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applications OF integer programming IN RADIO-FREQUENCY MANAGEMENT

MANAGEMENT SCIENCE 1985年第7期31卷 829-839页

作者： MATHUR, K SALKIN, HM NISHIMURA, K MORITO, S WASEDA UNIV DEPT IND ENGNTOKYO 160JAPAN

The radio frequency communication environment, for example, in large vessels, aircraft, space vehicles, and satellites, has become increasingly complex as more and more transmitters, receivers, and corresponding communication nets are being added to perform multiple functions. This paper discusses some of the problems faced by a decision maker in managing a communication network. A particular and important problem worth investigating occurs when different frequencies are simultaneously active in a network. This may cause various types of interference creating a disturbance in communication. One interesting and important type of interference, which may be expressed mathematically, is intermodulation. A typical problem scenario is thus to assign frequencies to the different nets of the network so that intermodulation interference is within desirable limits. A second problem is to add a net to an existing network, with previously assigned frequencies, so that the new net produces an acceptable level of intermodulation interference. Besides these, other related problems may be defined. For many problem scenarios, related integer nonlinear programming models may be derived. These models, corresponding algorithms and related software are discussed.

关键词： communications integer programming applications military

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College basketball scheduling with travel swings

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COMPUTERS & INDUSTRIAL ENGINEERING 2005年第2期48卷 163-172页

作者： Van Voorhis, T Liberty Univ Dept Math Lynchburg VA 24502 USA

The Missouri Valley Conference uses travel swings, in which a team plays two opponents during one road trip, to reduce the expenses for their college basketball programs. While these swings are financially beneficial, they significantly complicate the scheduling process. In particular, the swings alter the structure of the schedule by allowing games to occur outside of the standard time slots into which games are typically assigned. An integer programming formulation was developed that incorporates these swings into the scheduling problem. This program was solved efficiently by assigning swings first, then fitting remaining games around the swings. This generated a large number of candidate schedules, one of which was used for the 2001 season. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： recreation/sports scheduling integer programming applications

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Air Traffic Control Capacity Planning Under Demand and Capacity Provision Uncertainty

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TRANSPORTATION SCIENCE 2020年第4期54卷 882-896页

作者： Starita, Stefano Strauss, Arne K. Fei, Xin Jovanovic, Radosav Ivanov, Nikola Pavlovic, Goran Fichert, Frank Chulalongkorn Univ Sasin Sch Management Bangkok 10330 Thailand WHU Otto Beisheim Sch Management D-56179 Vallendar Germany Univ Warwick Warwick Business Sch Coventry CV4 7AL W Midlands England Univ Belgrade Fac Transport & Traff Engn Belgrade 11000 Serbia Worms Univ Appl Sci Fac Tourism & Transport D-67549 Worms Germany

In air traffic management, a fundamental decision with large cost implications is the planning of future capacity provision. Here, capacity refers to the available man-hours of air traffic controllers to monitor traffic. Airspace can be partitioned in various ways into a collection of sectors, and each sector has a fixed maximum number of flights that may enter within a given time period. Each sector also requires a fixed number of man-hours to be operated;we refer to them as sector-hours. Capacity planning usually takes place a long time ahead of the day of operation to ensure that sufficiently many air traffic controllers are available to manage the flow of aircrafts. However, at the time of planning, there is considerable uncertainty regarding the number and spatiotemporal distribution of non-scheduled flights and capacity provision, the former mainly due to business aviation, and the latter usually stemming from the impact of weather, military use of airspaces, etc. Once the capacity decision has been made (in terms of committing to a budget of sector-hours per airspace to represent long-term staff scheduling), on the day of operation, we can influence traffic by enforcing rerouting and tactical delays. Furthermore, we can modify which sectors to open at a given time (the so-called sector-opening scheme) subject to the fixed capacity budgets in each airspace. The fundamental trade-off is between reducing the capacity provision cost at the expense of potentially increasing displacement cost arising from rerouting or delays. To tackle this, we propose a scalable decomposition approach that exploits the structure of the problem and can take traffic and capacity provision uncertainty into account by working with a large number of traffic scenarios. We propose several decision policies based on the resulting pool of solutions and test them numerically using real-world data.

关键词： air transportation capacity ordering policies integer programming applications decomposition methods

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A sliding time window heuristic for open pit mine block sequencing

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OPTIMIZATION LETTERS 2011年第3期5卷 365-377页

作者： Cullenbine, Christopher Wood, R. Kevin Newman, Alexandra Colorado Sch Mines Div Econ & Business Golden CO 80401 USA USN Dept Operat Res Postgrad Sch Monterey CA 93943 USA

The open pit mine block sequencing problem (OPBS) seeks a discretetime production schedule that maximizes the net present value of the orebody extracted from an open-pit mine. This integer program (IP) discretizes the mine's volume into blocks, imposes precedence constraints between blocks, and limits resource consumption in each time period. We develop a "sliding time window heuristic" to solve this IP approximately. The heuristic recursively defines, solves and partially fixes an approximating model having: (i) fixed variables in early time periods, (ii) an exact submodel defined over a "window" of middle time periods, and (iii) a relaxed submodel in later time periods. The heuristic produces near-optimal solutions (typically within 2% of optimality) for model instances that standard optimization software fails to solve. Furthermore, it produces these solutions quickly, even though our OPBS model enforces standard upper-bounding constraints on resource consumption along with less standard, but important, lower-bounding constraints.

