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Multi-objective two-stage stochastic unit commitment model for wind-integrated power systems: A compromise programming approach

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2023年第1期152卷

作者： Mena, R. Godoy, M. Catalan, C. Viveros, P. Zio, E. Univ Tecn Federico Santa Maria Dept Ind Engn Santiago Chile MINES Paris PSL CRC Sophia Antipolis France Politecn Milan Energy Dept Milan Italy

In this paper, we introduce a compromise programming (CP) framework for solving a multi-objective two-stage stochastic unit commitment problem characterized by high penetration of wind power. The proposed framework aims at finding best-compromise Pareto efficient on/off schedules, accounting for wind and power demand uncertainties: such solutions must trade off the three objectives of operating cost, CO2 emissions, and wind power curtailment in accordance to the decision maker preferences. To achieve this, we introduce a practical procedure to compute the ideal and Nadir points associated to the multi-objective two-stage stochastic unit commitment problem and propose a linearized l(1) norm-based compromise program to design best-compromise on/off schedules that correspondingly minimize and maximize their weighted distances to the ideal point and to the Nadir point, considering the preference weights assigned by the decision maker to each of the three objective functions. The proposed CP framework is applied to a case study related to the New England IEEE-39 bus test system. The results show that, compared to the schedule obtained through the traditional minimization of operating cost, the designed best-compromised schedules considerably improve CO2 emissions reduction and wind power curtailment performance by conservatively sacrificing operating cost performance.

关键词： Power systems Wind energy Unit commitment Multi-objective optimization stochastic programming Compromise programming

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A stochastic programming model for hub-and-spoke network with uncertain flows

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International Journal of Industrial and Systems Engineering 2015年第3期21卷 302-319页

作者： Hu, Qing-Mi Hu, Zhi-Hua Logistics Research Center Shanghai Maritime University Shanghai201306 China School of Economics and Management Tongji University Shanghai 201306 Shanghai200092 China

Hub-and-spoke network (HSN) exploits economy of scale in transportation and reduces logistics operational cost through collaborations among nodes. Because of the uncertainty of origin-destination (OD) flows between nodes, the uncertainty increases the risk of selecting capacities for nodes and affects the analysis of contribution of the nodes to the HSN. First, considering the characteristics of the uncertainty of OD flows, the throughput capacities of spoke nodes are determined based on stochastic programming approach and expectation theory;then, a stochastic mixed-integer linear programming model for designing hub-and-spoke network is established based on the capacities of spokes, and the structure of the HSN and throughput capacities of the hubs are designed. Second, the classification method of nodes is formulated based on the transportation flows between spokes, resource utilisation degree, and the branch and trunk convective equilibrium degree. A multi-attribute utility evaluation function for evaluating contribution rates of nodes to the HSN is established based on the proposed evaluation indices. Finally, the existing problems about network operational and adjustment strategies are analysed based on the contribution rates of the nodes to the HSN. Copyright © 2015 Inderscience Enterprises Ltd.

关键词： stochastic programming

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Demand side management scheme in smart grid with cloud computing approach using stochastic dynamic programming

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Perspectives in Science 2016年 8卷 169-171页

作者： S. Sofana Reka V. Ramesh School of Electrical and Electronics VIT University Vellore 632014 Tamilnadu India

This paper proposes a cloud computing framework in smart grid environment by creating small integrated energy hub supporting real time computing for handling huge storage of data. A stochastic programming approach model is developed with cloud computing scheme for effective demand side management (DSM) in smart grid. Simulation results are obtained using GUI interface and Gurobi optimizer in Matlab in order to reduce the electricity demand by creating energy networks in a smart hub approach.

关键词： Demand side management Smart grid Smart hub stochastic programming

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A second-order cone programming-based microgrid bidding strategy considering real-time market price correlation

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ELECTRICAL ENGINEERING 2025年 1-14页

作者： El-Meligy, Mohammed A. Sharaf, Mohamed Alnowibet, Khalid A. Abdelgawad, Abdelatty E. King Saud Univ Adv Mfg Inst POB 800 Riyadh 11421 Saudi Arabia King Saud Univ Coll Sci Stat & Operat Res Dept Riyadh 11451 Saudi Arabia King Saud Univ Coll Engn Ind Engn Dept POB 800 Riyadh 11421 Saudi Arabia

