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A new decomposition algorithm for multistage stochastic programs with endogenous uncertainties

COMPUTERS & CHEMICAL ENGINEERING 2014年 62卷 62-79页

作者： Gupta, Vijay Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

In this paper, we present a new decomposition algorithm for solving large-scale multistage stochastic programs (MSSPs) with endogenous uncertainties. Instead of dualizing all the initial non-anticipativity constraints (NACs) and removing all the conditional NACs to decompose the problem into scenario subproblems, the basic idea relies on keeping a subset of NACs as explicit constraints in the scenario group subproblems while dualizing or relaxing the rest of the NACs. It is proved that the algorithm provides a dual bound that is at least as tight as the standard approach. Numerical results for process network examples and oilfield development planning problem are presented to illustrate that the proposed decomposition approach yields significant improvement in the dual bound at the root node and reduction in the total computational expense for closing the gap. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： multistage stochastic programming Endogenous uncertainties Non-anticipativity constraints Lagrangean decomposition Process networks Oil and gas explorationa

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Tree structure generation from ensemble forecasts for real time control

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HYDROLOGICAL PROCESSES 2013年第1期27卷 75-82页

作者： Raso, L. van de Giesen, N. Stive, P. Schwanenberg, D. van Overloop, P. J. Delft Univ Technol Dept Water Resources Management Delft Netherlands Deltares Dept Operat Water Management Delft Netherlands

This paper presents a new methodology to generate a tree from an ensemble. The reason to generate a tree is to use the ensemble in multistage stochastic programming. A correct tree structure is of critical importance because it strongly affects the performance of the optimization. A tree, in contrast to an ensemble, specifies when its trajectories diverge from each other. A tree can be generated from the ensemble data by aggregating trajectories over time until the difference between them becomes such that they can no longer be assumed to be similar, at such a point, the tree branches. The proposed method models the information flow: it takes into account which observations will become available, at which moment, and their level of uncertainty, i.e. their probability distributions (pdf). No conditions are imposed on those distributions. The method is well suited to trajectories that are close to each other at the beginning of the forecasting horizon and spread out going on in time, as ensemble forecasts typically are. Copyright (C) 2012 John Wiley & Sons, Ltd.

关键词： multistage stochastic programming ensemble forecasts tree structure information real time control optimal control

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Mitigation strategies against supply disruption risk: a case study at the Ford Motor Company

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2022年第19期60卷 5956-5976页

作者： Sanci, Ece Daskin, Mark S. Hong, Young-Chae Roesch, Steve Zhang, Don Univ Michigan Ind & Operat Engn Ann Arbor MI 48109 USA Univ Bath Sch Management Bath Avon England Ford Motor Co Dearborn MI 48121 USA

Supply chains are exposed to different risks, which can be mitigated by various strategies based on the characteristics and needs of companies. In collaboration with Ford, we develop a decision support framework to choose the best mitigation strategy against supply disruption risk, especially for companies operating with a small supplier base and low inventory levels. Our framework is based on a multistage stochastic programming model which incorporates a variety of plausible strategies, including reserving backup capacity from the primary supplier, reserving capacity from a secondary supplier, and holding backup inventory. We reflect disruption risk into the framework through decision makers' input on the time to recover and the disruption probability. Our results demonstrate that relying on the strategy which is optimal when there is no disruption risk can increase the expected total cost substantially in the presence of disruption risk. However, this increase can be reduced significantly by investing in the mitigation strategy recommended by our framework. Our results also show that this framework removes the burden of estimating the time to recover and the disruption probability precisely since there is often a small loss associated with using another strategy that is optimal in the neighbourhood of the estimated values.

关键词： Supply chain risk management disruption risk mitigation sourcing mitigation contingency planning multistage stochastic programming

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On the convergence of sampling-based decomposition algorithms for multistage stochastic programs

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2005年第2期125卷 349-366页

作者： Linowsky, K Philpott, AB Univ St Gallen St Gallen Switzerland Univ Auckland Auckland 1 New Zealand

The paper presents a convergence proof for a broad class of sampling algorithms for multistage stochastic linear programs in which the uncertain parameters occur only in the constraint right-hand sides. This class includes SDDP, AND, ReSa, and CUPPS. We show that, under some independence assumptions on the sampling procedure, the algorithms converge with probability 1.

关键词： multistage stochastic programming sampling almost sure convergence

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A time-consistent Benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2021年第1期79卷 67-99页

作者： Yu, Haodong Sun, Jie Wang, Yanjun Shanghai Lixin Univ Accounting & Finance Sch Stat & Math Shanghai Peoples R China Natl Univ Singapore Sch Business Singapore Singapore Shanghai Univ Finance & Econ Sch Math Shanghai Peoples R China

A computational method is developed for solving time consistent distributionally robust multistage stochastic linear programs with discrete distribution. The stochastic structure of the uncertain parameters is described by a scenario tree. At each node of this tree, an ambiguity set is defined by conditional moment constraints to guarantee time consistency. This method employs the idea of nested Benders decomposition that incorporates forward and backward steps. The backward steps solve some conic programming problems to approximate the cost-to-go function at each node, while the forward steps are used to generate additional trial points. A new framework of convergence analysis is developed to establish the global convergence of the approximation procedure, which does not depend on the assumption of polyhedral structure of the original problem. Numerical results of a practical inventory model are reported to demonstrate the effectiveness of the proposed method.

