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Step decision rules for multistage stochastic programming:: A heuristic approach

AUTOMATICA 2008年第6期44卷 1569-1584页

作者： Thenie, J. Vial, J. -Ph. Univ Geneva HEC Logilab Dept Management Studies CH-1211 Geneva 4 Switzerland OREDCSYS Geneva Switzerland

stochastic programming with step decision rules (SPSDR) aims to produce efficient solutions to multistage stochastic optimization problems. SPSDR, like plain multistage stochastic programming (SP), operates on a Monte Carlo "computing sample" of moderate size that approximates the stochastic process. Unlike SP, SPSDR does not strive to build a balanced event tree out of that sample. Rather, it defines a solution as a special type of decision rule, with the property that the decisions at each stage are piecewise constant functions on the sample of scenarios. Those pieces define a partition of the set of scenarios at each stage t, but the partition at t + 1 need not be refinement of the partition at t. However, the rule is constructed so that the non-anticipativity condition is met, a necessary condition to make the rules operational. To validate the method we show how to extend a non-anticipatory decision rule to arbitrary scenarios within a very large validation sample of scenarios. We apply three methods, SPSDR, SP and Robust Optimization, to the same 12-stage problem in supply chain management, and compare them relatively to different objectives and performance criteria. It appears that SPSDR performs better than SP in that it produces a more accurate estimate (prediction) of the value achieved by its solution on the validation sample, and also that the achieved value is better. (c) 2008 Elsevier Ltd. All rights reserved.

关键词： multistage stochastic programming

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On the impact of deep learning-based time-series forecasts on multistage stochastic programming policies

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INFOR 2022年第2期60卷 133-164页

作者： Wang, Juyoung Cevik, Mucahit Bodur, Merve Univ Toronto Dept Mech & Ind Engn Toronto ON Canada Ryerson Univ Dept Mech & Ind Engn Toronto ON Canada

multistage stochastic programming provides a modeling framework for sequential decision-making problems that involve uncertainty. One typically overlooked aspect of this methodology is how uncertainty is incorporated into modeling. Traditionally, statistical forecasting techniques with simple forms, e.g. (first-order) autoregressive time-series models, are used to extract scenarios to be added to optimization models to represent the uncertain future. However, often times, the performance of these forecasting models are not thoroughly assessed. Motivated by the advances in probabilistic forecasting, we incorporate a deep learning-based time-series forecasting method into multistage stochastic programming framework, and compare it with the cases where a traditional forecasting method is employed to model the uncertainty. We assess the impact of more accurate forecasts on the quality of two commonly used look-ahead policies, a deterministic one and a two-stage one, in a rolling-horizon framework on a practical problem. Our results illustrate that more accurate forecasts contribute substantially to the model performance, and enable obtaining high-quality solutions even from computationally cheap heuristics. They also show that the probabilistic forecasting capabilities of deep learning-based methods can be especially beneficial when used as a (conditional) sampling tool for scenario-based models, and to predict the worst-case scenario for risk-averse models.

关键词： multistage stochastic programming policy evaluation lot-sizing problem time-series forecasting deep learning autoregressive process

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Approximation of multistage stochastic programming problems by smoothed quantization

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REVIEW OF MANAGERIAL SCIENCE 2024年第7期18卷 2079-2114页

作者： Smid, Martin Kozmik, Vaclav Czech Acad Sci Inst Informat Theory & Automat Vodarenskou Vezi 4 Prague 8 Czech Republic Charles Univ Prague Fac Math & Phys Dept Probabil & Math Stat Sokolovska 49-83 Prague Czech Republic

We present an approximation technique for solving multistage stochastic programming problems with an underlying Markov stochastic process. This process is approximated by a discrete skeleton process, which is consequently smoothed down by means of the original unconditional distribution. Approximated in this way, the problem is solvable by means of Markov stochastic Dual Dynamic programming. We state an upper bound for the nested distance between the exact process and its approximation and discuss its convergence in the one-dimensional case. We further propose an adjustment of the approximation, which guarantees that the approximate problem is bounded. Finally, we apply our technique to a real-life production-emission trading problem and demonstrate the performance of its approximation given the "true" distribution of the random parameters.

关键词： multistage stochastic programming Approximation Markov dependence SDDP C61

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multistage stochastic programming Model for the Portfolio Problem of a Property-Liability Insurance Company

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Transactions of Tianjin University 2002年第3期8卷 203-206页

作者：王春峰杨建林蒋祥林天津大学管理学院天津300072

The current portfolio model for property-liability insurance company is only single period that can not meet the practical demands of portfolio management, and the purpose of this paper is to develop a multiperiod model for its portfolio problem. The model is a multistage stochastic programming which considers transaction costs, cash flow between time periods, and the matching of asset and liability; it does not depend on the assumption for normality of return distribution. Additionally, an investment constraint is added. The numerical example manifests that the multiperiod model can more effectively assist the property-liability insurer to determine the optimal composition of insurance and investment portfolio and outperforms the single period one.

