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On regular and parametric data envelopment analysis

MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2004年第1期60卷 15-28页

作者： Neralic, L Stein, O Univ Zagreb Fac Econ Zagreb 10000 Croatia Univ Aachen Dept Math C D-52056 Aachen Germany

We give a generic regularity condition under which each weakly efficient decision making unit in the CCR model of data envelopment analysis is also CCR-efficient. Then we interpret the problem of finding maximal parameters which preserve efficiency of CCR-efficient DMUs under directional perturbations as a general semi-infinite optimization problem and use a recently suggested numerical method for this problem class to calculate maximal directionally efficient DMUs. As a practical example we investigate the efficiency of Croatian banks under additive perturbations.

关键词： semi-infinite programming bilevel optimization constraint qualification multi-objective programming production planning

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A general inverse DEA model for non-radial DEA

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COMPUTERS & INDUSTRIAL ENGINEERING 2020年 142卷 106368-106368页

作者： Zhang, GuoJun Cui, JinChuan Chinese Acad Sci Acad Math & Syst Sci Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing 100049 Peoples R China

Traditional inverse DEA models could be called inverse radial DEA because they are based on radial efficiency measures. Due to the neglect of slacks in evaluating the efficiency score, inverse radial DEA may mislead decision-making in some cases where slacks play important roles. In this paper, we proposed an integrated framework of inverse DEA called inverse non-radial DEA since it is based on non-radial DEA by multi-objective programming, which covers existing inverse DEA models. To further illustrate the inverse non-radial DEA, we construct the concrete mathematical formula of inverse SBM and some properties. In contrast to the radial approach, inverse non-radial DEA can overcome the error caused by ignoring slacks and provides more valuable information about inputs and outputs for decision-making by considering slacks. Although inverse non-radial DEA models are usually non-linear, we can convert it into a one-dimensional search problem about efficiency score, which can be solved by many existing efficient algorithms. A practical example is provided to demonstrate the advantages of inverse non-radial DEA models over inverse radial DEA models.

关键词： Inverse DEA Non-radial DEA SBM multi-objective programming

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multi-objective storage location allocation optimization and simulation analysis of automated warehouse based on multi-population genetic algorithm

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CONCURRENT ENGINEERING-RESEARCH AND APPLICATIONS 2018年第4期26卷 367-377页

作者： Jiao, Yu-ling Xing, Xiao-cui Zhang, Peng Xu, Liang-cheng Liu, Xin-Ran Jilin Univ Coll Transportat Changchun 130022 Jilin Peoples R China Jilin Univ Architecture Coll Grad Changchun Jilin Peoples R China

Aiming at the requirement of working efficiency and security of automated warehouse and taking the operation time of outbound-inbound, the equivalent center of gravity of overall shelf and the degree of relative accumulation of related products as the multi-objective functions, the mathematical model is constructed for multi-objective storage location allocation optimization. According to the simple weighted genetic algorithm, it is easily prone to the problem of immature convergence when solving multi-objective programming problems. So, the multi-population genetic algorithm is proposed to solve the mathematical model of storage location allocation optimization. Combining with the experiment data of toy car assembly and automated warehouse, the results of the automated warehouse storage location allocation are obtained. FlexSim dynamic simulation model is established based on the storage location allocation solution, the physical parameters of automated warehouse and the experimental requirements plan of vehicle model assembly. The operation effect of the model and the utilization rate of the equipment are analyzed. The result of multi-population genetic algorithm is more reasonable and effective. It is proved that the result of multi-population genetic algorithm is superior to the result of simple weighted genetic algorithm, which provides an effective method for storage location allocation optimization and outbound-inbound dynamic simulation.

关键词： storage location allocation multi-population genetic algorithm multi-objective programming automated warehouse FlexSim simulation

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Fuzzy multi-period portfolio selection model with discounted transaction costs

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SOFT COMPUTING 2018年第1期22卷 177-193页

作者： Liu, Yong-Jun Zhang, Wei-Guo Zhao, Xue-Jin South China Univ Technol Sch Business Adm Guangzhou 510641 Guangdong Peoples R China

In this paper, we discuss a multi-period portfolio selection with discounted transaction costs in a fuzzy uncertain investment environment, which has not been given much attention before. We assume that an investor's motivation is to find the portfolio with maximizing terminal wealth and the cumulative skewness on portfolios, and minimizing the cumulative risk on portfolios. We consider the major criteria including wealth, risk, skewness, transaction costs, proportion entropy, transaction lots, the maximum holding number of assets in the portfolio and budge constraint. We propose a possbilistic mean-semivariance-skewness model with discounted transaction costs for multi-period fuzzy portfolio selection. To solve the multi-objective portfolio selection model, we first introduce a weighted max-min fuzzy goal programming approach to take investor's different investment preferences into account and transform it into a single-objective programming problem and then design a dynamic differential evolution algorithm for solution. Finally, we provide an empirical study with the sample data from Chinese stock market to analyze the application of the model and the performance of the solution algorithm.

