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A wake-induced two-phase planning framework for offshore wind farm maintenance with stochastic mixed-integer program

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APPLIED ENERGY 2025年 380卷

作者： Lee, Namkyoung Lee, Hyuntae Joung, Seulgi KEPCO Engn & Construct Co INC Power Engn Res Inst 269 Hyeoksin Ro Gimcheon Si 39660 Gyeongbuk Do South Korea Kumoh Natl Inst Technol Dept Digital Convergence Engn 61 Daehak Ro Gumi Si 39177 Gyeongsangbuk D South Korea Chonnam Natl Univ Dept Ind Engn 77 Yongbong Ro Gwangju 61186 South Korea Ajou Univ Dept Ind Engn 206 Worldcup Ro Suwon 16499 South Korea

Offshore wind farms are essential in fulfilling global renewable energy targets;yet, their maintenance poses substantial challenges due to remote marine locations and harsh environmental conditions. Effective maintenance strategies and implementation are crucial to enhance operational efficiency and reduce costs. Current models frequently overlook an integrated perspective on periodic factors and uncertainties inherent in metocean conditions and failure rates, leading to suboptimal planning and increased costs. This study bridges this gap by introducing a comprehensive maintenance planning framework that incorporates these uncertainties. We formulate an annual planning model as a stochastic mixed-integer linear programming problem. The annual planning process aims to minimize operations and maintenance costs, including losses from downtime, by employing wake model constraints and accounting for stochastic scenarios. By tackling the scheme challenge, we garner strategic allocations of maintenance resources, which specifies the requisite number of operational vehicles and teams to be deployed over the year. Tentatively, we establish a longterm strategy and devise a short-term program that encompasses failure parameters and weather-related conditions. To further refine planning, we address weekly short-term scheduling problems to elaborate detailed maintenance schedules. Each week, maintenance tasks are adjusted based on actual stochastic conditions, yielding precise, real-world schedules. Our weekly scheduling considers not only preventive and corrective maintenance but also opportunistic maintenance. In particular, we harness a flexible scheduling approach to accommodate the efficiency of maintenance vessels. Computational tests demonstrate that our framework remarkably reduces downtime losses by 19.0% and recovery delays by 38.2%, leveraging scheduling flexibility.

关键词： Offshore wind farm Maintenance scheduling mixed-integer program Stochastic program Wake effect

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A mixed-integer program (MIP) for One-Way Multiple-Type Shared Electric Vehicles Allocation With Uncertain Demand

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2022年第7期23卷 8972-8984页

作者： Huo, Xiang Wu, Xinkai Fan, Yuqi Ding, Chuan Beihang Univ Sch Transportat Sci & Engn Beijing Adv Innovat Ctr Big Data & Brain Comp Beijing 100191 Peoples R China

This paper proposes a mixed-integer program (MIP) to address a challenge issue of vehicle upgrade policy in current electric car rental market. i.e., idle luxury and high-end vehicles can be used as ordinary vehicles when the demand for ordinary vehicles is high. This model essentially is to maximize the total profit through balancing the demand and supply with a comprehensive consideration of revenue of rental operation, cost of potential demand loss, dispatching cost, energy consumption per kilometer, mileage limitation of electric vehicles (EVs), and the uncertainty of user demand for multi-type EVs. The proposed MIP model can he solved by CPLEX or Gurobi to search for the global optimal solution. Finally, real data from an electric carsharing system (ECS) with three types of EVs and 20 carsharing stations was used to validate the model. As a result, the daily increase of profit could reach 11.09% with an average of 8.08%.

关键词： Carsharing multi-type electric vehicles vehicle upgrade policy allocation mixed-integer program uncertain demand

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A closed-form representation of mixed-integer program value functions

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MATHEMATICAL programMING 1995年第2期71卷 127-136页

作者： Blair, C Business Administration Department University of Illinois Champaign United States

We identify a class of formulas computable in polynomial time such that the functions defined by these formulas are precisely the value functions of mixed-integer programs with rational constraint coefficients.

关键词： parametric optimization mixed-integer program value functions

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Applying a mixed-integer program to model re-screening women who test positive for C. trachomatis infection

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Health Care Management Science 2004年第2期7卷 135-144页

作者： Tao, Guoyu Abban, Bartholomew K. Gift, Thomas L. Chen, Guantao Irwin, Kathleen L. Division of STD Prevention Natl. Ctr. HIV STD and TB Prev. Centers for Dis. Contr. and Prev. Atlanta GA 30333 1600 Clifton Road NE United States Dept. of Mathematics and Statistics Georgia State University Atlanta GA United States Division of STD Prevention Centers for Dis. Contr. and Prev. Atlanta GA United States

We proposed a mixed-integer program to model the management of C. trachomatis infections in women visiting publicly funded family planning clinics. We intended to maximize the number of infected women cured of C. trachomatis infections. The model incorporated screening, re-screening, and treatment options for three age groups with respective age-specific C. trachomatis infection and re-infection rates, two possible test assays, and two possible treatments. Our results showed the total budget had a great impact on the optimal strategy incorporating screening coverage, test selection, and treatment. At any budget level, the strategy that used a relatively small per-patient budget increase to re-screen all women who tested positive 6 months earlier always resulted in curing more infected women and more cost-saving than the strategy that was optimal under the condition of not including a re-screening option.

