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A column-and-constraint generation algorithm for two-stage stochastic programming problems

TOP 2021年第3期29卷 781-798页

作者： Tonissen, Denise D. Arts, Joachim J. Shen, Zuo-Jun Max Vrije Univ Amsterdam Sch Business & Econ Dept Operat Analyt Amsterdam Netherlands Univ Luxembourg Ctr Logist & Supply Chain Management Luxembourg Luxembourg Univ Calif Berkeley Dept Ind Engn & Operat Res Berkeley CA 94720 USA

This paper presents a column-and-constraint generation algorithm for two-stage stochastic programming problems. A distinctive feature of the algorithm is that it does not assume fixed recourse and as a consequence the values and dimensions of the recourse matrix can be uncertain. The proposed algorithm contains multi-cut (partial) Benders decomposition and the deterministic equivalent model as special cases and can be used to trade-off computational speed and memory requirements. The algorithm outperforms multi-cut (partial) Benders decomposition in computational time and the deterministic equivalent model in memory requirements for a maintenance location routing problem. In addition, for instances with a large number of scenarios, the algorithm outperforms the deterministic equivalent model in both computational time and memory requirements. Furthermore, we present an adaptive relative tolerance for instances for which the solution time of the master problem is the bottleneck and the slave problems can be solved relatively efficiently. The adaptive relative tolerance is large in early iterations and converges to zero for the final iteration(s) of the algorithm. The combination of this relative adaptive tolerance with the proposed algorithm decreases the computational time of our instances even further.

关键词： stochastic programming Column-and-constraint generation Benders decomposition Facility location

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Reshore or not Reshore: A stochastic programming Approach to Supply Chain Optimization

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2023年 118卷

作者： Sawik, Tadeusz Reykjavik Univ Dept Engn IS-101 Reykjavik Iceland

This paper presents a scenario-based stochastic mixed integer programming model for risk-neutral or risk-averse optimization of supply chain reshoring to domestic region, under the ripple effect propagated from a foreign disruption source region. The reshoring decisions with respect to tier-one suppliers of parts and tier-zero OEM (Original Equipment Manufacturer) assembly plants are considered under disruptions in supply, manufacturing, logistics and demand rippling across the entire supply chain. The proposed in-novative approach integrates strategic supply chain reshoring and operational supply chain scheduling, which allows the decision maker to evaluate the operational impact of the strategic decision. Results of computational experiments, partially modeled after a supply chain reshoring problem in the smartphone industry, are provided. The findings indicate that reshoring decisions are strongly dependent on the level of government subsidy for capital expenditure and for risk-neutral reshoring, a portfolio of supply chain nodes with positive expected net savings can be considered only. In general, the reshored supply chain can better meet domestic market demand. Moreover, full reshoring of a supply chain improves its busi-ness as usual performance and even partial reshoring mitigates the impact of the ripple effect. However, for risk-averse decision-making, if reshoring is incapable of reducing worst-case cost, in particular, worst-case lost sales, no reshoring is selected.(c) 2023 Elsevier Ltd. All rights reserved.

关键词： supply chain risk management ripple effect reshoring stochastic programming mixed integer programming

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A stochastic programming approach to surgery scheduling under parallel processing principle

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2023年 115卷

作者： Celik, Batuhan Gul, Serhat Celik, Melih Bilkent Univ Dept Ind Engn Ankara Turkiye TED Univ Dept Ind Engn TR-06420 Ankara Turkiye Univ Bath Sch Management Bath Avon England

Parallel processing is a principle which enables simultaneous implementation of anesthesia induction and operating room (OR) turnover with the aim of improving OR utilization. In this article, we study the prob-lem of scheduling surgeries for multiple ORs and induction rooms (IR) that function based on the parallel processing principle under uncertainty. We propose a two-stage stochastic mixed-integer programming model considering the uncertainty in induction, surgery and turnover durations. We sequence patients and set appointment times for surgeries in the first stage and assign patients to IRs at the second stage of the model. We show that an optimal myopic policy can be used for IR assignment decisions due to the special structure of the model. We minimize the expected total cost of patient waiting time, OR idle time and IR idle time in the objective function. We enhance the model formulation using bounds on variables and symmetry-breaking constraints. We implement a novel progressive hedging algorithm by proposing a penalty update method and a variable fixing mechanism. Based on real data of a large academic hospi-tal, we compare our solution approach with several scheduling heuristics from the literature. We assess the additional benefits and costs associated with the implementation of parallel processing using near -optimal schedules. We examine how the benefits are inflated by increasing the number of IRs. Finally, we estimate the value of stochastic solution to underline the importance of considering uncertainty in durations. (c) 2022 Elsevier Ltd. All rights reserved.