关键词： Fuzzy portfolio selection Mean-semivariance-skewness model multi-objective programming Differential evolution algorithm

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An inverse DEA model for inputs/outputs estimate

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2000年第1期121卷 151-163页

作者： Wei, QL Zhang, JZ Zhang, XS City Univ Hong Kong Dept Math Tat Chee Ave Kowloon Peoples R China Renmin Univ China Inst OR & Math Econ Beijing Peoples R China Acad Sinica Inst Appl Math Beijing 100080 Peoples R China

In this paper we discuss such problems: if among a group of decision making units, we increase certain inputs to a particular unit and assume that the DMU maintains its current efficiency level with respect to other units, how much more outputs could the unit produce? or, if the outputs need to be increased to a certain level and the efficiency of the unit remains unchanged, how much more inputs should be provided to the unit? We treat them as inverse Data Envelopment Analysis (DEA) problems and propose a method to solve such problems. The problem is transformed into a multi-objective programming problem to solve, though in some special cases it can be answered by solving just one single-object LP problem. We use two examples to illustrate our computation method. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： data envelopment analysis inverse problem multi-objective programming Pareto solution

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Designing a green meat supply chain network: A multi-objective approach

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2020年 219卷 312-327页

作者： Mohebalizadehgashti, Fatemeh Zolfagharinia, Hossein Amin, Saman Hassanzadeh Ryerson Univ Dept Mech & Ind Engn Toronto ON Canada Ryerson Univ Ted Rogers Sch Management Toronto ON Canada

Traditional logistics management has not focused on environmental concerns when designing and optimizing food supply chain networks. However, the protection of the environment is one of the main factors that should be considered based on environmental protection regulations of countries. In this paper, environmental concerns are considered in formulating a mathematical model to design and configure a multi-period, multi-product, multi-echelon green meat supply chain network. We develop a multi-objective mixed-integer linear programming formulation to optimize three objectives simultaneously: minimization of the total cost, minimization of the total CO2 emissions released from transportation, and maximization of the total capacity utilization of facilities. To demonstrate the efficiency of the proposed optimization model, we design a green meat supply chain network for Southern Ontario, Canada. A solution approach based on augmented epsilon-constraint method is employed to solve the proposed model. As a result, a set of Pareto-optimal solutions is obtained. The set of Pareto-optimal solutions gives decision-makers the opportunity to make a trade-off between economic, environmental, and capacity utilization objectives. Our example shows that it is possible to keep emissions reasonably low without incurring high total costs. Finally, the impacts of uncertainty on the proposed model are investigated using several decision trees. Optimization of a food supply chain, particularly a meat supply chain, based on multiple objectives under uncertainty using decision trees is a new approach in the literature.

关键词： Meat supply chain Decision tree multi-objective programming Mixed-integer linear programming Augmented epsilon-constraint

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Constrained non-linear multi-objective optimisation of preventive maintenance scheduling for offshore wind farms

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2018年 104卷 347-369页

作者： Zhong, Shuya Pantelous, Athanasios A. Beer, Michael Zhou, Jian Natl Univ Singapore Logist Inst Asia Pacific Singapore Singapore Monash Univ Dept Econometr & Business Stat Clayton Vic Australia Univ Liverpool Inst Risk & Uncertainty Liverpool Merseyside England Univ Liverpool Dept Math Sci Liverpool Merseyside England Leibniz Univ Hannover Inst Risk & Reliabil Hannover Germany Tongji Univ Sch Civil Engn Shanghai Peoples R China Tongji Univ Shanghai Inst Disaster Prevent & Relief Shanghai Peoples R China Shanghai Univ Dept Management Sci & Engn Shanghai Peoples R China

