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two-stage stochastic programming of a hybrid SOFC-renewable integrated energy system considering time sequence correlation

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INTERNATIONAL JOURNAL OF GREEN ENERGY 2023年第1期20卷 1-14页

作者： Zhang, Yisong Chen, Ke Jiang, Jingjing Sun, Li Southeast Univ Sch Energy & Environm Key Lab Energy Thermal Convers & Control Minist Educ Nanjing 210096 Peoples R China Demand Side Multichina Elect Power Res Inst CEPR Beijing Key Lab Beijing Peoples R China Loughborough Univ Dept Aeronaut & Automot Engn Loughborough Leics England

In the face of the ever-increasing pressure on climate change, recent decades witnessed booming interests in the integrated energy systems (IES) consisting of intermittent renewable energy and dispatchable power sources, such as reformed gas-fed solid oxide fuel cells (SOFC). However, optimization of system design and operation is challenging due to the system complexity, inevitable couplings, and various constraints. To this end, this paper proposes a comprehensive model to describe integrated energy systems with combined cooling, heating, and power (CCHP). Optimal economic performance is formulated as the objective function. Constraints are derived based on the safety and operation requirements. The problem is solved by developing a two-stage stochastic programming framework to achieve the optimized results in terms of both design and operation. The second stage concerns the operation scheduling given the operation plan and stochastic characteristics, based on which the first stage concerns the design planning to realize the prescribed CCHP capacity. Considering the computation complexity of the second stage, the stochastic characteristics are represented by selected scenarios. And to present the mutual influence of energy demands and climate conditions, the time sequence correlation among energy demands and renewable energy availability is considered in the clustering-based scenario selection technique. To solve the proposed two-stage framework, the real-coded genetic algorithm and mixed integer linear programming method are applied in the first and second stages, respectively. A case study in San Francisco is carried out to verify the effectiveness of the proposed method, providing some intuitive guidance for future IES operation and system planning.

关键词： Integrated energy system SOFC two-stage stochastic programming time sequence correlation

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two-stage stochastic programming for Sustainable Utility Systems Optimization with Energy Storage 36

Two-Stage Stochastic Programming for Sustainable Utility Sys...

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36th Chinese Control and Decision Conference (CCDC)

作者： Yang, Kangyuan Zhao, Liang Liang, Chen East China Univ Sci & Technol Minist Educ Key Lab Smart Mfg Energy Chem Proc Shanghai 200237 Peoples R China

ISBN: (纸本)9798350387780;9798350387797

Utility systems consume fuels to provide steam and energy for industrial processes, resulting in significant carbon dioxide emissions. To enhance the economic and environmental efficiency of the system, a sustainable utility system integrating energy storage has been proposed. The scheduling optimization of sustainable utility systems involves multiple energy sources and various uncertainties, posing a challenging mathematical programming problem. An approach utilizing a two-stage stochastic programming method has been introduced to tackle the challenge of uncertainty. The optimal planning stage aims to minimize economic and environmental costs. In the first stage, deterministic programming is employed to solve the capacity planning problem for renewable energy and energy storage devices. In the second stage, weather scenarios are generated based on historical data, and stochastic programming methods are used to transform the uncertainty issue into a mixed-integer programming problem, addressing the operational scheduling optimization of the systems. Finally, the effectiveness of this method is validated using a real factory case study.

关键词： Utility system Renewable energy Energy Storage Uncertainty two-stage stochastic programming

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two-stage stochastic programming with robust constraints for the logistics network post-disruption response strategy optimization

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Frontiers of Engineering Management 2023年第1期10卷 67-81页

作者： Xiaotian ZHUANG Yuli ZHANG Lin HAN Jing JIANG Linyuan HU Shengnan WU JD Logistics Beijing 100176China School of Management and Economics Beijing Institute of TechnologyBeijing 100081China Yangtze Delta Region Academy of Beijing Institute of Technology Jiaxing 314019China

