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multistage stochastic inexact chance-constraint programming for an integrated biomass-municipal solid waste power supply management under uncertainty

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RENEWABLE & SUSTAINABLE ENERGY REVIEWS 2015年 41卷 1244-1254页

作者： Wu, C. B. Huang, G. H. Li, W. Xie, Y. L. Xu, Y. North China Elect Power Univ SC Resources & Environm Res Acad MOE Key Lab Reg Energy & Environm Syst Optimizat Beijing 102206 Peoples R China Chinese Acad Environm Planning Beijing 100012 Peoples R China

In this study, a multistage stochastic inexact chance-constraint programming (MSICCP) model is developed for power supply management under uncertainties. In the MSICCP model, methods of multistage stochastic programming (MSP), interval-parameter programming (IPP), and chance-constraint programming (CCP) are introduced into a general optimization framework, such that the developed model can tackle uncertainties described in terms of interval values and probability distribution s over a multistage context. Moreover, it can reflect dynamic and randomness of energy resources during the planning horizon. The developed method has been applied to a case of managing the process of power supply in an integrated biomass-municipal solid waste power plant. Useful solutions for the power supply management have been generated. Interval solutions associated with different risk levels of constraint violation have been obtained. The generated solutions can provide desired energy resource allocation with a minimized system cost, maximized system reliability and a maximized energy security. Tradeoffs between system costs and constraint-violation risks can also be tackled. Higher costs will increase system stability, while a desire for lower system costs will run into a risk of potential instability of the management system. They are helpful for supporting (a) adjustment or justification of allocation patterns of energy resources, and (b) analysis of interactions among economic cost, environmental requirement, and power supply security. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： multistage stochastic programming Chance-constraint programming Power supply management Uncertainty

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Variants to a knapsack decomposition heuristic for solving R&D pipeline management problems

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COMPUTERS & CHEMICAL ENGINEERING 2017年 96卷 18-32页

作者： Christian, Brianna Cremaschi, Selen Auburn Univ Dept Chem Engn 212 Ross Hall Auburn AL 36849 USA

The knapsack decomposition algorithm (KDA) (Christian and Cremaschi, 2015) decomposes the R&D pipeline management problem into a series of knapsack problems, which are solved along the planning horizon. It yields tight feasible solutions, and improves the solution times by several orders of magnitude for large instances. This paper investigates the impact of problem parameters and size, and KDA decision rules on KDA solution quality and time. The decision rules are (1) timing of new knapsack problem generations, and (2) formulation of the resource constraints in knapsack problems. The results revealed that the KDA decision trees were insensitive to problem parameters, and the KDA solution times grew super-linearly with linear increases in the length of the planning horizon and the number of products. The results suggest that the KDA where knapsack problems are generated after each realization with the original resource constraint yields the most accurate solutions in the quickest time. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： multistage stochastic programming Pharmaceutical R&D pipeline management Decision dependent uncertainty Endogenous uncertainty Knapsack decomposition algorithm

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The optimal harvesting problem under price uncertainty: the risk averse case

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ANNALS OF OPERATIONS RESEARCH 2017年第2期258卷 479-502页

作者： Pagnoncelli, Bernardo K. Piazza, Adriana Univ Adolfo Ibanez Escuela Negocios Diagonal Torres 2640 PenalolenOficina 533 C Santiago Chile Univ Tecn Federico Santa Maria Dept Matemat Ave Espana 1680Casilla 110-5 Valparaiso Chile

We study the exploitation of a one species, multiple stand forest plantation when timber price is governed by a stochastic process. Our model is a stochastic dynamic program with a weighted mean-risk objective function, and our main risk measure is the Conditional Value-at-Risk. We consider two stochastic processes, geometric Brownian motion and Ornstein-Uhlenbeck: in the first case, we completely characterize the optimal policy for all possible choices of the parameters while in the second, we provide sufficient conditions assuring that harvesting everything available is optimal. In both cases we solve the problem theoretically for every initial condition. We compare our results with the risk neutral framework and generalize our findings to any coherent risk measure that is affine on the current price.