Offshore wind farm is an emerging source of renewable energy, which has been shown to have tremendous potential in recent years. In this blooming area, a key challenge is that the preventive maintenance of offshore turbines should be scheduled reasonably to satisfy the power supply without failure. In this direction, two significant goals should be considered simultaneously as a trade-off. One is to maximise the system reliability and the other is to minimise the maintenance related cost. Thus, a non-linear multi-objective programming model is proposed including two newly defined objectives with thirteen families of constraints suitable for the preventive maintenance of offshore wind farms. In order to solve our model effectively, the nondominated sorting genetic algorithm II, especially for the multi-objective optimisation is utilised and Pareto-optimal solutions of schedules can be obtained to offer adequate support to decision-makers. Finally, an example is given to illustrate the performances of the devised model and algorithm, and explore the relationships of the two targets with the help of a contrast model. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Reliability Maintenance Scheduling Cost parameters Offshore wind farms multi-objective programming

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Integration of supplier selection, procurement lot sizing and carrier selection under dynamic demand conditions

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2007年第2期107卷 502-510页

作者： Liao, Zhiying Rittscher, Jens Univ Dortmund Chair Factory Org D-44221 Dortmund Germany Soptim AG D-45133 Essen Germany

This paper develops a multi-objective programming model, integrating supplier selection, procurement lot sizing and carrier selection decisions for a single purchasing item over multiple planning periods while demand quantities are known but inconstant, i.e. dynamic demand conditions. A genetic algorithm with problem specific operators is developed and a numerical example is presented. (C) 2006 Elsevier B.V. All rights reserved.

关键词： supplier selection procurement lot sizing carrier selection multi-objective programming genetic algorithm

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Non-dominated sorting genetic algorithm-II for possibilistic mean-semiabsolute deviation-Yager entropy portfolio model with complex real-world constraints

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MATHEMATICS AND COMPUTERS IN SIMULATION 2022年 202卷 59-78页

作者： Deng, Xue Chen, Jiaxing Wang, Xu Geng, Fengting South China Univ Technol Sch Math Guangzhou Peoples R China South China Univ Technol Sch Math Guangzhou 510610 Peoples R China

The purpose of our paper is to address the multi-objective portfolio model with complex real-world constraints under the assumption that the returns of risky assets are fuzzy variables. Firstly, a new possibilistic mean-semiabsolute deviationYager entropy portfolio model is proposed with transaction costs, cardinality and quantity constraints Secondly, to solve the proposed model efficiently, a non-dominated sorting genetic algorithm-II (NSGA-II) is presented, which can not only reduce the computational complexity but also enhance the solution accuracy. Then, a numerical example is provided to verify the feasibility and effectiveness of our proposed model and algorithm. Based on these results, we analyze the efficient frontiers with different quantity constraints and transaction costs, and illustrate the portfolio distributions with different transaction costs by using the boxplot figures. Finally, these solutions solved by NSGA-II and four traditional computation methods are compared. Our proposed algorithm outperforms the minimax method (Polakabb, 2010), two-stage method (Masson, 2016), extended two-stage method (Li, 2012) and compromise approach-based genetic algorithm (Li, 2013) in the efficient frontier, accuracy and number of solutions. (c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Portfolio Entropy multi-objective programming Non-dominated sorting genetic algorithm-II Cardinality constraint

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Modelling the effects of trade-offs between long and short-term objectives in fisheries management

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JOURNAL OF ENVIRONMENTAL MANAGEMENT 2002年第1期65卷 49-62页

作者： Mardle, S Pascoe, S Univ Portsmouth CEMARE Portsmouth PO4 8JF Hants England

Fisheries management is typically a complex problem, from both an environmental and political perspective. The main source of conflict occurs between the need for stock conservation and the need for fishing community well-being, which is typically measured by employment and income levels. For most fisheries, overexploitation of the stock requires a reduction in the level of fishing activity. While this may lead to long-term benefits (both conservation and economic), it also leads to a short-term reduction in employment and regional incomes. In regions which are heavily dependent on fisheries, short-term consequences of conservation efforts may be considerable. The relatively high degree of scientific uncertainty with respect to the status of the stocks and the relatively short lengths of political terms of office, generally give rise to the short-run view taking the highest priority when defining policy objectives. In this paper, a multi-objective model of the North Sea is developed that incorporates both long-term and short-term objectives. Optimal fleet sizes are estimated taking into consideration different preferences between the defined short-term and long-term objectives. The subsequent results from the model give the short-term and long-term equilibrium status of the fishery incorporating the effects of the short-term objectives. As would be expected, an optimal fleet from a short-term perspective is considerably larger than an optimal fleet from a long-run perspective. Conversely, stock sizes and sustainable yields are considerably lower in the long-term if a short-term perspective is used in setting management policies. The model results highlight what is essentially a principal-agent problem, with the objectives of the policy makers not necessarily reflecting the objectives of society as a whole. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： fisheries multi-objective programming short-run long-run North Sea

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