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Reliable Hub Location Model for Air Transportation Networks Under Random Disruptions

M&SOM-MANUFACTURING & SERVICE OPERATIONS MANAGEMENT 2021年第2期23卷 388-406页

作者： Shen, Hao Liang, Yong Shen, Zuo-Jun Max Renmin Univ China Sch Business Beijing 100872 Peoples R China Tsinghua Univ Sch Econ & Management Beijing 100084 Peoples R China Univ Calif Berkeley Dept Ind Engn & Operat Res Berkeley CA 94720 USA

Problem definition: In this paper, we study a reliable hub location model, the objective of which is to minimize the associated costs plus the penalty for unserved demands. The model assigns to each origin-destination pair a primary path and a backup path to hedge against the risk of random disruptions. Aside from the fixed costs of locating hubs, the fixed costs incurred by hub-connecting arcs that exhibit economies of scale in transportation are considered. Academic/practical relevance: The widely adopted hub-and-spoke architecture in the network designs can trigger cascading effects during and in the aftermath of disruption events and lead to further losses. By incorporating a general specification of disruptions, our model helps firms improve network reliability while inheriting the benefits of routing via hubs. Therefore, this work extends the literature on hub location problems by considering reliability under disruptions. Methodology: We present a path-based model and formulate a combinatorial optimization problem. By exploiting the structural properties of the problem, we introduce a tractable mixed-integer linear program reformulation and develop a constraint generation method to accelerate the solution procedure. We further construct two effective heuristics. Results: We demonstrate the necessity of considering disruptions and the profound benefits of employing backup paths. Moreover, we show via numerical studies that the path-based model delivers efficient and effective reliable hub-and-spoke designs. Managerial implications: We find that establishing backup paths according to the proposed model barely escalates network costs yet significantly enhances service levels, and that exploiting disruption correlation helps reduce the expected total cost especially when the underlying disruption correlation is strong. We also discover that the decisions of our model on the locations of hubs and hub arcs are relatively robust compared with those on path assignmen

关键词： air transportation network hub location hub and spoke disruptions mixed-integer linear program

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Efficient Identification of Bus Split Events Using Synchrophasor Data

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IEEE TRANSACTIONS ON POWER SYSTEMS 2021年第5期36卷 4800-4808页

作者： Zhou, Yuqi Zhu, Hao Univ Texas Austin Dept Elect & Comp Engn Austin TX 78712 USA

Accurate grid topology information is of paramount importance for routine power system operations, while the growing availability of synchrophasor data offers the opportunity to identify topology changes in real time. Identification of bus split events, where the substation becomes electrically disconnected, is becoming increasingly important for maintaining the security of power systems. This paper aims to provide an efficient modeling and monitoring framework for bus split events by using a concise bus-branch representation. The linear sensitivity analysis is first performed to quickly evaluate the grid-wide impact of such events. Furthermore, the synchrophasor data enabled identification problem is formulated by matching the changes in bus phase angles (and possibly line flows). To address the resultant bilinear multiplication involving the binary connectivity variables, the McCormick relaxation technique is leveraged to attain an equivalent mixed-integer linear program reformulation that is efficiently solvable. Numerical studies on the IEEE 14-bus and 300-bus systems demonstrate the validity and efficiency of the proposed identification algorithm towards real-time implementation.

关键词： Topology Substations Phasor measurement units Sensitivity analysis Analytical models Numerical models Real-time systems Bus split mixed-integer linear program phasor measurement units sensitivity analysis

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Global optimization for the three-dimensional open-dimension rectangular packing problem

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ENGINEERING OPTIMIZATION 2018年第10期50卷 1789-1809页

作者： Huang, Yao-Huei Hwang, F. J. Fu Jen Catholic Univ Dept Informat Management New Taipei Taiwan Univ Technol Sydney Sch Math & Phys Sci Ultimo Australia