关键词： Mine scheduling Mine planning Open pit mining Surface mining integer programming applications

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Practical integrated design strategies for opaque and all-optical DWDM networks: Optimization models and solution procedures

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TELECOMMUNICATION SYSTEMS 2006年第1期31卷 61-83页

作者： Birkan, GA Kennington, JL Olinick, EV Ortynski, A Spiride, G So Methodist Univ Sch Engn Dept Engn Management Informat & Syst Dallas TX 75275 USA Amazon Com Seattle WA 98104 USA Nortel Richardson TX 75082 USA

Dense wavelength division multiplexing (DWDM) opaque networks use expensive optical/electrical/optical (O/E/O) conversion at each end of a fiber link. Several technological advances have been used in an attempt to reduce the O/E/O conversion cost component: improved optical amplifiers using distributed Raman amplification allow signals to traverse longer distances without amplification and/or regeneration;optical switches allow the signal to remain in the optical domain most of the time. Networks that use this equipment to eliminate some of the O/E/O conversions are called transparent or all-optical networks and benefit from reduced capital costs at the expense of operational costs and complexity in order to handle potential adjustments in traffic demand. In this investigation, we develop optimization-based algorithms for DWDM network design and traffic routing for both opaque and all-optical networks. This study compares the performance of AMPL/CPLEX implementations of both algorithms on realistically sized networks with up to 36 nodes and 67 links. In all test cases considered the all-optical network design is substantially less expensive than the traditional opaque network design with cost reductions in the range of 12% to 26%.

关键词： integer programming applications network provisioning DWDM network design polarization mode dispersion

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Production Scheduling for Strategic Open Pit Mine Planning: A Mixed-integer programming Approach

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OPERATIONS RESEARCH 2020年第5期68卷 1425-1444页

作者： Rivera Letelier, Orlando Espinoza, Daniel Goycoolea, Marcos Moreno, Eduardo Munoz, Gonzalo Univ Adolfo Ibanez Doctoral Program Ind Engn & Operat Res Santiago 7941169 Chile Google Cambridge MA 02142 USA Univ Adolfo Ibanez Sch Business Santiago 7941169 Chile Univ Adolfo Ibanez Fac Engn & Sci Santiago 7941169 Chile Univ OHiggins Inst Engn Sci Rancagua 2820000 Chile

Given a discretized representation of an ore body known as a block model, the open pit mining production scheduling problem that we consider consists of defining which blocks to extract, when to extract them, and how or whether to process them, in such a way as to comply with operational constraints and maximize net present value. Although it has been established that this problem can be modeled with mixed-integer programming, the number of blocks used to represent real-world mines (millions) has made solving large instances nearly impossible in practice. In this article, we introduce a new methodology for tackling this problem and conduct computational tests using real problem sets ranging in size from 20,000 to 5,000,000 blocks and spanning 20 to 50 time periods. We consider both direct block scheduling and bench-phase scheduling problems, with capacity, blending, and minimum production constraints. Using new preprocessing and cutting planes techniques, we are able to reduce the linear programming relaxation value by up to 33%, depending on the instance. Then, using new heuristics, we are able to compute feasible solutions with an average gap of 1.52% relative to the previously computed bound. Moreover, after four hours of running a customized branch-and-bound algorithm on the problems with larger gaps, we are able to further reduce the average from 1.52% to 0.71%.

关键词： open pit mining production scheduling column generation heuristics cutting planes integer programming applications

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Optimization-Driven Scenario Grouping

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INFORMS JOURNAL ON COMPUTING 2020年第3期32卷 805-821页

作者： Ryan, Kevin Ahmed, Shabbir Dey, Santanu S. Rajan, Deepak Musselma, Amelia Watson, Jean-Paul Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA Lawrence Livermore Natl Lab Livermore CA 94550 USA Sandia Natl Labs Livermore CA 94550 USA