关键词： Surgery scheduling stochastic programming Parallel processing Progressive hedging

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Short-term uncertainty in the dispatch of energy resources for VPP: A novel rolling horizon model based on stochastic programming

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2023年第1期153卷

作者： Gulotta, F. del Granado, P. Crespo Pisciella, P. Siface, D. Falabretti, D. Politecn Milan Davide Falabretti & Francesco Gulotta Dept Energy Milan Italy Norwegian Univ Sci & Technol Pedro Crespo del Granado & Paolo Pisciella Dept In Trondheim Norway Dario Siface Dept Energy Syst Dev Ric Sistema Ener Milan Italy

The intermittent nature of distributed energy resources introduces new degrees of uncertainty in the operation of energy systems;hence, short-term decisions can no longer be considered fully deterministic. In this article, an energy management system (EMS) was proposed to optimize the market participation and the real-time operation of a virtual power plant (VPP) composed of photovoltaic generators, non-flexible loads, and storage systems (e-vehicle, stationary battery, and thermal storage). The market bidding process was optimized through a twostage stochastic formulation, which considered the day-ahead forecast uncertainty to minimize the energy cost and make available reserve margins in the ancillary service market. The real-time management of regulating resources was obtained through an innovative rolling horizon stochastic programming model, taking into account the effects of short-term uncertainties. Numerical simulations were carried out to demonstrate the effectiveness of the proposed EMS. The architecture proved to be effective in managing several distributed resources, enabling the provision of ancillary services to the power system. In particular, the model developed allowed an increase in the VPP's profits of up to 11% and a reduction in the energy imbalance of 25.1% compared to a deterministic optimization.

关键词： stochastic programming Rolling horizon Energy management system Uncertainty Virtual power plant

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Modeling and solution for hybrid flow-shop scheduling problem by two-stage stochastic programming

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EXPERT SYSTEMS WITH APPLICATIONS 2023年第1期233卷

作者： Huang, Yiping Deng, Libao Wang, Jianlei Qiu, Weiwei Liu, Jinfeng Qingdao Hatran Ocean Intelligence Technol Co Ltd Qingdao 266404 Peoples R China Harbin Inst Technol Sch Informat Sci & Engn Weihai 264209 Peoples R China Beijing Vatitude Technol Co Ltd Beijing 100089 Peoples R China Minist Nat Resources Informat Ctr Beijing 100830 Peoples R China Northeastern Univ Coll Informat Sci & Engn Shenyang 110006 Peoples R China

To adapt to the uncertainty of the real environment and solve the problem of high efficiency and high quality, this study comprehensively considers a variety of uncertainty factors, focusing on modeling and solving a hybrid flow-shop scheduling problem by two-stage stochastic programming (HFSP-TSP). First, this paper uses a twostage scenario tree to describe the uncertain factors, the probabilities and values are obtained under different discrete production scenarios, and stochastic programming theory is used to formulate a mixed-integer linear programming (MILP) model for HFSP-TSP. Second, based on a general discrete optimization algorithm framework, that is, pointer-based discrete differential evolution (PDDE) algorithm, a novel variant (H-PDDE) is proposed for effectively solving the HFSP-TSP. It adopts a permutation scheduling decoding method and introduces three new improvement strategies: the strategy of inconsistent code length of individuals in the population, adding local search in discrete mutation operation, using a heuristic algorithm to generate the initial population. Finally, computational experiments were conducted to illustrate the proposed mathematical model and optimization algorithm. The computational results show that the H-PDDE can solve the HFSP-TSP more effectively than existing algorithms and conventional PDDE variants. The stochastic programming model is increasingly superior to the deterministic model in an uncertain environment. The source code of the H-PDDE algorithm and its data files can be found at https://***/huangyiping-ai/***, which is publicly available.

