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Combining Polyhedral Approaches and stochastic Dual Dynamic Integer programming for Solving the Uncapacitated Lot-Sizing Problem Under Uncertainty

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INFORMS JOURNAL ON COMPUTING 2022年第2期34卷 1024-1041页

作者： Quezada, Franco Gicquel, Celine Kedad-Sidhoum, Safia Sorbonne Univ Lab Informat Paris 6 LIP6 Ctr Natl Rech Sci CNRS F-75005 Paris France Univ Santiago Chile USACH Program Dev Sustainable Prod Syst PDSPS Fac Engn Santiago Chile Univ Paris Saclay Lab Interdisciplinaire Sci Numer LISN F-91190 Gif Sur Yvette France Ctr Etud & Rech Informat & Commun CEDRIC Conservatoire Natl Arts & Metiers CNAM F-75003 Paris France

We study the uncapacitated lot-sizing problem with uncertain demand and costs. The problem is modeled as a multistage stochastic mixed-integer linear program in which the evolution of the uncertain parameters is represented by a scenario tree. To solve this problem, we propose a new extension of the stochastic dual dynamic integer programming algorithm (SDDiP). This extension aims at being more computationally efficient in the management of the expected cost-to-go functions involved in the model, in particular by reducing their number and by exploiting the current knowledge on the polyhedral structure of the stochastic uncapacitated lot-sizing problem. The algorithm is based on a partial decomposition of the problem into a set of stochastic subproblems, each one involving a subset of nodes forming a subtree of the initial scenario tree. We then introduce a cutting plane-generation procedure that iteratively strengthens the linear relaxation of these subproblems and enables the generation of an additional strengthened Benders' cut, which improves the convergence of the method. We carry out extensive computational experiments on randomly generated large-size instances. Our numerical results show that the proposed algorithm significantly outperforms the SDDiP algorithm at providing good-quality solutions within the computation time limit. Summary of Contribution: This paper investigates a combinatorial optimization problem called the uncapacitated lot-sizing problem. This problem has been widely studied in the operations research literature as it appears as a core subproblem in many industrial production planning problems. We consider a stochastic extension in which the input parameters are subject to uncertainty and model the resulting stochastic optimization problem as a multistage stochastic integer program. To solve this stochastic problem, we propose a novel extension of the recently published stochastic dual dynamic integer programming (SDDiP) algorithm. The prop

关键词： multistage stochastic programming stochastic lot sizing stochastic dual dynamic integer programming node aggregation valid inequalities partial decomposition

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A multistage formulation for generation companies in a multi-auction electricity market

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IMA JOURNAL OF MANAGEMENT MATHEMATICS 2010年第2期21卷 165-181页

作者： Musmanno, Roberto Scordino, Nadia Triki, Chefi Violi, Antonio Univ Calabria Supercomp Ctr Computat Engn I-87036 Arcavacata Di Rende Italy Univ Salento Dept Math I-73100 Lecce Italy Univ Calabria Dept Elect Informat & Syst I-87036 Arcavacata Di Rende Italy

In this paper. we deal with the definition of a decision model for a producer operating in a multi-auction electricity market. The decisions to be taken concern the commitment of the generation plants and the quantity of enemy required to offer to each auction and to cover the bilateral contracts. We propose a multistage stochastic programming model in which the randomness of the clearing prices is represented by means of a scenario tree. The risk is modelled using a Conditional Value at Risk term in the objective function. Experimental results are reported to show the validity of our model and to discuss the influence of the risk parameters on the optimal value.

关键词： electricity market multistage stochastic programming bidding strategy Conditional Value at Risk

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Gas storage valuation in incomplete markets

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第1期288卷 318-330页

作者： Loehndorf, Nils Wozabal, David Univ Luxembourg Luxembourg Ctr Logist & Supply Chain Management L-1511 Luxembourg Luxembourg Tech Univ Munich TUM Sch Management D-80333 Munich Germany