关键词： property-liability insurance company portfolio management multiperiod model multistage stochastic programming

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A NEW METHODOLOGY BASED ON multistage stochastic programming FOR QUALITY CHAIN DESIGN PROBLEM

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INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING-THEORY APPLICATIONS AND PRACTICE 2017年第1期24卷 12-31页

作者： Hejazi, Taha-Hossein Seyyed-Esfahani, Mirmehdi Antony, Jiju Amirkabir Univ Technol Tehran Polytech Dept Ind Engn Garmsar Iran Amirkabir Univ Technol Tehran Polytech Dept Ind Engn & Management Syst Tehran Iran Heriot Watt Univ Dept Business Management Edinburgh Midlothian Scotland

In multi-stage manufacturing/service systems, quality of final products depends on several decision variables and design factors from several stages of operations as well as environmental and operational nuisance factors. Typically, the effects of factors in one stage might remain significant at the next stages. Due to a high degree of interdependencies among the variables in/between the stages, multistage quality control methods have recently attracted special attentions. Multi-response optimization is a well-grounded method for an offline quality design that can consider several inputs and outputs. This study introduces a new multiresponse surface methodology by proposing two different modeling approaches for quality optimization in multistage systems with multiple response variables. Several stochastic parameters, including response surfaces and covariates, are to be considered the proposed models. In order to cope with the uncertainty, multistage stochastic programming is applied with a scenario generation algorithm based on Nataf transformation for correlated parameters. Also, a comprehensive numerical analysis is done to give more insights into the application of the proposed approach.

关键词： design of experiments multiresponse optimization multistage stochastic programming robust design quality chain design

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Seasonal operation planning of hydrogen-enabled multi-energy microgrids through multistage stochastic programming

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JOURNAL OF ENERGY STORAGE 2024年 85卷

作者： Sun, Xunhang Cao, Xiaoyu Li, Miaomiao Zhai, Qiaozhu Guan, Xiaohong Xi An Jiao Tong Univ Sch Automat Sci & Engn Xian 710049 Peoples R China Xi An Jiao Tong Univ Natl Innovat Platform Ctr Ind Educ Integrat Energy Xian 710049 Peoples R China Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA Tsinghua Univ Ctr Intelligent & Networked Syst Dept Automat Beijing 100084 Peoples R China

As a carbon-free storage medium, hydrogen has advantages in large-scale and long -term energy shifting, thereby mitigating the seasonal imbalance between energy supply and demands. By integrating hydrogen, electricity, heating and cooling, the hydrogen-enabled multi -energy microgrid (HMM) provides a desirable test bed for decarbonizing the energy and power systems. In this paper, we study the networked HMMs operation planning (NHOP) that optimizes the multi-timescale synergy of seasonal and short -term energy storage. To hedge against the complex demand-supply uncertainties (e.g., seasonal fluctuation and hourly variation of renewable power generation and energy demands), the NHOP problem is recast as a multistage stochastic mixed-integer program (MS-MIP). Moreover, to overcome the computational challenges, a nested decomposition algorithm based on stochastic dual dynamic integer programming (SDDiP) is tailored and implemented. Case studies on a 33 -bus test network with multiple HMMs demonstrate the economic benefits of our operation planning strategy. The proposed NHOP model can well capture the seasonal and intra-day dynamics of multi -type storage operation, which helps improve the cost-benefits under versatile practical situations. Also, the customized SDDiP algorithm shows a strong scalable capacity for efficiently computing large-scale MS-MIPs.

关键词： Hydrogen-enabled microgrids Multi-energy synergy Operation planning Seasonal hydrogen storage multistage stochastic programming

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Limited multistage stochastic programming for Water Distribution Systems Optimal Operation

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JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT 2016年第10期142卷 1-6页

作者： Schwartz, Rafael Housh, Mashor Ostfeld, Avi Technion Israel Inst Technol Fac Civil & Environm Engn IL-32000 Haifa Israel Univ Haifa Dept Nat Resources & Environm Management IL-31905 Haifa Israel

Least-cost operation of water distribution systems (WDS) is a well-known problem in water distribution systems optimization. The formulation of the problem started with deterministic modeling, and the problem was subsequently handled with more sophisticated stochastic models that incorporate uncertainties related to the problem's parameters. This work applied a recently developed algorithm entitled limited multistage stochastic programming (LMSP) to deal with the stochastic formulation of the least-cost operation of WDS and serves merely as a proof of concept on an illustrative network. The demand is considered as the uncertain parameter in the problem formulation. This algorithm reduces the complexity of the classical multistage stochastic programming (MSP) by adding constraints which result in a linear growth of the problem, as opposed to an exponential growth in the MSP problem. This is accomplished by clustering decision variables based on a postanalysis of the implicit stochastic program of the problem. The clusters allow reduction of the number of decision variables, thus reducing the complexity of the optimization problem. The LMSP is expected to increase the cost because of the additional constraints imposed on the problem;however, a trade-off exists between the computational complexity and the optimality of the objective value to the number of clusters considered. An illustrative example application is provided for demonstrating the suggested methodology abilities.