Logistics networks (LNs) are essential for the transportation and distribution of goods or services from suppliers to consumers. However, LNs with complex structures are more vulnerable to disruptions due to natural disasters and accidents. To address the LN post-disruption response strategy optimization problem, this study proposes a novel two-stage stochastic programming model with robust delivery time constraints. The proposed model jointly optimizes the new-line-opening and rerouting decisions in the face of uncertain transport demands and transportation times. To enhance the robustness of the response strategy obtained, the conditional value at risk (CVaR) criterion is utilized to reduce the operational risk, and robust constraints based on the scenario-based uncertainty sets are proposed to guarantee the delivery time requirement. An equivalent tractable mixed-integer linear programming reformulation is further derived by linearizing the CVaR objective function and dualizing the infinite number of robust constraints into finite ones. A case study based on the practical operations of the JD LN is conducted to validate the practical significance of the proposed model. A comparison with the rerouting strategy and two benchmark models demonstrates the superiority of the proposed model in terms of operational cost, delivery time, and loading rate.

关键词： logistics network design post-disruption response strategy two-stage stochastic programming conditional value at risk robust constraint

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Integrating environmental considerations and resilience in material sourcing for construction projects: A two-stage stochastic programming model

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COMPUTERS & INDUSTRIAL ENGINEERING 2025年 204卷

作者： Chen, Zixuan Hammad, Ahmed W. A. Alyami, Mana Haddad, Assed N. Univ New South Wales UNSW Sydney Sch Built Environm Sydney Australia Macroview Projects Sydney Australia Najran Univ Coll Engn Dept Civil Engn Najran Saudi Arabia Univ Fed Rio De Janeiro Environm Engn Program Rio De Janeiro Brazil

This study presents a multi-objective two-stage stochastic model to optimise supplier selections, material ordering, inventory management, and material trans-shipments within a construction project portfolio. The model is designed to address challenges faced by general contractors when managing a project portfolio, particularly in controlling financial costs and minimising the environmental impact associated with material transportation and storage. Material back-up sourcing is integrated into the model as a strategy to mitigate supply chain disruptions. The model focuses on assisting the general contractor's resilient material management decisions in response to supply disruptions influenced by multiple uncertain factors. To achieve this, disruption probabilities are estimated using a Bayesian network based on primary suppliers' reliabilities and the macro market conditions. An analysis is undertaken to assess the impact of the Bayesian network-based scenario modelling approach on model results. Additionally, sensitivity analysis reveals that higher penalties for material shortages or storage fees have a minimal effect on total supply chain costs due to the contractor's capacity to utilise back-up sourcing and trans-shipments. Similarly, while higher costs for back-up suppliers increase overall expenses, the total carbon dioxide equivalent emissions are reduced by approximately 20% due to decreasing deliveries and trans-shipment activities. This study uses a novel Bayesian network-based approach to model CSC disruption scenarios, and further contributes to construction supply chain resilience studies by integrating backup sourcing decisions and project portfolio material trans-shipments within a two-stage stochastic programming framework.

关键词： Construction supply chains Resilience Material trans-shipments Back-up sourcing two-stage stochastic programming Bayesian network

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Material and energy coupling systems optimization for large-scale industrial refinery with sustainable energy penetration under multiple uncertainties using two-stage stochastic programming

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APPLIED ENERGY 2024年 371卷

作者： Xu, Tiantian Long, Jian Zhao, Liang Du, Wenli East China Univ Sci & Technol Minist Educ Key Lab Smart Mfg Energy Chem Proc Shanghai 200237 Peoples R China Qingyuan Innovat Lab Quanzhou 362801 Peoples R China

The coupling of multimedia materials and energy with sustainable energy penetration in large-scale industrial refineries significantly lowers energy consumption and greenhouse gas (GHG) emissions. This paper presents a sustainable retrofitting framework for coupled production materials and steam systems (CPMSS) utilising twostage stochastic programming (TSSP). A novel sustainable energy-integrated CPMSS (SEICPMSS) model that includes wind, solar, and hydrogen energy and considers multiple operating modes and hydrogen consumption of the process units was established. First-principles models of wind turbines, solar thermal collectors, and proton exchange membrane electrolysers were adopted to sustainably retrofit the CPMSS. Latin hypercube sampling and Gaussian mixture model methods were applied to classify high volumes of uncertain wind speed and solar radiation data. A SEICPMSS optimisation model formulated as a mixed-integer nonlinear programming problem was developed by considering the investment costs, carbon taxes, and operational costs. Finally, a series of case studies from the industrial refinery's CPMSS were conducted to illustrate the effectiveness of the proposed method. The optimisation results indicate that the TSSP method can reduce operating costs by 5.3355 x 108 CNY/year and decrease GHG emissions by 7.4104 x 106 t/year compared to the traditional CPMSS without the integration of sustainable energy systems.