Natural gas storage valuation is an important problem in energy trading, yet most valuation approaches are based on heuristics or ignore that gas markets are incomplete. We propose an exact valuation model for incomplete gas markets based on multistage stochastic programming. Market incompleteness structurally changes the problem of storage valuation and asset backed trading and the resulting model requires analysis of a combined control problem of storage operation and futures trading that takes risk preferences into account. As the problem is subject to the curse of dimensionality, we reduce the stochastic process to a scenario lattice and solve the resulting problem using stochastic dual dynamic programming. We show that the intrinsic value of storage corresponds to the value under perfect risk aversion and that the rolling intrinsic value, which is popular among practitioners and has been found to be near-optimal when markets are complete, is an inconsistent price rule in incomplete markets. Our results inform managerial decisions on risk management and asset pricing for natural gas highlighting the importance of explicitly modeling risk preferences. (C) 2020 Elsevier B.V. All rights reserved.

关键词： multistage stochastic programming Asset pricing Natural gas industry Markov processes

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Scenario-based dynamic corporate bond portfolio management

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IMA JOURNAL OF MANAGEMENT MATHEMATICS 2012年第4期23卷 341-364页

作者： Beraldi, Patrizia De Simone, Francesco Violi, Antonio Consigli, Giorgio Iaquinta, Gaetano Univ Calabria Dept Elect Informat & Syst I-87030 Commenda Di Rende Italy Univ Bergamo Dept Math Stat & Comp Sci Bergamo Italy

The 2008 credit crisis has deeply affected the price of corporate liabilities in both equity and fixed income secondary markets leading to unprecedented portfolio losses by financial investors. A coordinated intervention by monetary institutions limited the systemic consequences of the crisis, without, however, avoiding a significant fall of corporate bond prices across international markets. In this article, we analyse alternative portfolio optimization approaches in the fixed income market over the 2008-2009 period, a time in which credit derivative markets became very illiquid. All policies are analysed relying on a unique set of market and credit scenarios generated by common and idiosyncratic risk factors on an extended investment universe. The crisis provides an interesting test period to analyse in particular the potential of dynamic versus static portfolio selection approaches. We also consider dynamic portfolio strategies based on multistage stochastic programming versus policy rule-based methods and analyse their relative performance against a corporate bond index widely adopted in practice as a market benchmark.

关键词： multistage stochastic programming scenario generation credit risk Monte Carlo simulation

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On the convergence of stochastic dual dynamic programming and related methods

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OPERATIONS RESEARCH LETTERS 2008年第4期36卷 450-455页

作者： Philpott, A. B. Guan, Z. Univ Auckland Dept Engn Sci Auckland New Zealand

We discuss the almost-sure convergence of a broad class of sampling algorithms for multistage stochastic linear programs. We provide a convergence proof based on the finiteness of the set of distinct cut coefficients. This differs from existing published proofs in that it does not require a restrictive assumption. (C) 2008 Elsevier B.V. All rights reserved.

关键词： multistage stochastic programming Monte-Carlo sampling Benders decomposition

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Addressing the scheduling of chemical supply chains under demand uncertainty

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AICHE JOURNAL 2006年第11期52卷 3864-3881页

作者： Guillen, Gonzalo Espuna, Antonio Puigjaner, Luis Univ Politecn Cataluna Dept Chem Engn ETSEIB E-08028 Barcelona Spain

A multistage stochastic optimization model is presented to address the scheduling of supply chains with embedded multipurpose batch chemical plants under demand uncertainty. In order to overcome the numerical difficulties associated with the resulting large-scale stochastic mixed-integer-linear-programming (MILP) problem, an approximation strategy comprising two steps, and based on the resolution of a set of deterministic and two-stage stochastic models is presented. The performance of the proposed strategy regarding computation time and optimality gap is studied through comparison with other traditional approaches that address optimization under uncertainty. Results indicate that the proposed strategy provides better solutions than stand-alone two-stage stochastic programming and two-stage shrinking-horizon algorithms for similar computational efforts and incurs much lower computation times than the rigorous multistage stochastic model. (c) 2006 American Institute of Chemical Engineers AIChE J, 52: 3864-3881, 2006.