关键词： Chlamydial infection Cost-saving mixed-integer program Optimization Re-screening Screening Sexually transmitted diseases

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Bridging theory and practice: Efficiently solving the unit commitment problem in production cost models

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ENERGY 2025年 322卷

作者： Bunnak, Phumthep Coniglio, Stefano Galelli, Stefano Cornell Univ Sch Civil & Environm Engn Ithaca NY 14850 USA Univ Bergamo Dept Econ Bergamo Italy

High-fidelity Production Cost Models are tools for scheduling the operations of power systems, but their computational complexity often necessitates trade-offs in model detail or solution quality. We argue that there are tangible opportunities for resolving this trade-off, or at least mitigating it. To explore this hypothesis, we contribute a holistic approach that simultaneously addresses both model building and solution process. Our model building relies on recent advances in the formulation of Unit Commitment Problems, while our solution processes is based on two novel heuristics (iterative rounding and column generation) that exploit specific attributes of the unit commitment problem. Extensive computational experiments carried out on country- scale grids (Laos, Cambodia, and Thailand) show that iterative rounding achieves substantial speed-ups (up to 10x) while maintaining an average optimality gap of no more than 1% with respect to our benchmark solver (Gurobi). Notably, this heuristic also scales very well with the problem size. Column generation is less successful in terms of runtime, but demonstrate potential for instances characterized by high penetration of renewables. Both heuristics are solver independent, allowing a seamless integration with virtually any mathematical-programming solver. The diverse characteristics of the power systems we experimented on further indicates the generalizability of the proposed heuristics, highlighting their potential to improve the computational efficiency of production cost modeling.

关键词： Production cost models Unit commitment mixed-integer program Decomposition techniques Optimization solvers

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Bi-attribute utility preference robust optimization: A continuous piecewise linear approximation approach

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2025年第1期323卷 170-191页

作者： Wu, Qiong Wang, Wei Zhang, Sainan Xu, Huifu Nanjing Normal Univ Sch Math Sci Nanjing 210046 Peoples R China Huazhong Univ Sci & Technol Sch Math & Stat Luoyu Rd 1037 Wuhan 430074 Peoples R China Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong 999077 Peoples R China

In this paper, we consider a bi-attribute decision making problem where the decision maker's (DM's) objective is to maximize the expected utility of outcomes with two attributes but where the true utility function which captures the DM's risk preference is ambiguous. To tackle this ambiguity, we propose a maximin bi-attribute utility preference robust optimization (BUPRO) model where the optimal decision is based on the worst- case utility function in an ambiguity set of plausible utility functions constructed using partially available information such as the DM's specific preference for certain lotteries. Specifically, we consider a BUPRO model with two attributes, where the DM's risk attitude is bivariate risk-averse and the ambiguity set is defined by a linear system of inequalities represented by the Lebesgue-Stieltjes integrals of the DM's utility functions. To solve the inner infinite-dimensional minimization problem, we propose a continuous piecewise linear approximation approach to approximate the DM's unknown true utility. Unlike the univariate case, we partition the domain of the utility function into a set of small non-overlapping rectangles and then divide each rectangle into two triangles by either the main diagonal (Type-1) or the counter diagonal (Type-2). The inner minimization problem based on the piecewise linear utility function can be reformulated as a mixed-integer linear program and the outer maximization problem can be solved efficiently by the derivative-free method. In the case that all the small triangles are partitioned either in Type-1 or in Type-2, the inner minimization can be formulated as a finite dimensional linear program and the overall maximin as a single mixed-integer program. To quantify the approximation errors, we derive, under some mild conditions, the error bound for the difference between the BUPRO model and the approximate BUPRO model in terms of the ambiguity set, the optimal value and the optimal solutions. Finally, we c

关键词： Decision analysis BUPRO Preference elicitation Piecewise linear approximation mixed-integer program

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Optimal rebalancing and charging of shared electric scooters using charging hubs

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2025年 196卷

作者： Osorio, Jesus Ouyang, Yanfeng Univ Illinois Champaign Urbana Champaign IL 61820 USA

This paper addresses the overnight e-scooter rebalancing and charging problem in which escooters can be charged at a set of capacitated charging hubs. Operators use capacitated vehicles to collect e-scooters that need charging, drop them off at the hubs for charging, and pick them up later for repositioning. First, a discrete mathematical formulation is presented to optimize the drop-offs and pickups of e-scooters, as well as the routing/scheduling of vehicles. E-scooters of different states of charge (SoC) are modeled as multiple commodities linked through an SoC transition function. To reduce computational burdens, a discrete-continuous hybrid model is developed such that asymptotic vehicle routing formulas can be used to approximate local tour lengths and operational costs, and at the same time provide guidelines for building near- optimum feasible solutions. The hybrid model produces close approximations to the feasible solution in short times and shows to be a potential tool for strategic decision-making. Numerical tests showed interesting interdependencies and trade-offs among the numbers and capacities of both hubs and vehicles. Running dispersed charging hubs, even smaller ones, could result in a superior system service than running a few centralized hubs.