关键词： Refinery Integrated sustainable energy system Mixed-integer nonlinear programming two-stage stochastic programming Uncertainty Greenhouse gas emission

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A two-stage stochastic programming approach for reserving and allocating of emission trading permits under uncertainties

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ENERGY SOURCES PART A-RECOVERY UTILIZATION AND ENVIRONMENTAL EFFECTS 2023年第4期45卷 11224-11241页

作者： Zhao, Shuqin Liu, Linzhong Zhao, Ping Wang, Xiaorong Zhang, Chunsheng Wang, Shijuan Lanzhou Jiaotong Univ Lanzhou Peoples R China Henan Univ Anim Husb & Econ Zhengzhou Peoples R China Sichuan Univ Chengdu Peoples R China

The Emissions Trading Scheme (ETS) is a market-based approach aiming at reducing greenhouse gas (GHG) emissions. It involves the allocation of emission allowances to entities that are permitted to emit certain levels of GHG, as well as the re-sale and re-allocation of these allowances among entities. Considering the uncertainty of urban traffic congestion, the problem of reserving and allocating Emission Trading Permits (ETP) under stochastic demand is investigated. The ETP reserve of each link is determined before congestion, the optimal allocation scheme of ETP is determined after congestion. A two-stage stochastic programming model is formulated to minimize the sum of the reserve cost of ETP before congestion and the expected total loss of ETP after congestion. First, the effectiveness of the stochastic programming model is verified by comparing with the traditional method. Second, the total cost increases with the increase of initial reserve cost and shortage cost, and decreases with the increase of selling price and the capacity of links by sensitivity analysis. The unit reserve cost has a negative effect on the reserve quantity, while shortage cost, selling price, and link capacity have a positive effect on the reserve quantity. At last, the validity of the stochastic programming solution can be verified by numerical analysis of the Nguyen-Dupuis network. The stochastic programming solution proposed in this study shows an 89% reduction in ETP reserve compared to the optimal initial capacity solution. When level E occurs, the total cost is correspondingly reduced by 11%.

关键词： Urban traffic emissions trading scheme travel stochastic demand two-stage stochastic programming China

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A two-stage stochastic programming model for collaborative asset protection routing problem enhanced with machine learning: a learning-based matheuristic algorithm

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2023年第1期61卷 81-113页

作者： Nikzad, Erfaneh Bashiri, Mahdi Shahed Univ Fac Engn Ind Engn Dept Tehran Iran Coventry Univ Ctr Business Soc Coventry W Midlands England

In this paper, a two-stage stochastic mathematical model is developed for an asset protection routing problem under a wildfire. The main aim of this study is to reduce the negative impact of a wildfire. Some parameters, such as travel and service times, obtaining profit by protecting an asset, and upper bounds of time windows, are considered as stochastic parameters. Generating proper scenarios for uncertain parameters has a large impact on the accuracy of the obtained solutions. Therefore, artificial neural networks are employed to extract possible scenarios according to previous actual wildfire events. The problem cannot be solved by exact solvers for large instances, so two matheuristic algorithms are proposed in this study to solve the problem in a reasonable time. In the first algorithm, a set of feasible routes is generated based on a heuristic approach, then a route-based mathematical model is used to obtain the final solution. Also, another matheuristic algorithm based on adaptive large neighbourhood search (ALNS) is proposed. In this algorithm, routing decisions are determined using the ALNS algorithm while other decisions are achieved by solving an intermediate mathematical model. The numerical analysis confirms the efficiency of both proposed algorithms;however, the first algorithm performs more efficiently.