This article addresses the three-dimensional open-dimension rectangular packing problem (3D-ODRPP), which aims to pack a given set of unequal-size rectangular boxes within an enveloping rectangular space such that the volume of the occupied space is minimized. Even though the studied 3D-ODRPP is NP hard, the development of sophisticated global optimization methods has been stimulated. The mathematical programming formulation for the 3D-ODRPP has evolved into an effective and efficient mixed-integer linear programming (MILP) model. This study proposes an advanced exact scheme yielding a guaranteed global optimal solution given that all the instance data are non-negative rational numbers. The developed MILP retains not only fewer variables but also fewer constraints than the state-of-the-art models. The superior effectiveness and efficiency of the developed scheme are demonstrated with numerical experiments, where two sets of benchmark instances from references, real-world instances and instances with rational data are included.

关键词： Rectangular packing problem global optimization exact method mixed-integer linear program

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Identifying production units with outstanding performance

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第3期287卷 1191-1194页

作者： Afsharian, Mohsen Bogetoft, Peter Tech Univ Carolo Wilhelmina Braunschweig Dept Business Sci Fallersleber Tor Wall 23 D-38100 Braunschweig Germany Copenhagen Business Sch Dept Econ Porcelaenshaven 16 A DK-2000 Frederiksberg Denmark

In many applications of data envelopment analysis, there are situations in which a central body manages a large set of similar units delivering some services. In such multi-unit organizations, the central management desires a mechanism by which the local management of each unit is incentivized to perform towards the improvement of the performance of the organization as a whole. In a recent paper, Afsharian et al. (2017) have proposed a system of incentives under these circumstances. In their approach, - which relies on the original concept of super-efficiency - units with outstanding performance are identified and incentivized by some reward compatible with the level of their impact on the overall performance of the organization. We discuss why the conventional super-efficiency approach may not be optimal in such situations. We revisit the definition of the collective impact and propose a new method, which can identify - in a controlled manner - a subset of k outstanding DMUs among n existing units in the system. The proposed approach is illustrated using data from a German retail bank. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Data envelopment analysis Units with outstanding performance Centralized management mixed-integer linear program

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Distributional utility preference robust optimization models in multi-attribute decision making

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MATHEMATICAL programMING 2024年 1-47页

作者： Hu, Jian Zhang, Dali Xu, Huifu Zhang, Sainan Univ Michigan Dearborn Dept Ind & Mfg Syst Engn Dearborn MI 48128 USA Shanghai Jiao Tong Univ Sino US Global Logist Inst Antai Coll Econ & Management Shanghai 200030 Peoples R China Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China

Utility preference robust optimization (PRO) has recently been proposed to deal with optimal decision-making problems where the decision maker's (DM's) preference over gains and losses is ambiguous. In this paper, we take a step further to investigate the case that the DM's preference is random. We propose to use a random utility function to describe the DM's preference and develop distributional utility preference robust optimization (DUPRO) models when the distribution of the random utility function is ambiguous. We concentrate on data-driven problems where samples of the random parameters are obtainable but the sample size may be relatively small. In the case when the random utility functions are of piecewise linear structure, we propose a bootstrap method to construct the ambiguity set and demonstrate how the resulting DUPRO can be solved by a mixed-integer linear program. The piecewise linear structure is versatile in its ability to incorporate classical non-parametric utility assessment methods into the sample generation of a random utility function. Next, we expand the proposed DUPRO models and computational schemes to address general cases where the random utility functions are not necessarily piecewise linear. We show how the DUPRO models with piecewise linear random utility functions can serve as approximations for the DUPRO models with general random utility functions and allow us to quantify the approximation errors. Finally, we carry out some performance studies of the proposed bootstrap-based DUPRO model and report the preliminary numerical test results. This paper is the first attempt to use distributionally robust optimization methods for PRO problems.

