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An airspace-planning and collaborative decision-making model: Part II - Cost model, data considerations, and computations

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TRANSPORTATION SCIENCE 2006年第2期40卷 147-164页

作者： Sherali, Hanif D. Staats, Raymond W. Trani, Antonio A. Virginia Polytech Inst & State Univ Grado Dept Ind & Syst Engn 0118 Blacksburg VA 24061 USA USAF Inst Technol Dept Operat Sci Wright Patterson AFB OH 45433 USA Virginia Polytech Inst & State Univ Charles Edward Via Jr Dept Civil & Environm Engn Blacksburg VA 24061 USA

In Part I of this paper, we presented a large-scale airspace-planning and collaborative decision-making (APCDM) model that is part of a Federal Aviation Administration (FAA)-sponsored effort to enhance the management of the National Airspace System (NAS). Given a set of flights that must be scheduled during some planning horizon, along with alternative surrogate trajectories for each flight, we developed a mixed-integer programming model to select a set of flight plans from among these alternatives, subject to flight safety, air-traffic control workload, and airline equity considerations. The present paper offers insights related to, and a detailed description of, implementing this APCDM model, including the development of a comprehensive cost model, a study for prescribing a set of appropriate parameter values for the overall model, and an investigation on incorporating a suitable set of valid inequalities in the model formulation. Computational results are presented based on several test cases derived from the Enhanced Traffic Management System (ETMS) data provided by the FAA. The results indicate that under plausible probabilistic trajectory error assumptions and with the incorporation of star subgraph convex hull-based valid inequalities, the model offers a viable tool that can be used by the FAA for both tactical and strategic applications.

关键词： air traffic management national airspace aircraft conflict resolution sector workload measures airline equity mixed-integer programming valid inequalities

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Solving fuzzy p-hub center problem by genetic algorithm incorporating local search

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APPLIED SOFT COMPUTING 2013年第5期13卷 2624-2632页

作者： Yang, Kai Liu, Yan-Kui Yang, Guo-Qing Hebei Univ Coll Math & Comp Sci Risk Management & Financial Engn Lab Baoding 071002 Hebei Peoples R China

The p-hub center problem has extensive applications in various real-world fields such as transportation and telecommunication systems. This paper presents a new risk aversion p-hub center problem with fuzzy travel times, in which value-at-risk (VaR) criterion is adopted in the formulation of objection function. For trapezoidal and normal fuzzy travel times, we first turn the original VaR p-hub center problem into its equivalent parametric mixed-integer programming problem, then develop a hybrid algorithm by incorporating genetic algorithm and local search (GALS) to solve the parametric mixed-integer programming problem. In our designed GALS, the GA is used to perform global search, while LS strategy is applied to each generated individual (or chromosome) of the population. Finally, we conduct two sets of numerical experiments and discuss the experimental results obtained by general-purpose LINGO solver, standard GA and GALS. The computational results show that the GALS achieves the better performance than LINGO solver and standard GA. (C) 2012 Elsevier B. V. All rights reserved.

关键词： p-Hub center problem Fuzzy travel time mixed-integer programming Genetic algorithm Local search

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Exploring the Impacts of Power Grid Signals on Data Center Operations Using a Receding-Horizon Scheduling Model

IEEE TRANSACTIONS ON SUSTAINABLE COMPUTING

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IEEE TRANSACTIONS ON SUSTAINABLE COMPUTING 2023年第2期8卷 245-256页

作者： Zhang, Weiqi Roald, Line Zavala, Victor Univ Wisconsin Dept Chem & Biol Engn Madison WI 53706 USA Univ Wisconsin Dept Elect & Comp Engn Madison WI 53706 USA

Data centers (DCs) can help decarbonize the power grid by helping absorb renewable power (e.g., wind and solar) due to their ability to shift power loads across space and time. However, to harness such load-shifting flexibility, it is necessary to understand how grid signals (carbon signals and market price/load allocations) affect DC operations. An obstacle that arises here is the lack of computationally-tractable DC operation models that can capture objectives, constraints, and information flows that arise at the interface of DCs and the power grid. To address this gap, we present a receding-horizon resource management model (a mixed-integer programming model) that captures the resource management layer between the DC scheduler and the grid while accounting for logical constraints, different types of objectives, and forecasts of incoming job profiles and of available computing capacity. We use our model to conduct extensive case studies based on public data from Microsoft Azure and MISO. Our studies show that DCs can provide significant temporal load-shifting flexibility that results in reduced carbon emissions and peak demand charges. Models and case studies are shared as easy-to-use Julia code.