关键词： multistage stochastic programming Limited multistage stochastic programming Water distribution system Operation Optimization

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Airline network revenue management by multistage stochastic programming

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COMPUTATIONAL MANAGEMENT SCIENCE 2008年第4期5卷 355-377页

作者： Moeller, Andris Roemisch, Werner Weber, Klaus Humboldt Univ Inst Math Unter Linden 6 D-10099 Berlin Germany AIDA Cruises D-18055 Rostock Germany

A multistage stochastic programming approach to airline network revenue management is presented. The objective is to determine seat protection levels for all itineraries, fare classes, points of sale of the airline network and all dcps of the booking horizon such that the expected revenue is maximized. While the passenger demand and cancelation rate processes are the stochastic inputs of the model, the stochastic protection level process represents its output and allows to control the booking process. The stochastic passenger demand and cancelation rate processes are approximated by a finite number of tree structured scenarios. The scenario tree is generated from historical data using a stability-based recursive scenario reduction scheme. Numerical results for a small hub-and-spoke network are reported.

关键词： Airline revenue management Seat inventory control multistage stochastic programming Scenario tree generation

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A primal-dual decomposition algorithm for multistage stochastic convex programming

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MATHEMATICAL programming 2005年第1期104卷 153-177页

作者： Berkelaar, A Gromicho, JAS Kouwenberg, R Zhang, SZ Vrije Univ Amsterdam NL-1081 HV Amsterdam Netherlands ORTEC Int Gouda Netherlands Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China

This paper presents a new and high performance solution method for multistage stochastic convex programming. stochastic programming is a quantitative tool developed in the field of optimization to cope with the problem of decision-making under uncertainty. Among others, stochastic programming has found many applications in finance, such as asset-liability and bond-portfolio management. However, many stochastic programming applications still remain computationally intractable because of their overwhelming dimensionality. In this paper we propose a new decomposition algorithm for multistage stochastic programming with a convex objective and stochastic recourse matrices, based on the path-following interior point method combined with the homogeneous self-dual embedding technique. Our preliminary numerical experiments show that this approach is very promising in many ways for solving generic multistage stochastic programming, including its superiority in terms of numerical efficiency, as well as the flexibility in testing and analyzing the model.

关键词： multistage stochastic programming convex objective interior point method homogeneous self-dual embedding

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Solving multistage stochastic linear programming via regularized linear decision rules: An application to hydrothermal dispatch planning

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第1期309卷 345-358页

作者： Nazare, Felipe Street, Alexandre Pontifical Catholic Univ Rio DeJaneiro Elect Engn Dept LAMPS PUC Rio Rio De Janeiro Brazil

The solution of multistage stochastic linear problems (MSLPs) represents a challenge for many applications. Long-term hydrothermal dispatch planning (LHDP) materializes this challenge in a real-world problem that affects electricity markets, economies, and natural resources worldwide. No closed-form solutions are available for MSLP and the definition of non-anticipative policies with high-quality outof-sample performance is crucial. Linear decision rules (LDRs) provide an interesting simulation-based framework for finding high-quality policies for MSLP through two-stage stochastic models. In practical applications, however, the number of parameters to be estimated when using an LDR may be close to or higher than the number of scenarios of the sample average approximation problem, thereby generating an in-sample overfit and poor performances in out-of-sample simulations. In this paper, we propose a novel regularized LDR to solve MSLP based on the AdaLASSO (adaptive least absolute shrinkage and selection operator). The goal is to use the parsimony principle, as largely studied in high-dimensional linear regression models, to obtain better out-of-sample performance for a LDR applied to MSLP. Computational experiments show that overfitting is a non-negligible threat when using the classical non-regularized LDR to solve the LHDP, one of the most studied MSLP with relevant applications in industry. Our analysis highlights the following benefits of the proposed framework in comparison to the non-regularized benchmark: 1) significant reductions in the number of non-zero coefficients (model parsimony), 2) substantial cost reductions in out-of-sample evaluations, and 3) improved spot-price profiles. (c) 2022 Elsevier B.V. All rights reserved.

关键词： OR in energy AdaLASSO Long -term hydrothermal dispatch planning multistage stochastic programming Regularized linear decision rules

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