关键词： Electric scooter Sharing Micromobility mixed-integer program Continuum approximation

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Combining regression and mixed-integer programming to model counterinsurgency

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ANNALS OF OPERATIONS RESEARCH 2020年第1期292卷 287-320页

作者： King, Marvin L. Galbreath, David R. Newman, Alexandra M. Hering, Amanda S. Colorado Sch Mines Dept Mech Engn Golden CO 80401 USA Baylor Univ Dept Stat Sci Waco TX USA

Counterinsurgencies are a type of violent struggle between state and non-state actors in which one group attempts to gain or maintain influence over a certain portion of the population. When an insurgency (i.e., non-state actor) challenges a host nation (i.e., state actor), often an external counterinsurgent force intervenes. While researchers have categorized insurgencies with social science techniques and United States Army doctrine has established possible counterinsurgency strategies, little research prescribes host nation and counterinsurgent force strength. To this end, we develop a mixed-integer program to provide an estimate of the number of forces required to maximize the probability of a favorable resolution to the counterinsurgent and host nation countries, while minimizing unfavorable resolutions and the number of counterinsurgent deaths. This program integrates: (i) a multivariate piecewise-linear regression model to estimate the number of counterinsurgent deaths each year and (ii) a logistic regression model to estimate the probability of four types of conflict resolution over a 15-year time horizon. Constraints in the model characterize: (i) upper and lower limits on the number of counterinsurgent and host nation forces and their annual rates of increase and decrease, (ii) the characteristics of the type of counterinsurgency, (iii) an estimation of the number of counterinsurgent deaths, and (iv) an estimation of the probability of one of four resolutions. We use Somalia as a case study to estimate how counterinsurgent strategies affect the probability of obtaining each conflict resolution. We conclude that a strategy focusing on building and empowering a stable host nation force provides the highest probability of achieving a positive resolution to the counterinsurgency. Senior leaders can use this information to guide strategic decisions within a counterinsurgency.

关键词： Counterinsurgent Conflict resolution Optimization mixed-integer program Regression

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Decomposing Inventory Routing Problems with Approximate Value Functions

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NAVAL RESEARCH LOGISTICS 2010年第8期57卷 718-727页

作者： Toriello, Alejandro Nemhauser, George Savelsbergh, Martin Univ So Calif Daniel J Epstein Dept Ind & Syst Engn Los Angeles CA 90089 USA Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA CSIRO Math Informat & Stat N Ryde NSW 1670 Australia

We present a time decomposition for inventory routing problems. The methodology is based on valuing inventory with a concave piecewise linear function and then combining solutions to single-period subproblems using dynamic programming techniques. Computational experiments show that the resulting value function accurately captures the inventory's value, and solving the multiperiod problem as a sequence of single-period subproblems drastically decreases computational time without sacrificing solution quality. (C) 2010 Wiley Periodicals, Inc. Naval Research Logistics 57: 718-727, 2010

关键词： inventory routing mixed-integer program approximate dynamic program

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Reconfigurable Low Voltage Direct Current Charging Networks for Plug-In Electric Vehicles

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IEEE TRANSACTIONS ON SMART GRID 2019年第5期10卷 5458-5467页

作者： Mokgonyana, Lesiba Smith, Kyle Galloway, Stuart Univ Strathclyde Dept Elect & Elect Engn Inst Energy & Environm Glasgow G1 1XW Lanark Scotland

An emerging theme in the development of supporting facilities for plug-in electric vehicles (EVs) is the cost-effective planning and utilization of charging networks consistent with the uptake of EVs. This paper proposes a low voltage direct current reconfigurable charging network for plug-in EVs and presents a functional energy management system (EMS) that is capable of planning and operating the charging network to minimize cost and to facilitate progressive infrastructure deployment based on EV demand. The charging network is connected to the main ac grid through one or more centralized ac/dc converters that supply a high power charge to EVs connected to the de side of the converters. The EMS accommodates multiple parking bays, charging sources, ac constraints, non-linear EV battery loads and user charging requirements with a novel approach to managing user inconvenience. The inconvenience model is founded on the presence of user flexibility, i.e., an allowance on charging time or battery SoC, providing the capability to increase asset utilization and enable access for additional network users. Through a series of case studies and a stochastic forecasting approach, the reconfigurable network and EMS demonstrate the capacity to achieve savings over fixed ac and sequential de systems.

关键词： Plug-in electric vehicles direct current charging systems mixed-integer program charging infrastructure planning multiple-charger control

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