关键词： PRO Multi-attribute decision-making Piecewise linear random utility function Bootstrap ambiguity set mixed-integer linear program 90-10

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A Novel Model and Decomposition Approach for the Integrated Airline Fleet Assignment, Aircraft Routing, and Crew Pairing Problem

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TRANSPORTATION SCIENCE 2017年第1期51卷 233-249页

作者： Shao, Shengzhi Sherali, Hanif D. Haouari, Mohamed Virginia Tech Grado Dept Ind & Syst Engn Blacksburg VA 24061 USA Qatar Univ Dept Mech & Ind Engn Doha Qatar

Given a daily flight schedule and a set of aircraft fleets, the airline scheduling problem assigns individual aircraft and groups of crew to each flight based on specific considerations of aircraft maintenance requirements and crew work rules, respectively. Traditionally, this problem has been sequentially broken down into several stages, where the fleet assignment problem, which is solved first, partitions the entire flight network into subnetworks according to fleet types, followed by respectively solving the aircraft routing and crew pairing problems to generate suitable aircraft and crew rotations. However, this sequential approach ignores the interdependencies among the stages, leading to suboptimal, or even infeasible, solutions. In this paper, we propose an integrated model and solution approach that incorporates the fleet assignment (with itinerary-based demands), aircraft routing, and crew pairing problems within a single framework. We solve the resulting formulation of the problem by using a Benders decomposition approach, along with several acceleration strategies. Computational results obtained by using real-life data from a major U.S. airline demonstrate the benefits of the integrated approach.

关键词： integrated airline scheduling problem mixed-integer linear program Benders decomposition deflected subgradient optimization reformulation-linearization technique ( RLT) branch-and-price

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Chance-Constrained Transmission Switching With Guaranteed Wind Power Utilization

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IEEE TRANSACTIONS ON POWER SYSTEMS 2015年第3期30卷 1270-1278页

作者： Qiu, Feng Wang, Jianhui Argonne Natl Lab Decis & Informat Sci Div Lemont IL 60439 USA

Due to the significant variability and uncertainty of wind power over short time scales, high penetration of wind power can be problematic in an electric grid. One of the critical issues is how to keep increasing wind penetration without jeopardizing grid security and reliability. This paper explores the possibility of changing transmission network topology, by transmission switching, to accommodate higher utilization of wind power and reduce the generation costs of thermal units. Considering the uncertainty in wind power output, we use chance constraints to ensure that the wind energy utilized exceeds a minimal usage level at a certain probability. We develop a deterministic approximation approach using sample average approximation and provide a strong extended formulation. Numerical results show the potential benefit the proposed model can achieve.

关键词： Chance constraint mixed-integer linear program transmission switching wind energy

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Data envelopment analysis of integer-valued inputs and outputs

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COMPUTERS & OPERATIONS RESEARCH 2006年第10期33卷 3004-3014页

作者： Lozano, S Villa, G Univ Sevilla Dept Ind Management Seville Spain

This paper addresses DEA scenarios whose inputs and outputs are naturally restricted to take integer values. Conventional DEA models would project the DMU onto targets that generally do not respect such type of integrality constraints. Although integer-valued inputs and outputs can be considered as a special case of ordinal inputs and outputs, the use of that type of models has many drawbacks. In this paper a MILP DEA model that guarantees the required integrality of the computed targets is proposed. Scope and purpose Data envelopment analysis (DEA) is a well-known OR technique for evaluating the relative efficiency of a set of similar decision making units (DMU). The number of applications of DEA is large, covering fields as diverse as finance, health, education, manufacturing, transportation, etc. Conventional DEA models are based on linear programming and consider continuous inputs and outputs. However, there are many occasions in which some inputs and/or outputs can only take integer values. Normally, it is assumed that the real-valued results of DEA would be rounded somehow ex post. In this paper, a different approach is proposed, consisting in introducing new DEA concepts and models that explicitly take into account integer inputs and outputs, thus guaranteeing ex ante the feasibility of the results. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： data envelopment analysis integer values mixed-integer linear program