关键词： Uncertainty Hybrid flow -shop scheduling stochastic programming Differential evolution Discrete optimization

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Improved Konno Yamazaki model: Portfolio optimization based on stochastic and fuzzy programming

JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GA...

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JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GAZI UNIVERSITY 2025年第2期40卷 995-1010页

作者： Kelce, Mehves Guliz Atalay, Kumru Didem Derya, Tusan Baskent Univ Fac Engn Dept Ind Engn TR-06790 Ankara Turkiye

Return is a term that refers to the financial results of an investment or financial asset, usually over a given period. Returns play an important role in investors' financial decision-making. Investors who want to maximize their returns should also consider the risk of the investment, the maturity and other factors. Financial life is full of uncertainties and it is difficult to predict what the future holds for investors. Since earnings are in most cases not certain and involve many uncertainties, the concept of expected return emerges, which provides an estimated return. In cases where the expected return cannot be determined exactly, rational investors choose investments with the highest expected return at a certain risk level;at a certain level of expected return, they prefer the investments with the lowest risk. Moreover, in order to improve the quality of investment, it is very important to provide investors with alternative portfolio options for the future. In this study, the fuzzy and stochastic Konno-Yamazaki model is considered to determine the investment amounts, risk and expected return values made in the stock by taking the end-of-day closing prices of the stocks in Borsa Istanbul 50 (BIST 50). Fuzzy linear programming and chance constrained programming approaches are used to solve the model under the assumptions that the expected returns are fuzzy and stochastic.

关键词： Portfolio optimization Chance constrained programming stochastic programming Fuzzy mathematical programming

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Reinforcement learning and stochastic dynamic programming for jointly scheduling jobs and preventive maintenance on a single machine to minimise earliness-tardiness

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2024年第3期62卷 705-719页

作者： Sabri, Abderrazzak Allaoui, Hamid Souissi, Omar Univ Artois Lab Genie Informat & Automatique Artois Bethune France Inst Natl postes Telecommun Rabat Morocco 801 Rue Horlogerie F-62400 Bethune France

This paper addresses the problem of stochastic jointly scheduling of resumable jobs and preventive maintenance on a single machine, subject to random breakdowns, to minimise the earliness tardiness cost. The main objective is to investigate using trending machine learning-based methods compared to stochastic optimisation approaches. We propose two different methods from both fields as we solve the same problem firstly with a stochastic dynamic programming model in an approximation way, then with an attention-based deep reinforcement learning model. We conduct a detailed experimental study according to solution quality, run time, and robustness to analyse their performances compared to those of an existing approach in the literature as a baseline. Both algorithms outperform the baseline. Moreover, the machine learning-based algorithm outperforms the stochastic dynamic programming-based heuristic as we report up to 30.5% saving in total cost, a reduction of computational time from 67 min to less than 1s on big instances, and a better robustness. These facts highlight clearly its potential for solving such problems.

关键词： Advanced planning and scheduling systems machine learning dynamic programming stochastic programming

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Probing-Enhanced stochastic programming

arXiv

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arXiv 2024年

作者： Ma, Zhichao Kim, Youngdae Linderoth, Jeff Luedtke, James R. Matthews, Logan R. Department of Industrial and Systems Engineering University of Wisconsin-Madison United States Wisconsin Institute for Discovery University of Wisconsin-Madison United States ExxonMobil Technology and Engineering Company United States

