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Progressive hedging for stochastic energy management systems The mixed-integer linear case

ENERGY SYSTEMS-OPTIMIZATION MODELING SIMULATION AND ECONOMIC ASPECTS 2021年第1期12卷 1-29页

作者： Kaisermayer, Valentin Muschick, Daniel Horn, Martin Goelles, Markus BEST Bioenergy & Sustainable Technol GmbH Inffeldgasse 21-B A-8010 Graz Austria Graz Univ Technol Inst Automat & Control Inffeldgasse 21-B A-8010 Graz Austria

Energy systems have increased in complexity in the past years due to the ever-increasing integration of intermittent renewable energy sources such as solar thermal or wind power. Modern energy systems comprise different energy domains such as electrical power, heating and cooling which renders their control even more challenging. Employing supervisory controllers, so-called energy management systems (EMSs), can help to handle this complexity and to ensure the energy-efficient and cost-efficient operation of the energy system. One promising approach are optimization-based EMS, which can for example be modelled as stochastic mixed-integer linear programmes (SMILP). Depending on the problem size and control horizon, obtaining solutions for these in real-time is a difficult task. The progressive hedging (PH) algorithm is a practical way for splitting a large problem into smaller sub problems and solving them iteratively, thus possibly reducing the solving time considerably. The idea of the PH algorithm is to aggregate the solutions of subproblems, where artificial costs have been added. These added costs enforce that the aggregated solutions become non-anticipative and are updated in every iteration of the algorithm. The algorithm is relatively simple to implement in practice, re-using almost all of a possibly existing deterministic implementations and can be easily parallelized. Although it has no convergence guarantees in the mixed-integer linear case, it can nevertheless be used as a good heuristic for SMILPs. Recent theoretical results shown that for applying augmented Lagrangian functions in the context of mixed-integer programmes, any norm proofs to be a valid penalty function. This is not true for squared norms, like the squared L-2-norm that is used in the classical progressive hedging algorithm. Building on these theoretical results, the use of the L-1 and L-infinity-norm in the PH algorithm is investigated in this paper. In order to incorporate these into the

关键词： Energy management system stochastic programming Progressive hedging Mixed-integer linear programming

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Integrated proactive and reactive strategies for sustainable berth allocation and quay crane assignment under uncertainty

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ANNALS OF OPERATIONS RESEARCH 2021年 1-32页

作者： Tan, Caimao He, Junliang Shanghai Maritime Univ China Inst FTZ Supply Chain Shanghai Peoples R China Shanghai Maritime Univ Engn Res Ctr Container Supply Chain Technol Minist Educ Shanghai Peoples R China

The berth allocation and quay crane assignment problem (BACAP) is a complex port operation planning problem susceptible to uncertainties, such as vessel arrival time fluctuation to its estimated time of arrival and maritime markets. For promoting reliability and sustainability of container terminals, this paper addresses the optimization of BACAP under the uncertain vessels' arrival times and fluctuation of loading and unloading volumes. We propose a proactive BACAP strategy considering minimum recovery cost under uncertainty using a reactive strategy. A stochastic programming model is formulated to minimize the basic cost in the baseline schedule, and the recovery cost in real uncertain scenarios. A two-stage meta-heuristic framework based on GA is developed for solving this problem. Numerical experiments and scenario analysis are conducted to validate the effectiveness of the proposed model and the proposed solution approaches.

关键词： Berth allocation Quay crane assignment stochastic programming Two-stage meta-heuristic Uncertainty Proactive strategy and reactive strategy

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Pension fund management with investment certificates and stochastic dominance

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ANNALS OF OPERATIONS RESEARCH 2021年第1-2期299卷 273-292页

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

This paper considers an extension of the common asset universe of a pension fund to investment certificates. Investment certificates are a class of structured products particularly interesting for their special payoff structures and they are acquiring relevancy in the worldwide markets. In fact, some subclasses of certificates offer loss protection and show high liquidity and, thus, they can be very appreciated by pension fund managers. We consider the problem of a pension fund manager who has to implement an Asset and Liability Management model trying to achieve a long-term sustainability. Therefore, we formulate a multi-stage stochastic programming problem adopting a discrete scenario tree and a multi-objective function. We propose a technique to price highly structured products such as investment certificates on a discrete scenario tree. Finally, we solve the investment problem considering some investment certificate types both in term of payoff structure and protection level, and we test whether they are preferred or not to standard hedging contract such as put options. Moreover, we test the inclusion of first-order and second-order stochastic dominance constraints on multiple stages with respect to a benchmark portfolio. Numerical results show that the portfolio composition reacts to the inclusion of the stochastic dominance constraints, and that the optimal portfolio is efficiently able to reach several targets such as liquidity, returns, sponsor's extraordinary contribution and funding gap.

