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Theory of integer-valued data envelopment analysis

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2009年第2期192卷 658-667页

作者： Kuosmanen, Timo Matin, Reza Kazemi MTT Agrifood Res Finland Econ Res Unit Helsinki 00410 Finland Islamic Azad Univ Dept Math Karaj Branch Tehran Iran

Conventional data envelopment analysis (DEA) models assume real-valued inputs and outputs. In many occasions, some inputs and/or outputs can only take integer values. In some cases, rounding the DEA solution to the nearest whole number can lead to misleading efficiency assessments and performance targets. This paper develops the axiomatic foundation for DEA in the case of integer-valued data, introducing new axioms of "natural disposability" and "natural divisibility". We derive a DEA production possibility set that satisfies the minimum extrapolation principle under our refined set of axioms, We also present a mixed integer linear programming formula for computing efficiency scores. An empirical application to Iranian university departments illustrates the approach. (C) 2007 Elsevier B.V. All rights reserved.

关键词： Data envelopment analysis Efficiency mixed integer linear programming Production theory

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On the effectiveness of scenario generation techniques in single-period portfolio optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2009年第2期192卷 500-511页

作者： Guastaroba, Gianfranco Mansini, Renata Speranza, M. Grazia Univ Brescia Dept Quantitat Methods I-25122 Brescia Italy Univ Brescia Dept Elect Automat I-25123 Brescia Italy

In single-period portfolio selection problems the expected value of both the risk measure and the portfolio return have to be estimated. Historical data realizations, used as equally probable scenarios, are frequently used to this aim. Several other parametric and non-parametric methods can be applied. When dealing with scenario generation techniques practitioners are mainly concerned on how reliable and effective such methods are when embedded into portfolio selection models. In this paper we survey different techniques to generate scenarios for the rates of return. We also compare the techniques by providing in-sample and out-of-sample analysis of the portfolios obtained by using these techniques to generate the rates of return. Evidence on the computational burden required by the different techniques is also provided. As reference model we use the Worst Conditional Expectation model with transaction costs. Extensive computational results based on different historical data sets from London Stock Exchange Market (FTSE) are presented and some interesting financial conclusions are drawn. (C) 2007 Elsevier B.V. All rights reserved.

关键词： Risk management Conditional value at risk Portfolio optimization Scenario generation mixed integer linear programming

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Resolution method for mixed integer bi-level linear problems based on decomposition technique

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JOURNAL OF GLOBAL OPTIMIZATION 2009年第1期44卷 29-51页

作者： Saharidis, G. K. Ierapetritou, M. G. Rutgers State Univ Dept Chem & Biochem Engn Piscataway NJ 08854 USA

In this article, we propose a new algorithm for the resolution of mixed integer bi-level linear problem (MIBLP). The algorithm is based on the decomposition of the initial problem into the restricted master problem (RMP) and a series of problems named slave problems (SP). The proposed approach is based on Benders decomposition method where in each iteration a set of variables are fixed which are controlled by the upper level optimization problem. The RMP is a relaxation of the MIBLP and the SP represents a restriction of the MIBLP. The RMP interacts in each iteration with the current SP by the addition of cuts produced using Lagrangian information from the current SP. The lower and upper bound provided from the RMP and SP are updated in each iteration. The algorithm converges when the difference between the upper and lower bound is within a small difference epsilon. In the case of MIBLP Karush-Kuhn-Tucker (KKT) optimality conditions could not be used directly to the inner problem in order to transform the bi-level problem into a single level problem. The proposed decomposition technique, however, allows the use of KKT conditions and transforms the MIBLP into two single level problems. The algorithm, which is a new method for the resolution of MIBLP, is illustrated through a modified numerical example from the literature. Additional examples from the literature are presented to highlight the algorithm convergence properties.

关键词： Bi-level optimization mixed integer linear programming Benders decomposition Active constraints

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Models and Simulations for Portfolio Rebalancing

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COMPUTATIONAL ECONOMICS 2009年第3期33卷 237-262页

作者： Guastaroba, Gianfranco Mansini, Renata Speranza, M. Grazia Univ Brescia Dept Quantitat Methods I-25122 Brescia Italy Univ Brescia Dept Elect Automat I-25123 Brescia Italy

In 1950 Markowitz first formalized the portfolio optimization problem in terms of mean return and variance. Since then, the mean-variance model has played a crucial role in single-period portfolio optimization theory and practice. In this paper we study the optimal portfolio selection problem in a multi-period framework, by considering fixed and proportional transaction costs and evaluating how much they affect a re-investment strategy. Specifically, we modify the single-period portfolio optimization model, based on the Conditional Value at Risk (CVaR) as measure of risk, to introduce portfolio rebalancing. The aim is to provide investors and financial institutions with an effective tool to better exploit new information made available by the market. We then suggest a procedure to use the proposed optimization model in a multi-period framework. Extensive computational results based on different historical data sets from German Stock Exchange Market (XETRA) are presented.