关键词： multistage stochastic programming Optimal harvesting Forestry Coherent risk measures

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Assessment of risk-averse policies for the long-term hydrothermal scheduling problem

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ENERGY SYSTEMS-OPTIMIZATION MODELING SIMULATION AND ECONOMIC ASPECTS 2017年第1期8卷 103-125页

作者： Larroyd, Paulo Vitor de Matos, Vitor Luiz Finardi, Erlon Cristian Univ Fed Santa Catarina Florianopolis SC Brazil Plan4 Florianopolis SC Brazil

The goal of the long-term hydrothermal scheduling (LTHS) problem is to determine an optimal policy that minimises the expected operational cost over a multi-annual planning horizon. In this problem, inflows are naturally random;thus, the development of policies requires the use of specialised techniques such as stochastic optimization algorithms. Although the optimal policy defined by means of the expected cost is economically efficient, the associated decisions can incur a high risk of energy deficit. To overcome such disadvantages, one alternative is to include a risk-measure approach in the LTHS modeling. In this study, we compared two different risk-measure strategies applied to the LTHS problem: (i) a convex combination between the conditional value at risk (CVaR) and the expected operational cost, (ii) a reservoir risk-curve. To accomplish the comparison, we consider the Brazilian power system with a 5-year planning horizon discretized in monthly stages. The policies supplied by the risk-averse strategies are simulated in a set of synthetic inflow scenarios. Thus, the results are obtained in terms of the expected long-term hydrothermal decisions, such as the total operational cost and the reservoir storage. In summary, the CVaR-based policies provided better operational results than the risk-curve one.

关键词： multistage stochastic programming Long-term hydrothermal scheduling CVaR Risk-curve

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Optimal pension fund composition for an Italian private pension plan sponsor

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COMPUTATIONAL MANAGEMENT SCIENCE 2017年第1期14卷 135-160页

作者： Vitali, Sebastiano Moriggia, Vittorio Kopa, Milos Univ Bergamo Dept Management Econ & Quantitat Methods Via Caniana 2 I-24127 Bergamo Italy Charles Univ Prague Fac Math & Phys Dept Probabil & Math Stat Sokolovska 83 Prague 18675 Czech Republic

We address the problem of a private pension plan sponsor who has to find the best pension funds for its members. Starting from a descriptive analysis of the pension plan members we identify a set of representative subscribers. Then, the optimal allocation for each representative will become a pension fund of the pension plan. For each representative, we propose a multistage stochastic program (MSP) which includes a multi-criteria objective function. The optimal choice is the portfolio allocation that minimizes the average value at risk deviation of the final wealth and satisfies a wealth target in the final stage and other constraints regarding pension plan regulations. stochasticity arises from the investor's salary process and from asset returns. Numerical results show the optimal dynamic portfolios with respect to the investor's preferences and then the best pension funds the sponsor might offer.

关键词： Pension fund Optimal policy multistage stochastic programming Cluster analysis

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Solution Approaches to Large Scale multistage stochastic Programs with Endogenous and Exogenous Uncertainty

Solution Approaches to Large Scale Multistage Stochastic Pro...

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作者： Christian, Brianna Auburn University

学位级别：Ph.D., Doctor of Philosophy

The focus of this dissertation is the investigation of approaches to address the computational challenges of solving multistage stochastic programs (MSSPs) with both endogenous and exogenous uncertainty. My work to date has considered two MSSP case study problems. The first problem is the pharmaceutical R&D pipeline management problem where the objective is to determine the clinical trial schedule which maximized expected net present value considering uncertainty in the outcome of each clinical trial. The second is a new technology evaluation problem where the objective is to determine an optimal investment strategy for new technology development given uncertainty in the cost of capacity expansion, yield, technology success, and product demand. The computational complexity of MSSPs increases as the size of the problem (i.e. number of uncertain parameters) increases. To address this complexity, this dissertation introduces three different approaches. In the first approach, the goal was to find a feasible solution for computationally intractable MSSPs. To accomplish this, two heuristic algorithms that generate feasible solutions for the pharmaceutical clinical trial planning problem were developed. The first heuristic solves a series of two-stage stochastic programs with shrinking planning horizon. The second one uses a knapsack problem based approach to select clinical trial investments. The knapsack problem-based heuristic was generalized to Expected Value Decomposition Algorithm (EVDA) and used to solve instances of the NTIP problem. The EVDA algorithm provided tight feasible bounds on the solution of the deterministic MSSP for the NTIP problem. In the second approach, the computational complexity of the MSSPs is addressed using a branch and bound algorithm to find the true MSSP solution. The algorithm pairs the knapsack problem based decomposition heuristic with either an upper bound generated and updated using progressive hedging or optimal scenario solutions (OS

关键词： Optimization under Uncertainty multistage stochastic programming Clinical Trial Planning New Technology Investment Planning

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A stochastic mixed integer program to model spatial wildfire behavior and suppression placement decisions with uncertain weather

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CANADIAN JOURNAL OF FOREST RESEARCH 2016年第2期46卷 234-248页