关键词： stochastic programming Portfolio selection Sensitivity analysis Asset and liability management Pension fund Investment certificates Discrete pricing

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stochastic Dynamic Cutting Plane for Multistage stochastic Convex Programs

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2021年第2期189卷 513-559页

作者： Guigues, Vincent Monteiro, Renato D. C. FGV Sch Appl Math Praia De Botafogo RJ Brazil Georgia Inst Technol Atlanta GA 30332 USA

We introduce stochastic Dynamic Cutting Plane (StoDCuP), an extension of the stochastic Dual Dynamic programming (SDDP) algorithm to solve multistage stochastic convex optimization problems. At each iteration, the algorithm builds lower bounding affine functions not only for the cost-to-go functions, as SDDP does, but also for some or all nonlinear cost and constraint functions. We show the almost sure convergence of StoDCuP. We also introduce an inexact variant of StoDCuP where all subproblems are solved approximately (with bounded errors) and show the almost sure convergence of this variant for vanishing errors. Finally, numerical experiments are presented on nondifferentiable multistage stochastic programs where Inexact StoDCuP computes a good approximate policy quicker than StoDCuP while SDDP and the previous inexact variant of SDDP combined with Mosek library to solve subproblems were not able to solve the differentiable reformulation of the problem.

关键词： stochastic programming Inexact cuts for value functions SDDP Inexact SDDP

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A compromise solution method for the multiobjective minimum risk problem

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OPERATIONAL RESEARCH 2021年第3期21卷 1913-1926页

作者： Bellahcene, Fatima Marthon, Philippe Mouloud Mammeri Univ Fac Sci LAROMAD Lab BP 17 RP Tizi Ouzou 15000 Algeria ENSEEIHT Informat 2 Rue CamichelBP 7122 F-31071 Toulouse 7 France

We develop an approach which enables the decision maker to search for a compromise solution to a multiobjective stochastic linear programming (MOSLP) problem where the objective functions depend on parameters which are continuous random variables with normal multivariate distributions. The minimum-risk criterion is used to transform the MOSLP problem into its corresponding deterministic equivalent which in turn is reduced to a Chebyshev problem. An algorithm based on the combined use of the bisection method and the probabilities of achieving goals is developed to obtain the optimal or epsilon optimal solution of this specific problem. An illustrated example is included in this paper to clarify the developed theory.

关键词： Multiobjective programming stochastic programming Nonlinear programming Minimum-risk criterion

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Optimization of pumped hydro energy storage systems under uncertainty: A review

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JOURNAL OF ENERGY STORAGE 2023年 73卷

作者： Toufani, Parinaz Karakoyun, Ece Cigdem Nadar, Emre Fosso, Olav B. Kocaman, Ayse Selin INSEAD Dept Technol & Operat Management F-77305 Fontainebleau France Erasmus Univ Econometr Inst NL-3062 PA Rotterdam Netherlands Bilkent Univ Dept Ind Engn TR-06800 Ankara Turkiye Norwegian Univ Sci & Technol Dept Elect Power Engn N-7491 Trondheim Norway MIT Energy Initiat Cambridge MA 02142 USA

This paper provides an overview of the research dealing with optimization of pumped hydro energy storage (PHES) systems under uncertainty. This overview can potentially stimulate the scientific community's interest and facilitate future research on this topic. We review the literature from various perspectives, including the optimization problem type, objective function, physical characteristics of the PHES facility, paradigm used to capture uncertainty, and solution method adopted. We then identify several research gaps and future research directions for energy researchers. This review highlights the need for developing optimization models such as Markov decision processes that can represent uncertainties in renewable energy sources and electricity markets more accurately, constructing multi-objective models that consider not only economic but also environmental impacts, investigating underrepresented solar-PHES systems and PHES sizing problems, addressing nonlinear characteristics of PHES facilities, and optimizing bidding strategies in sequential or coordinated electricity markets.

关键词： Pumped hydro energy storage Uncertainty Optimization stochastic programming Markov decision processes Heuristic

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Optimal offering strategy for wind-storage systems under correlated wind production

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APPLIED ENERGY 2023年 333卷

作者： Dirin, Sepehr Rahimiyan, Morteza Baringo, Luis Shahrood Univ Technol Fac Elect Engn Shahrood *** Iran Univ Castilla La Mancha Dept Elect Engn Campus Univ S-N Ciudad Real 13071 Spain

This paper formulates the offering problem for a cluster of wind-storage systems in the day-ahead energy market using a risk-constrained stochastic programming approach that anticipates different operating con-ditions in the real-time energy market. Wind-storage systems can be jointly operated as a cluster so as to achieve higher profitability. However, a meaningful positive correlation among the production provided by wind farms located in the cluster results in a higher level of uncertainty that imposes additional risk. A key issue is how this correlation influences the operation of the cluster in the energy markets. In order to study this subject, this paper presents the uncertainties involved by means of a number of correlated scenarios including: (i) the correlated prices in the day-ahead and the real-time markets, and (ii) the correlated wind power production of multiple wind farms jointly generated using an innovative scenario generation methodology. The comparative statistical analysis validates the good accuracy of the method proposed in order to capture the spatio-temporal correlation among the wind farms. The results of a realistic case study are, moreover, compared with those obtained by considering that the scenarios are generated individually for each wind farm. Upon considering the latter, the variability of wind power production is underestimated, which has a negligible impact on the expected profit;however, the profit risk modeled using the conditional value-at-risk is significantly overestimated. The overestimation error particularly concerns a less risk-averse operator of the cluster in the case of low wind power production.

