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Minimizing average project team size given multi-skilled workers with heterogeneous skill levels

COMPUTERS & OPERATIONS RESEARCH 2016年第Jun.期70卷 163-179页

作者： Walter, Matthias Zimmermann, Juergen Tech Univ Clausthal Inst Management & Econ Operat Res Grp Julius Albert Str 2 D-38678 Clausthal Zellerfeld Germany

Many firms face the challenging task of staffing concurrent projects such that the skill requirements of each project can be satisfied by the respective team of workers. We consider a staffing problem where each worker can be assigned to several projects at a time. A high total number of assignments implies large project teams and scattering of workers across projects. Large teams come along with productivity losses due to increased coordination effort and social loafing while scattering incurs losses due to frequent switching between projects. To curb these inefficiencies, we formulate a mixed-integer linear program that minimizes average project team size and, thus, scattering. The program accounts for multi skilled workers with heterogeneous skill levels who must also fulfill duties within their departments. We prove that the problem is NP-hard in the strong sense and outline valid inequalities that accelerate the solution by a commercial branch-and-cut solver. For large-scale instances, we devise three construction heuristics, each of which is embedded in a multi-pass procedure. Our performance analysis reveals that a heuristic based on the drop principle offers the best compromise between solution quality and computation time. Limitations of the proposed approach, managerial insights, and areas of application are discussed. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Multi-project staffing Multi-skilled workers Team size Social loafing mixed-integer programming Multi-pass heuristics

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Intersection Cuts with Infinite Split Rank

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MATHEMATICS OF OPERATIONS RESEARCH 2012年第1期37卷 21-40页

作者： Basu, Amitabh Cornuejols, Gerard Margot, Francois Univ Calif Davis Dept Math Davis CA 95616 USA Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA Univ Marseille Fac Sci Luminy LIF F-13288 Marseille France

We consider mixed-integer linear programs where free integer variables are expressed in terms of nonnegative continuous variables. When this model only has two integer variables, Dey and Louveaux characterized the intersection cuts that have infinite split rank. We show that, for any number of integer variables, the split rank of an intersection cut generated from a rational lattice-free polytope L is finite if and only if the integer points on the boundary of L satisfy a certain "2-hyperplane property." The Dey-Louveaux characterization is a consequence of this more general result.

关键词： mixed-integer programming cutting planes split rank

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Leveraging neural networks to optimize heliostat field aiming strategies in Concentrating Solar Power Tower plants

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Energy and AI 2025年 21卷

作者： Antonio Alcántara Pablo Diaz-Cachinero Alberto Sánchez-González Carlos Ruiz Universidad Carlos III of Madrid Department of Statistics Spain Universidad Carlos III of Madrid Department of Thermal and Fluids Engineering Energy Systems Engineering (ISE) Research Group Spain

Concentrating Solar Power Tower (CSPT) plants rely on heliostat fields to focus sunlight onto a central receiver. Although simple aiming strategies, such as directing all heliostats to the receiver’s equator, can maximize energy collection, they often result in uneven flux distributions that cause hotspots, thermal stresses, and reduced receiver lifetimes. This paper presents a novel, data-driven approach that combines constraint learning, neural network-based surrogates, and mathematical optimization to address these challenges. The methodology learns complex heliostat-to-receiver flux interactions from simulation data and embeds the resulting surrogate model in a tractable optimization framework. By maximizing a tailored quality score that balances energy collection with flux uniformity, the approach produces smoothly distributed flux profiles and mitigates excessive thermal peaks. An iterative refinement process, guided by a trust region strategy and progressive data sampling, ensures continual improvement of the surrogate model by exploring new solution spaces at each iteration. Results from a real CSPT case study show that the proposed approach outperforms conventional heuristic methods, delivering flatter flux distributions with nearly a 10% reduction in peak values and safer thermal conditions (reflected by up to a 50% decrease in deviations from safe concentration distributions), without significantly compromising overall energy capture.

关键词： Aiming strategies Concentrating Solar Power Tower plants Constraint learning Neural networks mixed-integer programming

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Green resource allocation for mobile edge computing

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Digital Communications and Networks 2023年第5期9卷 1190-1199页

作者： Anqi Meng Guandong Wei Yao Zhao Xiaozheng Gao Zhanxin Yang State Key Laboratory of Media Convergence and Communication Communication University of ChinaBeijing100024China Engineering Center of Digital Audio and Video Communication University of ChinaBeijing100024China School of Information and Electronics Beijing Institute of TechnologyBeijing100081China

We investigate the green resource allocation to minimize the energy consumption of the users in mobile edge computing systems,where task offloading decisions,transmit power,and computation resource allocation are jointly *** considered energy consumption minimization problem is a non-convex mixed-integer nonlinear programming problem,which is challenging to ***,we develop a joint search and Successive Convex Approximation(SCA)scheme to optimize the non-integer variables and integer variables in the inner loop and outer loop,***,in the inner loop,we solve the optimization problem with fixed task offloading *** to the non-convex objective function and constraints,this optimization problem is still non-convex,and thus we employ the SCA method to obtain a solution satisfying the Karush-Kuhn-Tucker *** the outer loop,we optimize the offloading decisions through exhaustive ***,the computational complexity of the exhaustive search method is greatly *** reduce the complexity,a heuristic scheme is proposed to obtain a sub-optimal *** results demonstrate the effectiveness of the developed schemes.