关键词： SCM multistage stochastic programming

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Scenario analysis of demand in a technology market using leading indicators

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IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING 2001年第1期14卷 65-75页

作者： Meixell, MJ Wu, SD George Mason Univ Sch Management Fairfax VA 22030 USA Lehigh Univ Dept Ind & Mfg Syst Engn Bethlehem PA 18015 USA

This paper proposes an approach to analyzing demand scenarios in technology-driven markets where product demands are volatile, but follow a few identifiable lifecycle patterns, After examining a large amount of semiconductor data, we found that not only can products be clustered by lifecycle patterns, but in each cluster there exists a leading indicator product that provides advanced indication of changes in demand trends, Motivated by this finding, we propose a scenario analysis structure in the context of stochastic programming. Specifically, the demand model that results from this approach provides a mechanism for building a scenario tree for semiconductor demand, Using the Bass growth model and a Bayesian update structure, the approach streamlines scenario analysis by focusing on parametric changes of the demand growth model over time, The Bayesian structure allows expert judgment to be incorporated into scenario generation while the Bass growth model allows an efficient representation of time varying demands. Further, by adjusting a likelihood threshold, the method generates scenario trees of different sizes and accuracy, This structure provides a practical scenario analysis method for manufacturing demand in a technology market. We demonstrate the applicability of this method using real semiconductor data.

关键词： bass diffusion model Bayesian structure growth models leading indicators manufacturing demand analysis manufacturing logistics multistage stochastic programming planning and decision making scenario analysis semiconductor manufacturing

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Risk neutral and risk averse stochastic Dual Dynamic programming method

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2013年第2期224卷 375-391页

作者： Shapiro, Alexander Tekaya, Wajdi da Costa, Joari Paulo Soares, Murilo Pereira Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA ONS Operador Nacl Sistema Eletr BR-20091005 Ctr Rio De Janeiro RJ Brazil

In this paper we discuss risk neutral and risk averse approaches to multistage (linear) stochastic programming problems based on the stochastic Dual Dynamic programming (SDDP) method. We give a general description of the algorithm and present computational studies related to planning of the Brazilian interconnected power system. (C) 2012 Elsevier B.V. All rights reserved.

关键词： multistage stochastic programming Dynamic equations stochastic Dual Dynamic programming Sample average approximation Risk averse Average Value-at-Risk

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Convergent cutting-plane and partial-sampling algorithm for multistage stochastic linear programs with recourse

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1999年第3期102卷 497-524页

作者： Chen, ZL Powell, WB Univ Penn Dept Syst Engn Philadelphia PA 19104 USA Princeton Univ Dept Civil Engn & Operat Res Princeton NJ 08544 USA

We propose an algorithm for multistage stochastic linear programs with recourse where random quantities in different stages are independent. The algorithm approximates successively expected recourse functions by building up valid cutting planes to support these functions from below. In each iteration, for the expected recourse function in each stage, one cutting plane is generated using the dual extreme points of the next-stage problem that have been found so far. We prove that the algorithm is convergent with probability one.

关键词： multistage stochastic programming cutting planes sampling convergence with probability one

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Optimization of R&D project portfolios under endogenous uncertainty

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第1期207卷 420-433页

作者： Solak, Senay Clarke, John-Paul B. Johnson, Ellis L. Barnes, Earl R. Univ Massachusetts Isenberg Sch Management Dept Finance & Operat Management Amherst MA 01003 USA Georgia Inst Technol Sch Aerosp Engn Atlanta GA 30332 USA Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

Project portfolio management deals with the dynamic selection of research and development (R&D) projects and determination of resource allocations to these projects over a planning period. Given the uncertainties and resource limitations over the planning period, the objective is to maximize the expected total discounted return or the expectation of some other function for all projects over a long time horizon. We develop a detailed formal description of this problem and the corresponding decision process, and then model it as a multistage stochastic integer program with endogenous uncertainty. Accounting for this endogeneity, we propose an efficient solution approach for the resulting model, which involves the development of a formulation technique that is amenable to scenario decomposition. The proposed solution algorithm also includes an application of the sample average approximation method, where the sample problems are solved through Lagrangian relaxation and a new lower bounding heuristic. The performance of the overall solution procedure is demonstrated using several implementations of the proposed approach. (C) 2010 Elsevier B.V. All rights reserved.

关键词： OR in research and development Project portfolio Technology management R&D multistage stochastic programming Endogenous uncertainty

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