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Optimal allocation of two fixed service units acting as M/G/1 queues

TRANSPORTATION SCIENCE 1996年第1期30卷 60-74页

作者： Filippi, C RomaninJacur, G UNIV PADUA DEPT ELECTR & INFORMATI-35131 PADUAITALY

We consider a districting problem placed in. the general context of optimal allocation of urgent services in. the presence of congestion. Customers are located in fixed points of a physical space and ash for urgent service according to Poisson processes. Two facilities, located in fixed points, supply the service by acting as M/G/1 queues. Each customer shall be assigned to one of the two facilities so that the mean expected response time is minimized, where the response time is the sum of the transportation time, the wait-in-queue time and the service time. We formalize the problem as an integer nonlinear programming model and we exactly solve it by a suitable branch-and-bound procedure. We show that the problem, if relaxed with respect to integrality constraints, can, be reduced to an equivalent convex minimization problem with only one variable. Actually, each step of the branch-and-bound procedure is performed by quickly solving a continuous single-variable minimization problem. We randomly generate a large amount of instances of practical size, and we solve them on a workstation. Short computing times (<50 sees CPU for the worst experimented case) are evidenced. Since the problem is recognized to be NP-hard, we also suggest a simple heuristic method with low complexity.

关键词： Optimal solutions Transportation objective functions Machine tools Integers Machinery Mathematical minima Poisson process Heuristics Network servers

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CONJUGATE RELATIONS AND WEAK SUBDIFFERENTIALS OF RELATIONS

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MATHEMATICS OF OPERATIONS RESEARCH 1981年第4期6卷 593-607页

作者： KAWASAKI, H

The duality theory for convex programs is based on a concept "conjugate" of functions, and the set of solutions is characterized by "subdifferential" of a function. The purpose of this paper is to extend the concepts "conjugate" and "subdifferential" to those of set-valued functions (relations) and to investigate their properties.

关键词： Mathematical duality objective functions Mathematical relations Mathematical concepts Continuous functions Real numbers

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Finding the Best System Nested Defense Under Budget Uncertainty

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MILITARY OPERATIONS RESEARCH 2019年第1期24卷 5-22页

作者： Lazzaro, Gary Carlyle, W. Matthew US Naval Acad Math Dept Annapolis MD 21402 USA Naval Postgrad Sch Operat Res Dept Monterey CA USA

We extend a defender-attacker-defender (DAD) trilevel optimization model to investigate system defense planning under uncertain budget scenarios, and how that uncertainty impacts optimality. A nested defense is a monotonic sequence of sets, where the set of defenses for a particular budget scenario contains the set of defenses for all smaller budget scenarios. The use of nested defenses is attractive to decision makers because it simplifies the choices of the best defenses under uncertain budgetary scenarios into a single list. However, a set of nested defenses over many budget scenarios is almost always suboptimal when compared to the optimal defense for each individual budget. We investigate both heuristic and parametric programming approaches to identify the set of nested defenses to a system that is as close as possible to the optimal defenses over all possible budget scenarios.

关键词： Military defense Defense budgets objective functions Mathematical vectors Heuristics Optimal solutions Military operations Operations research Fens Unit costs

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MULTILEVEL SCHEDULING OF MULTISTAGE PRODUCTION WITH LIMITED IN-PROCESS INVENTORY

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 1987年第7期38卷 651-664页

作者： SAWIK, TJ UNIV MIN & MET CRACOW CRACOWPOLAND

A multistage, multiproduct production scheduling with limited in-process buffers between the successive stages is considered. Each stage is made up of identical parallel machines. The problem objective is to determine an assignment of products to machines over a scheduling horizon, which minimizes the completion time of the production order, with the in-process inventory holding costs as low as possible. The problem is modelled by multilevel integer programmes, each of which is concerned with scheduling a different stage of production. The interactions among the stages are modelled by additional constraints, which take into account the semi-finished product's availability and the limited storage capacity of the intermediate buffers. An hierarchical scheduling algorithm is presented, and an illustrative example for a three-stage production is included.