关键词： Mobile edge computing Green communications mixed-integer programming Resource allocation

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Data-Model Hybrid Driven Topology Identification Framework for Distribution Networks

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CSEE Journal of Power and Energy Systems 2024年第4期10卷 1478-1490页

作者： Dongliang Xu Zaijun Wu Junjun Xu Qinran Hu School of Electrical Engineering Southeast UniversityNanjing 210096China College of automation Nanjing University of Posts and TelecommunicationsNanjing 210096China

Extensive penetration of distribution energy resources(DERs)brings increasing uncertainties to distribution *** topology identification is a critical basis to guarantee robust distribution network *** algorithms that estimate distribution network topology have already been ***,most are based on data-driven alone method and are hard to deal with ever-changing distribution network physical *** these backgrounds,this paper proposes a data-model hybrid driven topology identification scheme for distribution ***,a data-driven method based on a deep belief network(DBN)and random forest(RF)algorithm is used to realize the distribution network topology rough ***,the rough identification results in the previous step are used to make a model of distribution network *** model transforms the topology identification problem into a mixed integer programming problem to correct the rough topology *** of the proposed method is verified in an IEEE 33-bus test system and modified 292-bus system.

关键词： Data-model hybrid driven DBN-RF mixed-integer programming topology identification

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Solving a multi-floor layout design model of a dynamic cellular manufacturing system by an efficient genetic algorithm

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JOURNAL OF MANUFACTURING SYSTEMS 2014年第1期33卷 218-232页

作者： Kia, R. Khaksar-Haghani, F. Javadian, N. Tavakkoli-Moghaddam, R. Islamic Azad Univ Firoozkooh Branch Dept Ind Engn Firoozkooh Iran Islamic Azad Univ Najafabad Branch Dept Ind Engn Esfahan Iran Mazandaran Univ Sci & Technol Dept Ind Engn Babol Sar Iran Univ Tehran Coll Engn Sch Ind Engn Tehran Iran Univ Tehran Coll Engn Engn Optimizat Res Grp Tehran Iran

This paper presents a mixed-integer programming model for a multi-floor layout design of cellular manufacturing systems (CMSs) in a dynamic environment. A novel aspect of this model is to concurrently determine the cell formation (CF) and group layout (GL) as the interrelated decisions involved in the design of a CMS in order to achieve an optimal (or near-optimal) design solution for a multi-floor factory in a multi-period planning horizon. Other design aspects are to design a multi-floor layout to form cells in different floors, a multi-rows layout of equal area facilities in each cell, flexible reconfigurations of cells during successive periods, distance-based material handling cost, and machine depot keeping idle machines. This model incorporates with an extensive coverage of important manufacturing features used in the design of CMSs. The objective is to minimize the total costs of intra-cell, inter-cell, and inter-floor material handling, purchasing machines, machine processing, machine overhead, and machine relocation. Two numerical examples are solved by the CPLEX software to verify the performance of the presented model and illustrate the model features. Since this model belongs to NP-hard class, an efficient genetic algorithm (GA) with a matrix-based chromosome structure is proposed to derive near-optimal solutions. To verify its computational efficiency in comparison to the CPLEX software, several test problems with different sizes and settings are implemented. The efficiency of the proposed GA in terms of the objective function value and computational time is proved by the obtained results. (C) 2013 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

关键词： Dynamic cellular manufacturing systems Multi-floor layout mixed-integer programming Genetic algorithm

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Approximating Trajectory Constraints With Machine Learning - Microgrid Islanding With Frequency Constraints

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IEEE TRANSACTIONS ON POWER SYSTEMS 2021年第2期36卷 1239-1249页

作者： Zhang, Yichen Chen, Chen Liu, Guodong Hong, Tianqi Qiu, Feng Argonne Natl Lab Lemont IL 60439 USA Oak Ridge Natl Lab Oak Ridge TN 37831 USA

In this paper, we introduce a deep learning aided constraint encoding method to tackle the frequency-constraint microgrid scheduling problem. The nonlinear function between system operating condition and frequency nadir is approximated by using a neural network, which admits an exact mixed-integer formulation (MIP). This formulation is then integrated with the scheduling problem to encode the frequency constraint. With the stronger representation power of the neural network, the resulting commands can ensure adequate frequency response in a realistic setting in addition to islanding success. The proposed method is validated on a modified 33-node system. Successful islanding with a secure response is simulated under the scheduled commands using a detailed three-phase model in Simulink. The advantages of our model are particularly remarkable when the inertia emulation functions from wind turbine generators are considered.