作者： Belval, Erin J. Wei, Yu Bevers, Michael Colorado State Univ Dept Forest & Rangeland Stewardship Ft Collins CO 80523 USA USDA Forest Serv Rocky Mt Res Stn Ft Collins CO 80526 USA

Wildfire behavior is a complex and stochastic phenomenon that can present unique tactical management challenges. This paper investigates a multistage stochastic mixed integer program with full recourse to model spatially explicit fire behavior and to select suppression locations for a wildland fire. Simplified suppression decisions take the form of "suppression nodes", which are placed on a raster landscape for multiple decision stages. Weather scenarios are used to represent a distribution of probable changes in fire behavior in response to random weather changes, modeled using probabilistic weather trees. multistage suppression decisions and fire behavior respond to these weather events and to each other. Nonanticipativity constraints ensure that suppression decisions account for uncertainty in weather forecasts. Test cases for this model provide examples of fire behavior interacting with suppression to achieve a minimum expected area impacted by fire and suppression.

关键词： multistage stochastic programming wildfire growth wildfire suppression uncertain fire weather

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A mathematical model for vehicle routing problem under endogenous uncertainty

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2016年第2期54卷 579-590页

作者： Khaligh, F. Hooshmand MirHassani, S. A. Amirkabir Univ Technol Fac Math & Comp Sci Tehran Iran

In this study, a multistage stochastic programming (SP) model is presented for a variant of single-vehicle routing problem with stochastic demands from a dynamic viewpoint. It is assumed that the actual demand of a customer becomes known only when the customer is visited. This problem falls into the category of SP with endogenous uncertainty and hence, the scenario tree is decision-dependent. Therefore, nonanticipativity of decisions is ensured by conditional constraints making up a large portion of total constraints. Thus, a novel approach is proposed that considerably reduces the problem size without any effect on the solution space. Computational results on some test problems are reported.

关键词： multistage stochastic programming endogenous uncertainty vehicle routing problem dynamic strategy decision-dependent scenario tree nonanticipativity constraints

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An effective heuristic for multistage linear programming with a stochastic right-hand side

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COMPUTERS & OPERATIONS RESEARCH 2014年第Nov.期51卷 237-250页

作者： Beltran-Royo, C. Escudero, L. F. Monge, J. F. Rodriguez-Ravines, R. E. Rey Juan Carlos Univ Stat & Operat Res Dept Madrid Spain Miguel Hernandez Univ Stat Math & Comp Sci Dept Elche Spain Bayes Forecast Madrid Spain

The multistage stochastic Linear programming (SLP) problem may become numerically intractable for huge instances, in which case one can solve an approximation for example the well known multistage Expected Value (EV) problem. We introduce a new approximation to the SLP problem that we call the multistage Event Linear programming (ELP) problem. To obtain this approximation the SLP constraints are aggregated by means of the conditional expectation operator. Based on this new problem we derive the ELP heuristic that produces a lower and an upper bound for the SLP problem. We have assessed the validity of the ELP heuristic by solving large scale instances of the network revenue management problem, where the new approach has clearly outperformed the EV approach. One limitation of this paper is that it only considers randomness on the right-hand side, which is assumed to be discrete and stagewise independent. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： multistage stochastic programming Constraint aggregation Conditional expectation Scenario tree Revenue management

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multistage stochastic DECOMPOSITION: A BRIDGE BETWEEN stochastic programming AND APPROXIMATE DYNAMIC programming

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SIAM JOURNAL ON OPTIMIZATION 2014年第1期24卷 127-153页

作者： Sen, Suvrajeet Zhou, Zhihong Univ So Calif Daniel J Epstein Dept Ind & Syst Engn Los Angeles CA 90089 USA Univ Arizona SIE Dept MORE Inst Tucson AZ 85721 USA

Multistate stochastic programs pose some of the more challenging optimization problems. Because such models can become rather intractable in general, it is important to design algorithms that can provide approximations which, in the long run, yield solutions that are arbitrarily close to an optimum. In this paper, we propose such a sequential sampling method which is applicable to multistage stochastic linear programs, and we refer to it as the multistage stochastic decomposition (MSD) algorithm. This algorithm represents a dynamic extension of a regularized version of stochastic decomposition (SD). While the method allows general correlation structures, specialized streamlined versions are also possible for special cases of stagewise independent and autoregressive processes commonly incorporated in stochastic programming. As with its two-stage counterpart, the MSD algorithm is shown to provide an asymptotically optimal solution, with probability one. As a by-product of this study, we also show that SD algorithms draw upon features of both approximate dynamic programming as well as stochastic programming.

关键词： multistage stochastic programming sequential sampling stochastic decomposition approximate dynamic programming

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