关键词： Scheduling Production technology Algorithms Carrying costs Buffer inventories Integers Buffer storage objective functions Heuristics Machining

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A METHOD FOR DIRECT ESTIMATION OF ORIGIN-DESTINATION TRIP MATRICES

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TRANSPORTATION SCIENCE 1981年第1期15卷 32-49页

作者： CAREY, M HENDRICKSON, C SIDDHARTHAN, K CARNEGIE MELLON UNIV PITTSBURGHPA 15213

Estimates of the volume of travel between zones or locations is often a necessary step in transportation studies. This paper suggests a method of estimating origin/destination volumes, using a direct demand function and incomplete, aggregate data. Most attention is devoted to demand functions which are linear in their parameters. With such demand functions, volume estimates are obtained from a quadratic programming problem, which minimizes the sum of squared errors from a direct demand function, subject to constraints derived from observations of some travel volumes. A decomposition algorithm is suggested for solving the programming problem and is proven to converge. The method may also be used in the trip distribution phase of the conventional urban transportation model systems (UTMS).

关键词： Algorithms objective functions Trip matrices Traffic estimation Travel time Transportation demand Quadratic programming Mathematical vectors

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A Skeleton-Based Electromagnetic Recovery for Explicit Adaptive Mesh Refinement

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 2024年第9期72卷 5155-5166页

作者： Wang, Yin-Da Zhan, Qiwei Wang, Yi-Yao Zhang, Jingwei Zhang, Nian-En Yin, Wen-Yan Zhejiang Univ Innovat Inst Electromagnet Informat & Elect Integr Coll ISEE Key Lab Adv Micronano Elect Devices & Smart Syst Z Hangzhou 310027 Peoples R China

We present a novel adaptive mesh refinement (AMR) algorithm for microwave modeling, specifically focusing on computational electromagnetic analysis using the tangential vector finite element method (TVFEM). For a posteriori error estimation, the proposed explicit recovery-based algorithm uses H(div)-conforming (Brezzi-Douglas-Marini) and H(curl)-conforming (Nedelec) basis functions to recover the artificial electric displacement flux and magnetic vortex density on the mesh skeleton, respectively. Compared with implicit approaches, our approach avoids the need for an auxiliary system with a finer mesh or higher polynomial order. Compared with residual-based approaches, it does not rely on a priori error inequalities, so that it yields a global estimate of the solution quality. Notably, the algorithm aligns mesh topology adjustments with goal-oriented objective functions rather than solely with the numerical solution. Validation is performed using an analytical model with smooth field distribution, a Fichera model with nonsmooth field distribution, a Mie scattering model with a goal-oriented function for monostatic radar cross section (RCS), and a real-world RF filter with a goal-oriented function for insertion loss. Comparative analyses against uniform refinement, nongoal-oriented refinement, and traditional implicit goal-oriented refinement unequivocally demonstrate the superiority of our algorithm.

关键词： A posteriori error estimation adaptive mesh refinement (AMR) mesh skeleton objective functions tangential vector finite element method (TVFEM)

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GLOBAL MAXIMIZATION OF A CONVEX FUNCTION WITH LINEAR INEQUALITY CONSTRAINTS

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OPERATIONS RESEARCH 1974年第3期22卷 602-609页

作者： ZWART, PB WASHINGTON UNIV ST LOUISMO 63130

This paper presents an algorithm for the global maximization of a convex function subject to linear inequality constraints. It is computationally finite and is designed to converge rapidly on problems in which there a... 详细信息

关键词： Local maximum Linear inequalities Algorithms objective functions Quadratic functions

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Exergy optimization of a multi-stage solar micro-cogeneration system

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IET RENEWABLE POWER GENERATION 2023年第2期17卷 217-228页

作者： Kallio, Sonja Siroux, Monica Strasbourg Univ INSA Strasbourg ICUBE Strasbourg France

This paper proposes a dynamic model of a solar-based micro-cogeneration system called photovoltaic-thermal (PVT) collector to perform a design optimization of the multi-stage PVT system. The parametric study reveals the most important design parameters influencing the water-based flat-plate PVT system performance. The analysis also shows an existing trade-off between thermal and electrical efficiencies during the PVT operation. A novel exergy-based multi-objective design optimization method is demonstrated to find a trade-off design solution of the multi-stage PVT collector which compromises between the electrical and thermal exergy efficiencies under different weather conditions. The electrical and thermal exergy efficiencies are defined to be the objective functions of the Matlab gamultiobj-function, which is a multi-objective evolutionary algorithm using non-dominated sorting genetic algorithm-II (NSGA-II). As a result of the algorithm, the Pareto optimal sets were derived that revealed the optimal solutions taking into account the trade-off nature of the optimization problem. The decision-making method called an ideal point method was used in the decision-making process to find the final optimal solutions for different weather conditions. The results revealed that the optimal number of the PVT collectors in series depended on the weather conditions and decreased from 3 to 2 if the conditions got cooler.