关键词： Generators Wind turbines Microgrids Frequency response Indexes Trajectory Dynamic scheduling Microgrid trajectory constrained scheduling mixed-integer programming deep neural network inertia emulation wind turbine generator

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Efficient Formulations and Decomposition Approaches for Power Peak Reduction in Railway Traffic via Timetabling

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TRANSPORTATION SCIENCE 2021年第3期55卷 747-767页

作者： Baermann, Andreas Martin, Alexander Schneider, Oskar Friedrich Alexander Univ Erlangen Nurnberg Dept Math D-91058 Erlangen Germany Fraunhofer Inst Integrierte Schaltungen IIS Grp Optimizat Fraunhofer Arbeitsgrp Supply Chain Serv SCS D-90411 Nurnberg Germany

Over the last few years, optimization models for the energy-efficient operation of railway traffic have received more and more attention, particularly in connection with timetable design. In this work, we study the effect of load management via timetabling. The idea is to consider trains as time-flexible consumers in the railway power supply network and to use slight shifts in the departure times from the stations to avoid too many simultaneous departures. This limits peak consumption and can help to improve the stability of the power supply. To this end, we derive efficient formulations for the problem of an optimal timetable adjustment based on a given timetable draft, two of which even allow for totally unimodular polyhedral descriptions. The proper choice of the objective function allows the incorporation of the priorities of either the train operating companies or the infrastructure manager. These include the avoidance of large peaks in average or instantaneous consumption and the improved use of recuperated braking energy. To solve the arising optimization models efficiently, we develop specially tailored exact Benders decomposition schemes that allow for the computation of high-quality solutions within a very short time. In an extensive case study for German railway passenger traffic, we show that our methods are capable of solving the problem on a nationwide scale. We see that the optimal adjustment of timetables entails a tremendous potential for reducing energy consumption.

关键词： railway timetabling energy efficiency total unimodularity decomposition mixed-integer programming

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Examination timetabling problem with scarce resources: a case study

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EUROPEAN JOURNAL OF INDUSTRIAL ENGINEERING 2018年第6期12卷 855-874页

作者： Keskin, Muhammed Emre Doyen, Alper Akyer, Hasan Guler, Mehmet Guray Ataturk Univ Dept Ind Engn TR-25240 Erzurum Turkey Konya Tech Univ Engn & Nat Sci Fac Ind Engn Dept Alaaddin Keykubad Campus TR-42130 Selcuklu Konya Turkey Pamukkale Univ Dept Ind Engn Kirikli Denizli Turkey Yildiz Tech Univ Fac Mech Engn Dept Ind Engn A-308 TR-34349 Istanbul Turkey

Examination timetabling problem (ETP) is one of the hardest administrative tasks that has to be undertaken at each semester in all faculties. Although the major structure of the problem remains intact, requirements may change from faculty to faculty causing major changes in the solution procedures. The number of academic staff and the level of infrastructures of newly established universities cannot keep up with the increasing number of departments and students. This scarcity brings several additional constraints to the ETP. In this study, we propose a two stage solution procedure for the ETP of such universities. We apply our solution method to a real problem. We show that better feasible solutions can be found in shorter computation times compared to commercial softwares. Moreover we show that the total examination period length can be reduced from seven days to six days with the proposed method.

关键词： examination timetabling scarce resources mixed-integer programming optimisation decomposition two stage solution strategy heuristic industrial engineering

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Using integer programming for balancing return and risk in problems with individual chance constraints

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COMPUTERS & OPERATIONS RESEARCH 2014年第Sep.期49卷 59-70页

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

In this paper, we study probabilistically constrained problems involving individual chance constraints, random univariate right-hand sides, and risk tolerances defined as decision variables which affect part of the objective function. Built on the concept of efficient points, we formulate the problems as mixed-integer programs by using binary variables to determine an optimal risk tolerance for each chance constraint. We develop two benchmark approaches, both of which solve chance-constrained programs with fixed risk values in a bisection algorithm or by enumeration. We specify our approaches for a minimum cost flow problem and a network capacity design problem, both of which involve chance constraints for bounding the risk of demand shortages. We test instances with diverse size and complexity of the two network problems, and demonstrate the computational efficacy as well as give managerial insights. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Chance-constrained programming Risk management mixed-integer programming Minimum cost flow Network capacity design

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