-product, dynamic, non-stationary, stochastic inventory problem with capacity commitment, in which a buyer purchases a fixed capacity from a supplier at the beginning of a planning horizon and the buyer's total cumulative order quantity over the planning horizon is constrained with the capacity. The objective of the buyer is to choose the capacity at the beginning of the planning horizon and the order quantity in each period to minimize the expected total cost over the planning horizon. We characterize the structure of the minimum sum of the expected ordering, storage and shortage costs in a period and thereafter and the optimal ordering policy for a given capacity. Based on the structure, we identify conditions under which a myopic ordering policy is optimal and derive an equation for the optimal capacity commitment. We then use the optimal capacity and the myopic ordering policy to evaluate the effect of the various parameters on the minimum expected total cost over the planning horizon. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Additive function Capacity Inventory Myopic policy stochastic dynamic programming

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A deep learning method for pricing high-dimensional American-style options via state-space partition

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COMPUTATIONAL & APPLIED MATHEMATICS 2024年第3期43卷 1-26页

作者： Han, Yuecai Zheng, Xudong Jilin Univ Sch Math Qianjin St Changchun 130012 Jilin Peoples R China

This paper proposes a deep learning approach for solving optimal stopping problems and high-dimensional American-style options pricing problems. Through state-space partition, the method does not require recalculation of the structure of networks when the price of the asset changes, which makes tracking valuation more efficient. This paper also offers theoretical proof for the existence of a deep learning network that can determine the optimal stopping time via state-space partition. We present convergence proofs for the estimators and also test the method on Bermuda max-call options as examples.

关键词： Deep learning High-dimensional American-style option Optimal stopping stochastic dynamic programming

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Structural properties of a class of robust inventory and queueing control problems

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NAVAL RESEARCH LOGISTICS 2018年第8期65卷 699-716页

作者： Turgay, Zeynep Karaesmen, Fikri Ormeci, Egemen Lerzan Migros TAS R&D Ctr TR-34758 Istanbul Turkey Koc Univ Dept Ind Engn TR-34450 Istanbul Turkey

In standard stochastic dynamic programming, the transition probability distributions of the underlying Markov Chains are assumed to be known with certainty. We focus on the case where the transition probabilities or other input data are uncertain. Robust dynamic programming addresses this problem by defining a min-max game between Nature and the controller. Considering examples from inventory and queueing control, we examine the structure of the optimal policy in such robust dynamic programs when event probabilities are uncertain. We identify the cases where certain monotonicity results still hold and the form of the optimal policy is determined by a threshold. We also investigate the marginal value of time and the case of uncertain rewards.(c) 2017 Wiley Periodicals, Inc. Naval Research Logistics 65: 699-716, 2018

关键词： stochastic dynamic programming robust optimization inventory control queueing control

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Optimal and robust strategies for freeway traffic management under demand and supply uncertainties: an overview and general theory

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TRANSPORTMETRICA A-TRANSPORT SCIENCE 2014年第10期10卷 849-877页

作者： Zhong, R. X. Sumalee, A. Pan, T. L. Lam, William H. K. Sun Yat Sen Univ Sch Engn Res Ctr Intelligent Transportat Guangzhou 510275 Guangdong Peoples R China Hong Kong Polytech Univ Dept Civil & Environm Engn Hong Kong Hong Kong Peoples R China King Mongkuts Inst Technol Ladkrabang Dept Civil Engn Bangkok Thailand Beijing Jiaotong Univ Sch Traff & Transportat Beijing Peoples R China

This paper investigates optimal decision-making for traffic management under demand and supply uncertainties by stochastic dynamic programming. Traffic flow dynamics under demand and supply uncertainties is described by a simplified version of the stochastic cell transmission model. Based on this model, the optimal traffic management problem is analysed wherein the existence of solution is guaranteed by verifying the well-posed condition. An analytical optimal control law is derived in terms of a set of coupled generalised recursive Riccati equations. As optimal control laws may be fragile with respect to model misspecification, a robust (optimal) decision-making law that aims to act robust with respect to the parameter misspecification in the traffic flow model (which can be originated from model calibration), and to attenuate the effect of disturbances in freeway networks (wherein demand uncertainty is usually regarded as a kind of disturbance) is proposed. Conventionally, network uncertainties have been considered to induce negative effects on traffic management in transportation literature. In contrast, the proposed methodology outlines an interesting issue that is to make benefit (or trade-off) from the inherent network uncertainties. Finally, some practical issues in traffic management that can be addressed by extending the current framework are briefly discussed.