关键词： Conditional value-at-risk Correlated scenarios Offering strategy stochastic programming Wind-storage systems

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A two-stage stochastic model for a multi-objective blood platelet supply chain network design problem incorporating frozen platelets

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COMPUTERS & INDUSTRIAL ENGINEERING 2023年 185卷

作者： Suen, Tsz Yu Song, Xiang Jones, Dylan Univ Portsmouth Sch Math & Phys Portsmouth PO1 3HF England

Platelet supply chain (PLT SC) management is always a challenging task for healthcare systems due to the nature of platelets (PLTs). PLTs have an extremely short shelf life and their demand is highly uncertain, which may lead to a high percentage of wastage and shortage in the corresponding PLT SC. This paper proposes a two-stage stochastic programming (2SSP) model to investigate the opportunity of incorporating frozen PLTs (FPLTs) into the PLT SC to see how it can improve the performance of the PLT SC in which the PLTs are used only in liquid form with respect to the platelet shortage, wastage and substitution penalties in transfusions. To investigate a more realistic situation when clear targets of blood shortage, wastage and substitution penalties are available, an extended goal programming model is built based on the proposed 2SSP model. Furthermore, we generate scenarios based on the real data provided by healthcare practitioners using the combination of a topdown forecasting approach and a Monte Carlo based scenario generation method. From the experimental results we note that, when comparing the model that incorporates FPLTs with the one that doesn't, the average reduction rates for platelet shortages, wastage, and substitution penalties in transfusions are 0.55, 0.55, and 0.23, respectively, when 40% of the overall demand is from patients who can receive both liquid PLTs and thawed PLTs sourced from FPLTs (Patient Type I). These rates can be further improved to 0.64, 0.55 and 0.23 or 0.65, 0.55 and 0.23 when 50% or 60% of the total demand is from Patient Type I. Furthermore, in contrast to realworld performance, the output of the 2SSP model, when not incorporating FPLTs, results in notable reductions in platelet shortage, wastage, and substitution penalties by 95%, 56% and 18%, respectively.

关键词： OR in health services Platelet supply chain stochastic programming Goal programming Scenario generation

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Multi-product Inventory Routing Problem Considering Demand Uncertainty 12

Multi-product Inventory Routing Problem Considering Demand U...

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12th International Congress on Advanced Applied Informatics, IIAI-AAI 2022

作者： Kawamura, T. Sato, T. Shiina, T. Waseda University School of Creative Science and Engineering Department of Industrial and Management Systems Engineering Tokyo Japan

ISBN: (数字)9781665497558

ISBN: (纸本)9781665497558

The inventory routing problem simultaneously considers both the inventory problem and the delivery problem;it determines the amount of delivery of inventory and the delivery route such that the total cost is minimized. In this study, we use stochastic programming to consider a multi-product inventory routing problem that considers the demand variation throughout multiple periods. Determining the delivery route for each period is difficult. Therefore, we propose a model that fixes the delivery route throughout the planning period and compare the calculation results to prove its practicality. In addition, the problem in this study is an integer programming problem, and solving a large-scale problem using the direct method would be time-consuming. Therefore, we apply the accelerated Benders decomposition method, which combines two cuts: the optimality cut with the solution of the linear relaxation problem, and the Pareto-optimal cut. We demonstrate its effectiveness through numerical experiments. © 2022 IEEE.

关键词： stochastic programming

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An integrated opioid prescription optimization framework for total joint replacement surgery patients

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IISE TRANSACTIONS ON HEALTHCARE SYSTEMS ENGINEERING 2021年第3期11卷 209-223页

作者： Lee, Sujee Bain, Philip A. Musa, Albert J. Baker, Christine Li, Jingshan Univ Wisconsin Madison Ind & Syst Engn Madison WI USA Dean Hlth Syst Madison WI USA SSM Hlth St Marys Hosp Madison WI USA Univ Wisconsin Madison Ind & Syst Engn Madison WI 53706 USA

Opioid overdose, addiction, and death have become a nationwide crisis in recent years. Opioid leftover due to over-prescription at hospitals to treat chronic or surgical pains is one of the main contributors to the epidemic. To reduce leftovers, opioid prescriptions should be adjusted and tailored to patients' needs. However, insufficient prescription may result in frequent refills for patients with high opioid-use levels, which can lead to inefficiency to patients, physicians, and pharmacists. Therefore, developing an optimal opioid prescription model to provide the necessary and patient-specific amount of opioids with minimal refills has a significant importance. In this paper, we introduce an integrated analytical framework, which intends to optimize both opioid prescription and number of refills based on stratification of patients' opioid usage levels and corresponding stochastic programming. A case study for total joint replacement surgery patients at a community hospital is then introduced to illustrate the applicability and benefits of the framework.

关键词： Opioid prescription total joint replacement classification stochastic programming optimization

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