This study establishes a non-deterministic microgrid bidding strategy methodology participating in a day-ahead energy market. In this regard, a stochastic programming-based model is mathematically constructed, fully considering the uncertainty of day-ahead market prices, electricity demand, and renewable generation by creating several scenarios. The real-time electricity market is also considered, where the real-time price uncertainty is modeled using robust optimization. Even though robust optimization has already been employed to model real-time price uncertainty, the correlation among real-time prices at different hours is neglected. Thus, how real-time price correlation affects the optimal microgrid bidding strategy remains unclear. This study develops a novel mathematical model that captures real-time price correlations by constructing an ellipsoidal uncertainty set. In this context, unlike the current approaches in which the real-time price deviation ranges are modeled as constants at each hour, they are assumed to lie within a prespecified ellipsoidal uncertainty set. In doing so, a mixed-integer second-order cone programming problem is created, which existing solving methods can efficiently handle. The presented scheme is applied to a typical microgrid, and the efficiency and excellence of the presented framework are validated by comparing numerical results with traditional models.

关键词： Correlation Ellipsoidal uncertainty set Microgrid bidding strategy Robust optimization Second-order cone programming stochastic programming

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An approximate dynamic programming approach to dynamic slot allocation of spot containers with random arrivals, cancellations, and no-shows

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2025年 193卷

作者： Gu, Yuyun Wang, Yadong Wang, Tingsong Nanjing Univ Sci & Technol Sch Econ & Management Nanjing 210094 Peoples R China Shanghai Univ Sch Management Shanghai 200444 Peoples R China

Container shipping demands are usually classified into long-term contract demands from large shippers and ad hoc demands from spot shippers. Compared with stable long-term contract demands, spot container shipping demands are often unstable due to their high frequent cancellations during the slot booking period and their uncertain arrivals even no-shows. This poses a challenge for shipping companies in making precise and profitable decisions on slot allocations for these spot demands, to avoid the loss of slot utilization and shipping profit. This paper thus focuses on a dynamic slot allocation problem for spot containers with consideration of their random arrivals and cancellations during the booking period to maximize the expected shipping profit, and formulates it as a Markov decision process (MDP) model. Due to the well-known curse of dimensionality of MDP models, this paper uses the approximate dynamic programming (ADP) approach to approximate our MDP model, and consequently develops a series of stochastic programming models, which can yield a near-optimal slot allocation policy. Numerical experiments are conducted to examine the effectiveness and superiority of our models obtained by the ADP approach. The computational results show that our dynamic slot allocation strategy can make shipping companies achieve a high slot utilization rate, up to 91.36 %. Furthermore, compared with various slot allocation policies commonly used by shipping companies in practice, the policy obtained by the approach used in this paper performs best in terms of profit, with an improvement of up to 33.26 %.

关键词： Liner container shipping Slot allocation Markov decision process Dynamic approximate programming stochastic programming

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New extremal principles with applications to stochastic and semi-infinite programming

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MATHEMATICAL programming 2021年第1-2期189卷 527-553页

作者： Mordukhovich, Boris S. Perez-Aros, Pedro Wayne State Univ Dept Math Detroit MI 48202 USA Univ OHiggins Inst Ciencias Ingn Rancagua Chile

This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These extremal principles concern measurable set-valued mappings/multifunctions with values in finite-dimensional spaces and are established in both approximate and exact forms. The obtained principles are instrumental to derive via variational approaches integral representations and upper estimates of regular and limiting normals cones to essential intersections of sets defined by measurable multifunctions, which are in turn crucial for novel applications to stochastic and semi-infinite programming.

关键词： Variational analysis Generalized differentiation Normal cone calculus stochastic programming Semi-infinite programming

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A chance-constrained programming approach to optimal management of car-rental fleets of electric vehicles

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SUSTAINABLE ENERGY GRIDS & NETWORKS 2025年 41卷

作者： Zanvettor, Giovanni Gino Casini, Marco Giannitrapani, Antonio Paoletti, Simone Vicino, Antonio Univ Siena Dipartimento Ingn Informaz & Sci Matematiche Via Roma 56 I-53100 Siena Italy

In the current context of growing electrification of the transport sector, offering rental and sharing programs for electric vehicles is considered one of the strategies to achieve decarbonization targets. Such programs should be supported by suitable optimization tools to manage the vehicle fleet, and make rental provision profitable for its operator. In this paper, we consider a rental system having a single station for electric vehicle pickup and delivery. For this system, we address the operational problem of simultaneously assigning rental requests to vehicles and determining the charging policies during inactivity intervals. The objective is to maximize the profit for the operator by minimizing the costs for electricity. The considered problem is complicated by uncertainty regarding the battery energy level when a vehicle returns to the station. This leads to a chance-constrained programming formulation, where the request-to-vehicle assignment and charging policies are determined by minimizing electricity costs while ensuring that the energy demand of the served requests is met with a prescribed high probability. Since the formulated mixed-integer problem with probabilistic constraints is hard to solve, a suboptimal approach is proposed, consisting of two sequential steps. In the first step, request-to-vehicle assignment is accomplished via a suitably designed heuristic procedure. Then, for a given assignment, the charging policy of each vehicle is determined by solving a relaxed chance-constrained problem. Numerical results are presented to assess the performance of both the assignment procedure and the optimization problem which determines the electric vehicle charging policies.