Scenario decomposition algorithms for stochastic programs compute bounds by dualizing all nonanticipativity constraints and solving individual scenario problems independently. We develop an approach that improves on these bounds by reinforcing a carefully chosen subset of nonanticipativity constraints, effectively placing scenarios into groups. Specifically, we formulate an optimization problem for grouping scenarios that aims to improve the bound by optimizing a proxy metric based on information obtained from evaluating a subset of candidate feasible solutions. We show that the proposed grouping problem is NP-hard in general, identify a polynomially solvable case, and present two formulations for solving the problem: a matching formulation for a special case and a mixed-integer programming formulation for the general case. We use the proposed grouping scheme as a preprocessing step for a particular scenario decomposition algorithm and demonstrate its effectiveness in solving standard test instances of two-stage 0-1 stochastic programs. Using this approach, we are able to prove optimality for all previously unsolved instances of a standard test set. Additionally, we implement this scheme as a preprocessing step for PySP, a publicly available and widely used implementation of progressive hedging, and compare this grouping approach with standard grouping approaches on large-scale stochastic unit commitment instances. Finally, the idea is extended to propose a finitely convergent algorithm for two-stage stochastic programs with a finite feasible region.

关键词： stochastic programming integer programming applications computational methods

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Unified Optimization of Traffic Flows Through Airports

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TRANSPORTATION SCIENCE 2016年第1期50卷 77-93页

作者： Bertsimas, Dimitris Frankovich, Michael MIT Alfred P Sloan Sch Management Cambridge MA 02139 USA MIT Ctr Operat Res Cambridge MA 02139 USA Aviat Edge LLC Belmont MA 02478 USA

We present a novel integer optimization approach to optimize, in a tractable and unified manner, the airport operations optimization problem. This includes solving the entirety of key air traffic flow management problems faced at an airport: (a) selecting a runway configuration sequence, i.e., determining which runways are open at which times and in which mode they operate;(b) assigning flights to runways and determining the sequence in which flights are processed (i.e., when they take off or land);(c) determining the gate-holding duration of departures;and (d) routing flights to their assigned runway and onward within the terminal area and the near-terminal airspace. The key contribution of this paper is the modeling of these problems, which until present have been studied in isolation, under a framework that is both unified and tractable. This allows the possibility of obtaining system-optimal solutions in a practical amount of time. Furthermore, the approach is implemented on historic data sets from both Boston Logan International and Dallas/Fort Worth International airports. Computational experience indicates that significant reductions in delays, fuel use, and emissions can be achieved from this optimization and that computational tractability is such that real-world instances can be solved within five to 10 minutes.

关键词： air traffic flow management integer programming applications

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Minimum Violations and Predictive Meta-Rankings for College Football

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NAVAL RESEARCH LOGISTICS 2014年第1期61卷 17-33页

作者： Coleman, B. Jay Univ N Florida Dept Management Coggin Coll Business Jacksonville FL 32224 USA

This article presents two meta-ranking models that minimize or nearly minimize violations of past game results while predicting future game winners as well as or better than leading current systemsa combination never before offered for college football. Key to both is the development and integration of a highly predictive ensemble probability model generated from the analysis of 36 existing college football ranking systems. This ensemble model is used to determine a target ranking that is used in two versions of a hierarchical multiobjective mixed binary integer linear program (MOMBILP). When compared to 75 other systems out-of-sample, one MOMBILP was the leading predictive system while getting within 0.64% of the retrodictive optimum;the other MOMBILP minimized violations while achieving a prediction total that was 2.55% lower than the best mark. For bowls, prediction sums were not statistically significantly different from the leading value, while achieving optimum or near-optimum violation counts. This performance points to these models as potential means of reconciling the contrasting perspectives of predictiveness versus the matching of past performance when it comes to ranking fairness in college football. (c) 2013 Wiley Periodicals, Inc. Naval Research Logistics 61: 17-33, 2014

关键词： sports minimum violations ranking integer programming applications forecasting

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Design procedures for backbone transport networks with shared protection: optimization-based models, exact and heuristic algorithms, and unavailability computations

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TELECOMMUNICATION SYSTEMS 2009年第2期41卷 97-120页

作者： Birkan, G. Kennington, J. So Methodist Univ Sch Engn Dept Engn Management Informat & Syst Dallas TX 75275 USA Capital One Financial Serv Richmond VA 23238 USA

This manuscript presents optimization-based design models and algorithms for reliable backbone transport networks. Due to their efficiency in providing data services and high data rates, dense wavelength division multiplexing (DWDM) networks became the technology of choice for these transport networks. DWDM networks achieve these high rates by enabling several wavelengths of light to be transmitted on a single strand of fiber. Optimization-based practical methods to design DWDM networks with both link-based and path-based shared protection schemes are introduced and compared in an empirical analysis. These design models address various restrictions inherent to DWDM technology including polarization mode dispersion and attenuation requirements. Furthermore, approximations are developed to determine unavailability for any given origin-destination pair in a DWDM network. Finally, path-based and link-based shared protection models are compared based on design costs and unavailability.

关键词： integer programming applications Network provisioning DWDM network design Polarization mode dispersion Shared protection Availability

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