关键词： multistage stochastic programming Distributionally robust Scenario tree model Decomposition method

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Optimal scheduling for enhanced coal bed methane production through CO₂ injection

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APPLIED ENERGY 2014年 113卷 1475-1483页

作者： Huang, Yuping Zheng, Qipeng P. Fan, Neng Aminian, Kashy Univ Cent Florida Dept Ind Engn & Management Syst Orlando FL 32816 USA Univ Arizona Dept Syst & Ind Engn Tucson AZ 85721 USA W Virginia Univ Dept Petr & Nat Gas Engn Morgantown WV 26506 USA

Enhanced coal bed methane production with CO2 injection (CO2-ECBM) is an effective technology for accessing the natural gas embedded in the traditionally unmineable coal seams. The revenue via this production process is generated not only by the sales of coal bed methane, but also by trading CO2 credits in the carbon market. As the technology of CO2-ECBM becomes mature, its commercialization opportunities are also springing up. This paper proposes applicable mathematical models for CO2-ECBM production and compares the impacts of their production schedules on the total profit. A novel basic deterministic model for CO2-ECBM production including the technical and chemical details is proposed and then a multistage stochastic programming model is formulated in order to address uncertainties of natural gas price and CO2 credit. Both models are nonlinear programming problems, which are solved by commercial nonlinear programming software BARON via GAMS. Numerical experiments show the benefits (e.g., expected profit gain) of using stochastic models versus deterministic models. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Coal bed methane production CO2 injection multistage stochastic programming Nonlinear programs Optimal scheduling

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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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Two-Scale stochastic Optimization for Controlling Distributed Storage Devices

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IEEE TRANSACTIONS ON SMART GRID 2018年第4期9卷 2691-2702页

作者： Gangammanavar, Harsha Sen, Suvrajeet Southern Methodist Univ Dept Engn Management Informat & Syst Dallas TX 75275 USA Univ Southern Carolina Daniel J Epstein Dept Ind & Syst Engn Los Angeles CA 90089 USA

This paper is motivated by a power system with storage devices at multiple locations which need to be controlled at a much finer timescale than that necessary for conventional generation units. We present a stochastic optimization model of the power system which captures interactions of decisions at these two timescales through a novel state-variable formulation. The model also includes transmission constraints approximated by a linearized de network, fast response operating reserves, and renewable generation. To tackle this high-dimensional multistage stochastic optimization problem, we present a sequential sampling method which we refer to as the stochastic dynamic linear programming. This algorithm is a dynamic extension of regularized two-stage stochastic decomposition for stagewise independent multistage stochastic linear programs, and is targeted at the class of problems where decisions are made at two different timescales. We compare our algorithm with the stochastic dual dynamic programming (SDDP) which has been effectively applied in planning power systems operations. Our computational results show that our sequential Monte-Carlo approach provides prescriptive solutions and values which are statistically indistinguishable from those obtained from SDDP, while improving computational times significantly.

关键词： multistage stochastic programming sampling-based algorithm distributed storage control

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Order Fulfillment Under Pick Failure in Omnichannel Ship-From-Store Programs

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M&SOM-MANUFACTURING & SERVICE OPERATIONS MANAGEMENT 2023年第2期25卷 508-523页

作者： Das, Sagnik Ravi, R. Sridhar, Srinath Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA Onera Inc San Francisco CA 94107 USA

Problem definition: We consider the setting where a retailer with many physical stores and an online presence seeks to fulfill online orders using an omnichannel fulfillment program, such as buy-online ship-from-store. These fulfillment strategies try to minimize cost while fulfilling orders within acceptable service times. We focus on single-item orders. Typically, all online orders for the item are sent to a favorable set of locations to be filled. Failed trials are sent back for further stages of trial fulfillment until the process times out. The multistage order fulfillment problem is thus an interplay of the pick-failure probabilities at the stores where they may be shipped from and the picking, shipping, and cancellation costs from these locations. Methodology: We model the problem as one of sequencing the stores from which an order is attempted to be picked and shipped in the most cost-effective way over multiple stages. We solve the fulfillment problem optimally by taking into account the changing pick-failure probabilities as a result of other online order fulfillment trials by casting it as a network flow problem with convex costs. We incorporate this as the second stage of a two-stage online order acceptance problem and generalize earlier results to the case with pick failures at stores. Results: We investigate the real-world performance of our methods and models on real order data of several of the top U.S. retailers that use our collaborating e-commerce solutions provider to optimize their fulfillment strategies. Academic/Practical Relevance: Our work enables retailers to incorporate pick failure in their order management systems for ship-from-store programs. Our new online order acceptance policies that take into account pick failures can thus create significant savings for omnichannel retailers.

关键词： omnichannel fulfillment pick failure multistage stochastic programming dynamic programming infinitesimal perturbation analysis

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Adaptation and approximate strategies for solving the lot-sizing and scheduling problem under multistage demand uncertainty

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2018年 202卷 81-96页

作者： Curcio, Eduardo Amorim, Pedro Zhang, Qi Almada-Lobo, Bernardo INESC TEC Porto Portugal Univ Porto Fac Engn INESC TEC Porto Portugal Univ Minnesota Dept Chem Engn & Mat Sci 421 Washington Ave SE Minneapolis MN 55455 USA

This work addresses the lot-sizing and scheduling problem under multistage demand uncertainty. A flexible production system is considered, with the possibility to adjust the size and the schedule of lots in every time period based on a rolling-horizon planning scheme. Computationally intractable multistage stochastic programming models are often employed on this problem. An adaptation strategy to the multistage setting for two-stage programming and robust optimization models is proposed. We also present an approximate heuristic strategy to address the problem more efficiently, relying on multistage stochastic programming and adjustable robust optimization. In order to evaluate each strategy and model proposed, a Monte Carlo simulation experiment under a rolling-horizon scheme is performed. Results show that the strategies are promising in solving large-scale problems: the approximate strategy based on adjustable robust optimization has, on average, 6.72% better performance and is 7.9 times faster than the deterministic model.

关键词： Lot-sizing and scheduling problem GLSP Adjustable robust optimization multistage stochastic programming Rolling-horizon

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