关键词： Risk management Conditional value at risk Portfolio rebalancing Multi-period portfolio analysis mixed integer linear programming

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Development of a new approach for deterministic supply chain network design

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2009年第1期198卷 121-128页

作者： Bidhandi, Hadi Mohammadi Yusuff, Rosnah Mohd. Ahmad, Megat Mohamad Hamdan Megat Abu Bakar, Mohd Rizam Univ Putra Malaysia Dept Mech & Mfg Engn Serdang 43400 Selangor Malaysia Univ Putra Malaysia Dept Math Serdang 43400 Malaysia

This paper proposes a mixed integer linear programming model and solution algorithm for solving supply chain network design problems in deterministic, multi-commodity, single-period contexts. The strategic level of supply chain planning and tactical level planning of supply chain are aggregated to propose an integrated model. The model integrates location and capacity choices for suppliers, plants and warehouses selection, product range assignment and production flows. The open-or-close decisions for the facilities are binary decision variables and the production and transportation flow decisions are continuous decision variables. Consequently, this problem is a binary mixed integer linear programming problem. In this paper, a modified version of Benders' decomposition is proposed to solve the model. The most difficulty associated with the Benders' decomposition is the solution of master problem, as in many real-life problems the model will be NP-hard and very time consuming. In the proposed procedure, the master problem will be developed using the surrogate constraints. We show that the main constraints of the master problem can be replaced by the strongest surrogate constraint. The generated problem with the strongest surrogate constraint is a valid relaxation of the main problem. Furthermore, a near-optimal initial solution is generated for a reduction in the number of iterations. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Facilities planning and design Supply chain network design Combinatorial optimization mixed integer linear programming Benders' decomposition Surrogate constraints

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Nonlinear Optimization of Low-Thrust Trajectory for Satellite Formation: Legendre Pseudospectral Approach

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2009年第4期32卷 1371-1381页

作者： Wu, Baolin Wang, Danwei Poh, Eng Kee Xu, Guangyan Nanyang Technol Univ Sch Elect & Elect Engn Aerosp Elect Lab Singapore 639798 Singapore Def Sci Org Natl Labs Singapore 118230 Singapore

In this paper, we focus on the design of a fuel-optimal maneuver strategy to reconfigure satellite formation using a low-thrust propulsion system. We cast it as an optimization problem with a desired final satellite formation configuration subject to collision avoidance constraints on the paths of the chief and all deputy satellites. The satellite terminal orbit states corresponding to this desired formation configuration are ensured by imposing an energy-matching condition and final geometry configuration constraints in the problem formulation. In addition, we adopt our recently developed relative satellite kinematics model to accurately describe relative satellite orbit geometry in the presence of J(2) effects. The resulting nonlinear optimal control problem is converted into a nonlinear programming problem by the application of the Legendre pseudospectral method and is then solved by using a sparse nonlinear optimization software named TOMLAB/SNOPT. Simulation results demonstrate the efficiency of our proposed method in designing fuel-optimal maneuvers for a wide class of satellite formation problems.

关键词： Satellite Formation Thrust Trajectory Optimization mixed integer linear programming Fuel Consumption Legendre Pseudospectral Method Orbital Transfer Closed Loop Control Sequential Quadratic programming Nonlinear Dynamics

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Path-Planning with Avoidance Using Nonlinear Branch-and-Bound Optimization

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2009年第2期32卷 384-394页

作者： Eele, Alison Richards, Arthur Univ Bristol Dept Aerosp Engn Bristol BS8 1TR Avon England

This paper describes a novel method for finding optimal trajectories for a vehicle constrained to avoid fixed obstacles. The key property of the method is that it provides globally optimal solutions while retaining the full nonlinear dynamics model. Applications for the method include guidance of unmanned aerial vehicles, air traffic control,and robot path planning. The core concept is the direct application of branch-and-bound optimization to find guaranteed, globally optimal solutions to nonconvex problems. The method tailors the branch-and-bound approach specifically for avoidance problems by exploiting two new ideas: first, using a geometric branching strategy based on the decision between passing an obstacle clockwise or counterclockwise;and second, solving the resulting subproblems by constructing simple solutions on each chosen "side" and using them to initialize an interior-point optimization. The algorithm is refined by comparing nine geometric branching strategies. The solution time of the method depends on the choice of branching strategy, which determines how the solution tree is explored. A good strategy is one requiring fewer tree branches to be enumerated before the global optimal is found. The best of these branching strategies has been compared with an existing mixed-integer linear programming approach and demonstrated a significant improvement on mixed-integer linear programming solve times.