关键词： genetic algorithms Optimisation techniques water-based flat-plate PVT system performance trade-off nature objective functions Solar power stations and photovoltaic power systems multiobjective evolutionary algorithm dynamic model Pareto optimisation sorting genetic algorithm-II multistage PVT collector PVT collectors photovoltaic-thermal collector evolutionary computation optimization problem microcogeneration system final optimal solutions PVT operation solar absorber-convertors important design parameters electrical efficiencies multistage PVT system cogeneration novel exergy-based multiobjective design optimization method Other direct energy conversion optimal number existing trade electrical exergy efficiencies thermal exergy efficiencies exergy Optimisation decision-making method exergy optimization decision making trade-off design solution optimisation Pareto optimal sets

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Differential Characteristics of Efficient Frontiers in Data Envelopment Analysis

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OPERATIONS RESEARCH 2010年第6期58卷 1743-1754页

作者： Podinovski, Victor V. Forsund, Finn R. Univ Warwick Warwick Business Sch Coventry CV4 7AL W Midlands England Univ Oslo Dept Econ N-0317 Oslo Norway

The implicit definition and nondifferentiability of efficient frontiers used in data envelopment analysis are two major obstacles to obtaining their differential characteristics, including various elasticity measures and marginal rates of substitution. In this paper we invoke the theorem of the directional derivative of the optimal value function and show how this can be used to define and calculate the required elasticities without any simplifying assumptions. This approach allows us to extend the known elasticity measures and introduce new ones to the entire efficient frontier, including all its extreme points, in one single development. We also construct linear programs that are required for the calculation of elasticity measures. Our main development is undertaken in the variable returns-to-scale technology but extends to other polyhedral technologies of efficiency analysis.

关键词： Efficiency metrics Optimal solutions objective functions Production efficiency Productivity Emerging technology Economic elasticity Economic models

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A market-based approach to optimal resource allocation in integrated-services connection-oriented networks

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OPERATIONS RESEARCH 2002年第4期50卷 603-616页

作者： Thomas, P Teneketzis, D Mackie-Mason, JK Motorola Inc Adv Network Technol Arlington Hts IL 60004 USA Univ Michigan Dept Elect Engn & Comp Engn Ann Arbor MI 48109 USA Univ Michigan Dept Econ Ann Arbor MI 48109 USA Univ Michigan Sch Informat Ann Arbor MI 48109 USA

We present an approach to the admission control and resource allocation problem in connection-oriented networks that offer multiple services to users. Users' preferences are summarized by means of their utility functions, and each user is allowed to request more than one type of service. Multiple types of resources are allocated at each link along the path of a connection. We assume that the relation between Quality of Service (QoS) and resource allocation is given, and we incorporate it as a constraint into a static optimization problem. The objective of the optimization problem is to determine the amount of and required resources for each type of service to maximize the sum of the users' utilities. We prove the existence of a solution of the optimization problem and describe a competitive market economy that implements the solution and satisfies the informational constraints imposed by the nature of the decentralized resource allocation problem. The economy consists of four different types of agents: resource providers, service providers, users, and an auctioneer that regulates the prices based on the observed aggregate excess demand. The goods that are sold are: (i) the resources at each link of the network, and (ii) services constructed from these resources and then delivered to users. We specify an iterative procedure that is used by the auctioneer to update the prices, and we show that it leads to an allocation that is arbitrarily close to a solution of the optimization problem in a finite number of iterations.

关键词： Auctioneers Mathematical vectors objective functions Economic resources Market prices Integers Continuous functions Information resources Price takers Price vector

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