关键词： Load modeling Computational modeling Resource management Job shop scheduling Servers Electricity supply industry Processor scheduling Data centers load shifting flexibility scheduling rolling-horizon electricity markets mixed-integer programming

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Weekly airline fleet assignment with homogeneity

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2006年第4期40卷 306-318页

作者： Bélanger, N Desaulniers, G Soumis, F Desrosiers, J Lavigne, J HEC Montreal Montreal PQ H3T 2A7 Canada GERAD 3000 Montreal PQ H3T 2A7 Canada Ecole Polytech Montreal PQ H3C 3A7 Canada GERAD Math & Gen Ind Montreal PQ H3C 3A7 Canada Air Canada Ctr Dorval PQ H4Y 1C2 Canada

Given the flight schedule of an airline, the fleet assignment problem consists of determining the aircraft type to assign to each flight leg in order to maximize the total expected profits while satisfying aircraft routing and availability constraints. The profit for a leg is a function of the leg's stochastic passenger demand, the capacity of the aircraft assigned to the leg, and the aircraft operational costs. This paper considers the weekly fleet assignment problem in the case where homogeneity of aircraft type is sought over legs sharing the same flight number. Homogeneity allows, among other things, easier ground service planning. An exact mixed-integer linear programming model, as well as a heuristic solution approach based on mathematical programming, are presented. Computational results obtained on Air Canada instances involving up to 4400 flight legs are reported. The system produces realistic solutions arising from a trade-off between profits and homogeneity, and solves large-scale instances in short times with very small optimality gaps. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： linear programming mixed-integer programming airline fleet assignment

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Optimal design of reliable integrated chemical production sites

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COMPUTERS & CHEMICAL ENGINEERING 2010年第12期34卷 1919-1936页

作者： Terrazas-Moreno, Sebastian Grossmann, Ignacio E. Wassick, John M. Bury, Scott J. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA Dow Chem Co USA Midland MI 48674 USA

Since plants that form the process network are subjected to fluctuations in product demand or random mechanical failures, design decisions such as adding redundant units and increasing storage between units can increase the flexibility and reliability of an integrated site. In this paper, we develop a bi-criterion optimization model that captures the trade-off between capital investment and process robustness in the design of an integrated site. Design decisions considered are increases in process capacity, introduction of parallel units, and addition of intermediate storage. The mixed-integer linear programming (MILP) formulation proposed in this paper includes the representation of the material levels in the intermediate storage by means of a probabilistic model that captures the effects of the discrete, uncertain events. We also integrate a superstructure optimization with stochastic modeling techniques such as continuous-time Markov chains. The application of the proposed model is illustrated with two example problems. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Reliability Flexibility mixed-integer programming Markov chains Stochastic programming

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integer programming Approaches for Appointment Scheduling with Random No-Shows and Service Durations

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OPERATIONS RESEARCH 2017年第6期65卷 1638-1656页

作者： Jiang, Ruiwei Shen, Siqian Zhang, Yiling Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA

We consider a single-server scheduling problem given a fixed sequence of appointment arrivals with random no-shows and service durations. The probability distribution of the uncertain parameters is assumed to be ambiguous, and only the support and first moments are known. We formulate a class of distributionally robust (DR) optimization models that incorporate the worst-case expectation/conditional value-at-risk penalty cost of appointment waiting, server idleness, and overtime into the objective or constraints. Our models flexibly adapt to different prior beliefs of no-show uncertainty. We obtain exact mixed-integer nonlinear programming reformulations and derive valid inequalities to strengthen the reformulations that are solved by decomposition algorithms. In particular, we derive convex hulls for special cases of no-show beliefs, yielding polynomial-sized linear programming models for the least and the most conservative supports of no-shows. We test various instances to demonstrate the computational efficacy of our approaches and to compare the results of various DR models given perfect or ambiguous distributional information.

关键词： appointment scheduling no-show uncertainty distributionally robust optimization mixed-integer programming valid inequalities totally unimodularity convex hulls

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The mixing-MIR set with divisible capacities

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MATHEMATICAL programming 2008年第1期115卷 73-103页

作者： Zhao, M. de Farias, I. R., Jr. Univ Buffalo Dept Ind & Syst Engn Buffalo NY 14260 USA SUNY New York NY USA

We study the set = {(x, y) is an element of R+ x Z(n) : x + B(j)y(j) >= b(j), j=1,..., n}, where B-j, b(j) is an element of R+ -{0}, j = 1,..., n, and B-1 vertical bar...vertical bar B-n. The set S generalizes the ... 详细信息

We study the set = {(x, y) is an element of R+ x Z(n) : x + B(j)y(j) >= b(j), j=1,..., n}, where B-j, b(j) is an element of R+ -mixed-integer programming, j = 1,..., n, and B-1 vertical bar...vertical bar B-n. The set S generalizes the mixed-integer rounding (MIR) set of Nemhauser and Wolsey and the mixing-MIR set of Gunluk and Pochet. In addition, it arises as a substructure in general mixed-integer programming (MIP), such as in lot-sizing. Despite its importance, a number of basic questions about S remain unanswered, including the tractability of optimization over S and how to efficiently find a most violated cutting plane valid for P = conv (S). We address these questions by analyzing the extreme points and extreme rays of P. We give all extreme points and extreme rays of P. In the worst case, the number of extreme points grows exponentially with n. However, we show that, in some interesting cases, it is bounded by a polynomial of n. In such cases, it is possible to derive strong cutting planes for P efficiently. Finally, we use our results on the extreme points of P to give a polynomial-time algorithm for solving optimization over S.