We consider a two-stage stochastic decision problem where the decision-maker has the opportunity to obtain information about the distribution of the random variables ξ that appear in the problem through a set of discrete actions that we refer to as probing. Probing components of a random vector η that is jointly-distributed with ξ allows the decision-maker to learn about the conditional distribution of ξ given the observed components of η. We propose a three-stage optimization model for this problem, where in the first stage some components of η are chosen to be observed, and decisions in subsequent stages must be consistent with the obtained information. In the case that η and ξ have finite support, Goel and Grossmann gave a mixed-integer programming (MIP) formulation of this problem whose size is proportional to the square of cardinality of the sample space of the random variables. We propose to solve the model using bounds obtained from an information-based relaxation, combined with a branching scheme that enforces the consistency of decisions with observed information. The branch-and-bound approach can naturally be combined with sampling in order to estimate both lower and upper bounds on the optimal solution value and does not require η or ξ to have finite support. We conduct a computational study of our method on instances of a stochastic facility location and sizing problem with the option to probe customers to learn about their demands before building facilities. We find that on instances with finite support, our approach scales significantly better than the MIP formulation and also demonstrate that our method can compute statistical bounds on instances with continuous distributions that improve upon the perfect information bounds. © 2024, CC BY.

关键词： stochastic programming

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Controlling Large Electric Vehicle Charging Stations via User Behavior Modeling and stochastic programming

arXiv

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arXiv 2024年

作者： Puech, Alban Rigaut, Tristan Templier, William Tournoud, Maud Schneider Digital - AI Hub Schneider Electric Grenoble France Lausanne Switzerland

This paper introduces an Electric Vehicle Charging Station (EVCS) model that incorporates real-world constraints, such as slot power limitations, contract threshold overruns penalties, or early disconnections of electric vehicles (EVs). We propose a formulation of the problem of EVCS control under uncertainty, and implement two Multi-Stage stochastic programming approaches that leverage user-provided information, namely, Model Predictive Control and Two-Stage stochastic programming. The model addresses uncertainties in charging session start and end times, as well as in energy demand. A user’s behavior model based on a sojourn-time-dependent stochastic process enhances cost reduction while maintaining customer satisfaction. The benefits of the two proposed methods are showcased against two baselines over a 22-day simulation using a real-world dataset. The two-stage approach demonstrates robustness against early disconnections by considering a wider range of uncertainty scenarios for optimization. The algorithm prioritizing user satisfaction over electricity cost achieves a 20% and 36% improvement in two user satisfaction metrics compared to an industry-standard baseline. Additionally, the algorithm striking the best balance between cost and user satisfaction exhibits a mere 3% relative cost increase compared to the theoretically optimal baseline — for which the nonanticipativity constraint is relaxed — while attaining 94% and 84% of the user satisfaction performance in the two used satisfaction metrics. © 2024, CC BY-NC-ND.

关键词： stochastic programming

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Two-stage stochastic programming model of US Army aviation allocation of utility helicopters to task forces

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JOURNAL OF DEFENSE MODELING AND SIMULATION-APPLICATIONS METHODOLOGY TECHNOLOGY-JDMS 2023年

作者： Nelson, Russell J. Werner, Jack Kay, Michael G. King, Russell E. McConnell, Brandon M. Thoney-Barletta, Kristin US Mil Acad Dept Math Sci West Point NY 10996 USA NC State Univ Dept Ind & Syst Engn Raleigh NC USA NC State Univ Ctr Addit Mfg & Logist Raleigh NC USA NC State Univ Operat Res Grad Program Raleigh NC USA

US Army aviation units often organize into task forces to meet mission requirements. The manner in which they allocate assets affects their long-term capabilities to provide aviation support. We propose a model to allocate utility helicopters across geographically separated task forces to minimize the total time of flight and unsupported air movement air mission requests (AMRs) by priority level. We model the allocation problem with a two-stage stochastic program, with the first-stage problem allocating a fleet's helicopter teams to task forces. The stochastic demand for each task force is then revealed. The second-stage US Army aviation air movement operations planning problem is modeled as a stochastic mixed integer linear program (MILP). A practical application uses the air movement operations planning heuristic to solve the second-stage problem at scale and generate an optimal stochastic solution task force allocation. This paper provides evidence for the practical use of the proposed two-stage stochastic programming model for US Army aviation asset allocation by military decision-makers. Furthermore, this research provides a novel first formulation of a stochastic programming dial-a-ride problem with multinode refuel and a sound framework for military aviation asset allocation decision-making.

关键词： stochastic programming allocation dial-a-ride problem heuristic multiple refuel nodes demand priority helicopter routing aircraft military aviation

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