关键词： Path Planning mixed integer linear programming Nonlinear Dynamics Uninhabited Aerial Vehicle Obstacle Avoidance Branch and Bound Algorithm Air Traffic Management Air Traffic Control Optimization Algorithm Vehicle Trajectories

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Scheduling of a continuous plant with recycling of byproducts: A case study from a tissue paper mill

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COMPUTERS & CHEMICAL ENGINEERING 2009年第1期33卷 347-358页

作者： Castro, Pedro M. Westerlund, Joakim Forssell, Sebastian INETI Dept Modelacao & Simulacao Proc P-1649038 Lisbon Portugal Abo Akad Univ Proc Design Lab FIN-20500 Turku Finland Borealis Polymers Oy BU Phenol FIN-06101 Porvoo Finland

This paper considers an industrial scheduling problem. It involves profit maximization and the determination of the optimal cycle time, while meeting the minimum demands for the several products. Resource-Task Network-based formulations are employed and a detailed comparison between continuous- and discrete-time models is provided. Both have the improved capability of handling tasks with flexible proportions of input materials in order to consider the incorporation of different flowrates of byproducts that are recycled back to the first production stage. The continuous-time formulation is shown to be more efficient and the resulting mixed integer nonlinear program (MINLP) can be solved to optimality within reasonable computational time. A new recycling policy is proposed that achieves the double goal of making the process more profitable due to important savings oil the more expensive raw-materials and also more environmentally friendly, due to the reduction of waste disposal requirements. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Production planning mixed integer linear programming Uniform time grid Event points Continuous plant Intermediate storage

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Design of Extrapolated Impulse Response FIR Filters With Residual Compensation in Subexpression Space

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2009年第12期56卷 2621-2633页

作者： Yu, Ya Jun Shi, Dong Lim, Yong Ching Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

In this paper, an extrapolated impulse response filter with residual compensation is proposed for the design of discrete coefficient finite-impulse response (FIR) filters using subexpression sharing. The proposed technique utilizes the quasi-periodic nature of the filter impulse response to approximate the filter coefficients. The reduced degree of freedom of filter coefficients due to the quasi-periodic approximation is perfectly restored by introducing a residual compensation technique. The resulting subexpression sharing synthesis of discrete coefficient FIR filters has lower complexities than that of the conventional synthesis techniques in terms of number of adders. To further reduce the synthesis complexity, filter coefficients and residuals may be optimized in subexpression spaces. mixed integer linear programming is formulated for the optimization. Numerical examples show that the number of adders required by synthesizing the filters in the proposed structure is significantly reduced compared to that of the conventional synthesis schemes synthesized in direct or transposed direct form.

关键词： Common subexpression sharing extrapolated impulse response finite-impulse response (FIR) filters mixed integer linear programming residual compensation subexpression space

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Inexact Minimax Regret integer programming for Long-Term Planning of Municipal Solid Waste Management - Part A: Methodology Development

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ENVIRONMENTAL ENGINEERING SCIENCE 2009年第1期26卷 209-218页

作者： Li, Yongping Huang, Gordon H. Peking Univ Coll Urban & Environm Sci Beijing 100871 Peoples R China Univ Regina Fac Engn Environm Syst Engn Program Regina SK S4S 0A2 Canada Beijing Normal Univ Chinese Res Acad Environm Sci Beijing *** Peoples R China

In real-world municipal solid waste (MSW) management systems, identification of proper policies under uncertainty for accomplishing desired waste-disposal targets is critical. An inexact minimax regret integer programming (IMMRIP) method for the long-term planning of MSW management is developed. It incorporates the technique of minimax regret analysis (MMR) into an interval-parameter mixed-integer linear programming (IMILP) framework. The IMMRIP method can handle dual uncertainties presented as both random variables and interval values;it only needs a list of scenarios without any assumption on their probability distributions. It can facilitate dynamic analysis for decisions of system-capacity expansion and/or development within a multi-facility and multi-period context. Moreover, it can also be used for analyzing multiple scenarios associated with different system costs and risk levels. An interval-element cost matrix can be transformed into an interval-element regret matrix based on an interactive algorithm. Solutions based on an inexact minimax regret criterion can identify desired alternatives for MSW management and planning under a variety of uncertainties. In a companion paper, the developed method will be applied to a real case study in the City of Regina, Canada.

关键词： decision making environment inexact optimization minimax regret mixed integer linear programming solid waste uncertainty

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