关键词： Asset protection location routing two-stage stochastic programming neural network matheuristic algorithm

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Multiperiod two-stage stochastic programming of Supply Chain for Co-Processing System of Bio-Oil and Heavy Oil

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ACS SUSTAINABLE CHEMISTRY & ENGINEERING 2023年第9期11卷 3850-3860页

作者： Xie, Chaoliang Tian, Yanmei Wu, Le Northwest Univ Sch Chem Engn Xian 710069 Peoples R China

Bio-oil and heavy oil are co-processed in an existing fluid catalytic cracker of a refinery to reduce the biofuel cost and add biocarbon into cracked products. The supply chain design is one of the fundamental methods to further reduce the production cost of the co-processing system. In this work, a two-stage stochastic programming integrating the fluctuations of straw supply and price, algae growth rate, algae nutrients price, crude oil price, and bio-oil yield is built to design the supply chain of co-processing the system including biomass and crude oil. The sample average approximation method is adopted to solve the proposed two-stage stochastic programming. A fluid catalytic cracker with 1.2 Mt/y is used as an example to illustrate the model. The results show that optimal capacities of the algae cultivation process, fast pyrolysis and depot, integration of crude oil supply and biomass supply, and minimized total annual cost under multiperiod and uncertainties can be obtained. A comparison of the stochastic programming and the deterministic programming is also conducted and the result shows that the total annual cost decreases if uncertainties are considered. The uncertainties in the co-processing system should be considered when designing the supply chain to increase the model's feasibility.

关键词： co-processing bio-oil multiperiod two-stage stochastic programming supply chain sample average approximation

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two-stage stochastic programming approach for limited medical reserves allocation under uncertainties

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COMPLEX & INTELLIGENT SYSTEMS 2021年第6期7卷 3003-3013页

作者： Zhang, Yuwei Li, Zhenping Jiao, Pengbo Zhu, Shen Capital Univ Econ & Business Sch Management & Engn 121 Zhangjialukou Beijing 100070 Peoples R China Beijing Wuzi Univ Sch Informat 1 Fuhe St Beijing 101149 Peoples R China

At the early stage of public health emergencies, when the conventional medical reserves prepared are insufficient, and productivity could temporarily not meet the surge in demand, donations can be used to cover excess demand for medical supplies to a large extent. This paper explicitly considers the allocation problem of limited medical reserves during a public health emergency, incorporating uncertainty in demand and donated supplies and the priorities of health care centers. The problem is formulated as a two-stage stochastic program that regards the donated supplies as an efficient recourse action, aiming to minimize the total losses. The optimal allocation strategy of limited medical reserves and donations is obtained by solving the model using Gurobi solver. Finally, the effectiveness of the proposed approach is verified by a series of computational results, which show that the solutions of our method not only benefit the emergency demand fulfill rate but reduce the total losses as well.

关键词： Limited medical reserves allocation Donations Uncertain demand Priority two-stage stochastic programming

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A two-stage stochastic programming Approach for Energy-Oriented Lot-Sizing 43rd

A Two-Stage Stochastic Programming Approach for Energy-Orien...

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43rd IFIP WG 5.7 International Conference on Advances in Production Management Systems (APMS)

作者： Liao, Ruiwen Quezada, Franco Gicquel, Celine Kedad-Sidhoum, Safia Univ Paris Saclay LISN Gif Sur Yvette France Univ Santiago Chile Fac Engn Ind Engn Dept Santiago Chile Lab CEDRIC Conservatoire Natl Arts & Metiers Paris France

ISBN: (纸本)9783031716317;9783031716294;9783031716287

We consider an industrial plant equipped with an on-site power generation system based on intermittent renewable energy. We investigate the problem of simultaneously planning the industrial production and the energy supply in this plant on a short-therm horizon. We propose to handle the resulting energy-oriented lot-sizing problem by a two-stage scenario-based stochastic programming approach. We discuss two alternative models differing with respect to when the decision on the production quantities is made. Preliminary computational results aimed at assessing the value of the stochastic solution are provided for both models.

关键词： Energy-efficient manufacturing Lot-sizing Renewable energy two-stage stochastic programming Mathematical programming

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