关键词： Electric vehicles Car-rental system Resource allocation stochastic programming Chance-constrained optimization

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stochastic dynamic programming approach for proactive replacement of power cables

Stochastic dynamic programming approach for proactive replac...

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CIRED Workshop 2016

作者： Swati Sachan Chengke Zhou Geraint Bevan Babakalli Alkali Glasgow Caledonian University Glasgow Glasgow GB Glasgow Caledonian University - UK

ISBN: (纸本)9781510834675

The purpose of this paper is to present a stochastic dynamic programming based model to solve the optimization problem of cable replacement. The proposed methodology can be implemented on cables with known failure distribution and insulation degradation level; the methodology to estimate both of the elements is based on previously developed Non-homogenous Poisson Process model (NHPP) and stochastic degradation model, respectively. The model gives the sequence of decisions for each year of the planning horizon such that it optimizes the overall cost and improves the reliability by lowering the frequency of unplanned outage. The model was tested on an unjacketed XLPE cable.

关键词： XLPE insulation dynamic programming power cable insulation stochastic processes stochastic programming Power cables stochastic programming dynamic programming cable degradation model stochastic models stochastic Processes Markov chain Power cable insulation stochastic XLPE insulation Planning Horizon

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A Two-Stage stochastic Integer programming Approach to Integrated Staffing and Scheduling with Application to Nurse Management

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OPERATIONS RESEARCH 2015年第6期63卷 1431-1451页

作者： Kim, Kibaek Mehrotra, Sanjay Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA

We study the problem of integrated staffing and scheduling under demand uncertainty. This problem is formulated as a two-stage stochastic integer program with mixed-integer recourse. The here-and-now decision is to find initial staffing levels and schedules. The wait-and-see decision is to adjust these schedules at a time closer to the actual date of demand realization. We show that the mixed-integer rounding inequalities for the second-stage problem convexify the recourse function. As a result, we present a tight formulation that describes the convex hull of feasible solutions in the second stage. We develop a modified multicut approach in an integer L-shaped algorithm with a prioritized branching strategy. We generate 20 instances (each with more than 1.3 million integer and 4 billion continuous variables) of the staffing and scheduling problem using 3.5 years of patient volume data from Northwestern Memorial Hospital. Computational results show that the efficiency gained from the convexification of the recourse function is further enhanced by our modifications to the L-shaped method. The results also show that compared with a deterministic model, the two-stage stochastic model leads to a significant cost savings. The cost savings increase with mean absolute percentage errors in the patient volume forecast.

关键词： stochastic programming hospitals personnel scheduling

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Two-stage chance-constrained programming based on Gaussian mixture model and piecewise linear decision rule for refinery optimization

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COMPUTERS & CHEMICAL ENGINEERING 2024年 184卷

作者： Yang, Yu Calif State Univ Long Beach Dept Chem Engn Long Beach CA 90840 USA

The two -stage chance -constrained program (CCP) is studied for a refinery optimization problem. In stage -I, the refinery decision -makers determine the type and quantity of crude oil procurement under operational uncertainties to maximize the expected profit under all possibilities. In stage -II, process unit flowrates are adjusted based on the realized uncertainties and available crude oil, while introducing probabilistic constraints to manage the off -spec risk. To solve such a two -stage optimization problem, we propose a novel approach using Gaussian mixture model (GMM) to characterize uncertainties, and piecewise linear decision rule for stage -II operations. Comparing to the conventional scenario -based mixed -integer linear program (MILP), our new approach offers three advantages. First, it leverages a well -developed global optimization scheme for joint CCP to avoid scenario generation and potential bias. Second, the data -driven GMM enables CCP to handle uncertainties with general distributions. Third, the stage -II variables are parameterized via Gaussian component induced piecewise linear decision rule to strike an excellent trade-off between optimality and computational time. A simplified refinery plant, consisting of distillation, cracker, reformer, isomerization, and desulfurization units, is used as a test bed to demonstrate the superiority of the proposed optimization method in solution time, probabilistic feasibility, and optimality over the large-scale scenario -based MILP.

关键词： stochastic programming Chance-constrained optimization Gaussian mixture model Piecewise linear decision rule

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