关键词： mixed-integer programming branch-and-cut polyhedral combinatorics simple-set cutting plane simple mixed-integer set lot-sizing computational complexity

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A novel reformulation for the single-sink fixed-charge transportation problem

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MATHEMATICAL programming 2023年第1-2期202卷 169-198页

作者： Legault, Robin Cote, Jean-Francois Gendron, Bernard Laval Univ Dept Operat & Decis Syst Quebec City PQ Canada CIRRELT Quebec City PQ Canada Univ Montreal Dept Comp Sci & Operat Res Montreal PQ Canada CIRRELT Montreal PQ Canada

The single-sink fixed-charge transportation problem is known to have many applications in the area of manufacturing and transportation as well as being an important subproblem of the fixed-charge transportation problem. However, even the best algorithms from the literature do not fully leverage the structure of this problem, to the point of being surpassed by modern general-purpose mixed-integer programming solvers for large instances. We introduce a novel reformulation of the problem and study its theoretical properties. This reformulation leads to a range of new upper and lower bounds, dominance relations, linear relaxations, and filtering procedures. The resulting algorithm includes a heuristic phase and an exact phase, the main step of which is to solve a very small number of knapsack subproblems. Computational experiments are presented for existing and new types of instances. These tests indicate that the new algorithm systematically reduces the resolution time of the state-of-the-art exact methods by several orders of magnitude.

关键词： mixed-integer programming Fixed-charge transportation problem Lagrangian relaxation Knapsack problem

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Optimizing Flow Thinning Protection in Multicommodity Networks with Variable Link Capacity

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OPERATIONS RESEARCH 2016年第2期64卷 273-289页

作者： Pioro, Michal Fouquet, Yoann Nace, Dritan Poss, Michael Warsaw Univ Technol Inst Telecommun PL-00665 Warsaw Poland Lund Univ Dept Elect & Informat Technol S-22100 Lund Sweden Univ Technol Compiegne Univ Paris 04 UMR CNRS Heudiasyc 7253 F-60203 Compiegne France Univ Montpellier UMR CNRS LIRMM 5506 161 Rue Ada F-34392 Montpellier 5 France

Flow thinning (FT) is a concept of a traffic routing and protection strategy applicable to communication networks with variable capacity of links. In such networks, the links do not attain their nominal (maximum) capacity simultaneously, so in a typical network state only some links are fully available whereas on each of the remaining links only a fraction of its maximum capacity is usable. Every end-to-end traffic demand is assigned a set of logical tunnels whose total capacity is dedicated to carry the demand's traffic. The nominal (i.e., maximum) capacity of the tunnels, supported by the nominal (maximum) link capacity, is subject to state-dependent thinning to account for variable capacity of the links fluctuating below the maximum. Accordingly, the capacity available on the tunnels is also fluctuating below their nominal levels and hence the instantaneous traffic sent between the demand's end nodes must accommodate to the current total capacity available on its dedicated tunnels. The related multi-commodity flow optimization problem is NP-hard and its noncompact linear programming formulation requires path generation. For that, we formulate an integer programming pricing problem, at the same time showing the cases when the pricing is polynomial. We also consider an important variant of FT, affine thinning, that may lead to practical FT implementations. We present a numerical study illustrating traffic efficiency of FT and computational efficiency of its optimization models. Our considerations are relevant, among others, for wireless mesh networks utilizing multiprotocol label switching tunnels.

关键词： survivable network design multiple partial link failures mixed-integer programming multicommodity flows path generation robust optimization

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Hospital resident scheduling problem

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PRODUCTION PLANNING & CONTROL 2002年第2期13卷 220-233页

作者： Sherali, HD Ramahi, MH Saifee, QJ Virginia Polytech Inst & State Univ Grado Dept Ind & Syst Engn 0118 Blacksburg VA 24061 USA Delta Technol Inc Dept 709 Atlanta GA USA WIT Inc St Clair Shores MI 48080 USA

This paper addresses the resident scheduling problem (RSP) at hospitals concerned with prescribing work-nights for residents while considering departmental staffing and skill requirements as well as residents' preferences. Three scenarios that represent most situations and account for various departmental requirements and needs are described. Although similar scheduling problems are considered in the literature, no analysis exists that adequately deals with the specific nature of this problem. The problem is modeled as a mixed-integer program and heuristic solution procedures are developed for the different identified scheduling scenarios. These procedures exploit the inherent network structure of the problem which is an important feature that enhances problem solvability. For the sake of comparison, the problem is also solved exactly via the CPLEX-MIP (version 6.0) package. The contribution of this work is important since many hospitals are still utilizing manual techniques in preparing their own schedules, expending considerable effort and time and yet contending with limited scheduling flexibility.

关键词： resident scheduling mixed-integer programming network flows sequential heuristics

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