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Estimating DLMP confidence intervals in distribution networks with AC power flow model and uncertain renewable generation

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IET GENERATION TRANSMISSION & DISTRIBUTION 2020年第8期14卷 1467-1475页

作者： Wei, Wei Shen, Ziqi Wu, Lei Li, Fangxing Ding, Tao Tsinghua Univ Dept Elect Engn State Key Lab Power Syst Beijing Peoples R China Stevens Inst Technol Dept Elect & Comp Engn Hoboken NJ 07030 USA Univ Tennessee Dept Elect Engn & Comp Sci Knoxville TN USA Xi An Jiao Tong Univ Dept Elect Engn Xian Peoples R China

This study proposes a systematic approach for estimating intervals of distribution locational marginal price (DLMP) and corresponding confidence levels without requiring an exact probability distribution of renewable generation. The DLMP is evaluated based on a variant of the alternating current (AC) power flow model, namely, the branch flow model, in which network losses, bus voltage, and reactive power are taken into account. Based on the exactness of convex relaxation of optimal power flow, the authors developed a linear AC power flow model by applying second-order cone relaxation and global polyhedral approximation. Given a set of renewable power volatility, interval prediction of the DLMP is formulated as a bilevel linear program, which is solved via a mixed-integer linear program (MILP). Considering variances and unimodality of renewable power forecast error, a conservative estimation of the confidence level is expressed by a generalised Gauss inequality, which comes down to semidefinite programming. The proposed method is a natural extension of existing interval and probabilistic forecast methods, leveraging the proposed linear AC power flow model and inexact probability distributions of renewable power output, and could be promising in future distribution power markets. Case studies corroborate the effectiveness of the proposed method.

关键词： probability convex programming pricing power markets load flow integer programming linear programming power distribution economics approximation model DLMP confidence intervals distribution networks uncertain renewable generation radial power distribution network distribution locational marginal price confidence levels exact probability distribution renewable power volatility alternating current power flow model branch flow model reactive power optimal power flow linear AC power flow model second-order cone relaxation bilevel linear program mixed-integer linear program renewable power forecast error probabilistic forecast methods inexact probability distributions renewable power output future distribution power markets nodal prices

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Approximating Input-Output Curve of Pumped Storage Hydro Plant: A Disjunctive Convex Hull Method

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IEEE TRANSACTIONS ON POWER SYSTEMS 2023年第1期38卷 63-74页

作者： Wang, Siyuan Liu, Jian Bo, Rui Chen, Yonghong Missouri Univ Sci & Technol Dept Elect & Comp Engn Rolla MO 65409 USA Midcontinent Independent Syst Operator Inc Carmel IN 46032 USA

Pumped storage hydro (PSH) plant is a valuable resource with storage and fast ramp capabilities, which can manage the intermittency of renewable energy. An accurate model for the input-output curve of PSH plant can capture its varying efficiency feature and enable accurate evaluations of available generating/pumping capability. However, the trade-off between approximation accuracy and computation time poses a significant challenge for input-output curve modeling. In this paper, we develop a hypograph-relaxation-based input-output curve modeling framework, wherein sufficient conditions for exact hypograph relaxation are defined, proved, and analyzed for fixed-speed PSH considering the value of water in the upper reservoir. Under this framework, a novel disjunctive convex hull model is proposed to balance the aforementioned trade-off. Our model can take advantage of high accuracy in time-consuming piece-wise approximation models, and acceptable computation burden in less-accurate convex hull models. To divide a given input-output curve into various components that can be approximated by their respective convex hulls, we propose to use an approximate convex decomposition (ACD) based approach. The proposed model is tested for profit maximization problems using real-world Ludington PSH station data. Numerical results demonstrated the superior computational advantage of the proposed approach.

关键词： Pumped storage hydro input-output curve hypograph relaxation disjunctive convex hull mixed-integer linear program

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