关键词： optimal traffic management stochastic dynamic programming robustness approximate dynamic programming ramp metering dynamic pricing

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Neuro-dynamic programming for designing water reservoir network management policies

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CONTROL ENGINEERING PRACTICE 2007年第8期15卷 1031-1038页

作者： Castelletti, A. de Rigo, D. Rizzoli, A. E. Soncini-Sessa, R. Weber, E. Politecn Milan Dipartimento Elettron & Informat I-20133 Milan Italy IDSIA CH-6928 Manno Lugano Switzerland

stochastic dynamic programming (SDP) can improve the management of a multipurpose water reservoir by generating management policies which are efficient with respect to the management objectives (flood protection, water supply for irrigation, hydropower generation, etc.). The improvement in efficiency is even more remarkable for networks of reservoirs. Unfortunately, SDP is affected by the well-known 'curse of dimensionality', i.e. computational time and computer memory occupation increase exponentially with the dimension of the problem (number of reservoirs), and the problem rapidly becomes intractable. Neuro-dynamic programming (NDP) can sensibly mitigate this limitation by approximating Bellman functions with artificial neural networks (ANNs). In this paper the application of NDP to the problem of the management of reservoir networks is introduced. Results obtained in a real-world case study are finally presented. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： water reservoir network reservoir management stochastic dynamic programming neuro-dynamic programming

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Hierarchical production control in dynamic stochastic jobshops with long-run average cost

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2000年第2期106卷 231-264页

作者： Sethi, SP Zhang, H Zhang, Q Univ Texas Sch Management Richardson TX 75080 USA Acad Sinica Inst Appl Math Beijing 100080 Peoples R China Univ Georgia Dept Math Athens GA 30602 USA

We consider a production planning problem for a dynamic jobshop producing a number of products and subject to breakdown and repair of machines. The machine capacities are assumed to be finite-state Markov chains. As the rates of change of the machine states approach infinity, an asymptotic analysis of this stochastic manufacturing systems is given. The analysis results in a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability. The long-run average cost for the original problem is shown to converge to the long-run average cost of the limiting problem. The convergence rate of the long-run average cost for the original problem to that of the limiting problem together with an error estimate for the constructed asymptotic optimal control is established.

关键词： hierarchical control manufacturing systems stochastic dynamic programming optimal control long-run average cost

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Comparison of risk-based optimization models for reservoir management

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CANADIAN JOURNAL OF CIVIL ENGINEERING 2010年第1期37卷 112-124页

作者： Mahootchi, M. Ponnambalam, K. Tizhoosh, H. R. Univ Waterloo Dept Syst Design Engn Waterloo ON N2L 3G1 Canada Amirkabir Univ Technol Dept Ind Engn Tehran Iran

Risk minimization in stochastic systems is a challenging problem and this paper compares results of three different techniques in reservoir management. Two-stage stochastic programming (TSP) for maximizing expected benefits is a well-known method, Fletcher and Ponnambalam (FP) and Q-Learning are the two new methods in reservoir management, all of which can include risk minimization in the objective function. The water price uncertainties caused by deregulated markets are considered in addition to random inflows in optimization and simulation is used to compare the results and to develop a risk versus return trade-off curve. One of the contributions of this paper is to consider risk in the Q-Learning algorithm.

关键词： water reservoirs stochastic dynamic programming Q-Learning risk stochastic programming

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stochastic Long-Term Hydrothermal Scheduling With Parameter Uncertainty in Autoregressive Streamflow Models

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IEEE TRANSACTIONS ON POWER SYSTEMS 2017年第2期32卷 999-1006页

作者： Bezerra, Bernardo Veiga, Alvaro Barroso, Luiz Augusto Pereira, Mario Pontificia Univ Catolica Rio de Janeiro Dept Elect Engn BR-22453900 Rio de Janeiro Brazil PSR BR-22224006 Rio De Janeiro Brazil PSR Consulting Rio De Janeiro Brazil Comillas Pontifical Univ Inst Res Technol IIT Madrid Spain

The optimal scheduling of hydrothermal systems requires the representation of uncertainties in future streamflows to devise a cost-effective operations policy. stochastic optimization has been widely used as a powerful tool to solve this problem but results will necessarily depend on the stochastic model used to generate future scenarios for streamflows. Periodic autoregressive (PAR) models have been widely used in this task. However, its parameters are typically unknown and must be estimated from historical data, incorporating a natural estimation error. Furthermore, the model is just a linear approximation of the real stochastic process. The consequence is that the operator will be uncertain about the correct linear model that should be used at each period. The objective of this work is to assess the impacts of incorporating the uncertainty of the parameters of the PAR models into a stochastic hydrothermal scheduling model. The proposed methodology is tested with case studies based on data from the Brazilian hydroelectric system. It is shown that when the uncertainty of the parameters is ignored, the policies given by the stochastic optimization tend to be too optimistic.

关键词： Bootstrap hydro scheduling parameter uncertainty stochastic dynamic programming uncertainty assessment

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