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A Method for the Solution of Educational Investment

Journal of Applied Mathematics and Physics 2016年第6期4卷 1131-1142页

作者： Jun’e Liu Le Yu Xiaolin Liu The School of Information Beijing Wuzi University Beijing China Graduate Department Beijing Wuzi University Beijing China

In order to improve the performance of higher education in the United States, the Goodgrant Foundation intends to donate a total of $100,000,000 (US 100 million) to an appropriate group of schools per year, for five years, starting in July 2016. For this, our team puts forward upon an optimal investment strategy, which includes the schools to invest, the investment amount of each school, and the return due to investment, to solve this problem. Our main idea is as follows. First of all, we choose suitable investment school universities in the United States. Secondly, we use Analytic Hierarchy Process to get the rate of return on investment and venture capital. Thirdly, we establish a venture capital return model. Finally, solving the mathematical model ensures the investment amount of each school and the return due to investment. To implement this strategy, first of all, we obtain the candidate school based on students score card. Then, according to the factor analysis, we analyze the factors which mainly affect the choice of school. Secondly, we employ Analytic Hierarchy Process to get the rate of return on investment and capital risk. In the end, we establish a risk return model to get investment amount for each school, amount of risk and return. In order to ensure the minimum risk and the maximum return, we set up a multi objective programming model and solve it by using the constraint method. We get the result that includes the maximum net profit of the investment and risk loss rate. According to statistical analysis, we can get the overall return of net income within five years. Finally, we choose 320 candidate schools and get the investment amount of each school according to the principle of as many schools as possible. We have proved that the foundation will receive a return of more than 295.363 million in the next 5 years. After-verification, our strategy can be directly applied to the investment field and get good results.

关键词： AHP multi-objective programming Risk Investment Return

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multiobjective programming under (phi,d)-V-type I univexity

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OPSEARCH 2015年第1期52卷 168-185页

作者： Kharbanda, Pallavi Agarwal, Divya Sinha, Deepa Banasthali Univ Ctr Math Sci Vanasthali Rajasthan India ITM Univ Dept Appl Sci & Humanities Gurgaon India South Asian Univ Dept Math New Delhi India

In this paper, we have introduced a new class of (phi,d)-V-type I univex, quasi (phi,d)-V- type I univex, pseudo (phi,d)-V-type I univex, quasi-pseudo (phi,d)-V-type I univex and pseudo-quasi (phi,d)-V-type I univex functions in case of nonlinear multiobjective programming problem where functions involved are nondifferentiable and illustrated through non- trivial examples that this class extends some known classes in literature. Various Karush-Kuhn-Tucker type sufficient optimality conditions are obtained under this newly introduced class of functions. Also, for mixed type multiobjective dual program, we have established weak, strong, converse and strict converse duality results in order to relate the efficient and weak efficient solutions of primal and dual problem.

关键词： multi-objective programming d-V-type I functions Directional derivative Lipschitz function

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The sufficiency of Solution for multi-objective Semi-infinite programming 10

The sufficiency of Solution for Multi-objective Semi-infinit...

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10th International Conference on Computational Intelligence and Security CIS 2014

作者： Li, Xiangxou Zhang, Qingxiang Yanan Univ Coll Math & Comp Sci Yanan 716000 Shaanxi Peoples R China

ISBN: (纸本)9781479974344

In this paper, new classes of generalized invex functions called (h, phi) - rho invex functions, (h, phi) - rho quasi invex functions and (h, phi) - rho pseudo invex functions are introduced, multi-objective semi-infinite programming involving new generalized functions is researched, the sufficient optimality conditions are obtained under weaker convexity.

关键词： multi-objective programming (h, phi) - rho invex functions efficient solution optimality

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multi-objective decision-making framework for an electricity retailer in energy markets using lexicographic optimization and augmented epsilon-constraint

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INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2015年第12期25卷 3660-3680页

作者： Nezhad, Ali Esmaeel Ahmadi, Abdollah Javadi, Mohammad Sadegh Janghorbani, Mohammadreza Islamic Azad Univ Marvdasht Branch Dept Elect Engn Marvdasht Iran Univ New S Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia Islamic Azad Univ Shiraz Branch Dept Elect Engn Shiraz Iran Islamic Azad Univ Cent Tehran Branch Young Researchers & Elite Club Tehran Iran

The objective of the retailer in medium-term planning is managing the portfolio of contracts from different sources as well as determining the optimal selling price offered to its customers. When supplying the electricity sold to the costumers, two main challenges are faced by retailers. The first problem occurs during the electricity procurement procedure. In this stage, the retailer must deal with the uncertainty due to the pool price that propels the retailers to move towards agreeing to forward contracts signed at higher average prices. Besides, when the retailer decides on selling the electricity, another problem is to face the uncertainty caused by the demand while taking into consideration the possibility of reducing its clients in the case of high selling price. In this regard, this paper proposes a stochastic multi-objective framework for the retailer with profit maximization and risk minimization as two objective functions. The risk, due to the market price uncertainty, is modeled, employing the expected downside risk. The problem is formulated as mixed-integer programming while the stochastic optimization problem is characterized using the roulette wheel mechanism and lattice Monte Carlo simulation. Furthermore, lexicographic optimization and augmented epsilon-constraint method are used to solve the proposed multi-objective problem, and the best compromise solution is determined employing a fuzzy satisfying method. The presented model has been implemented using a realistic case study to verify the effectiveness of the method used in this paper. Copyright (C) 2015 John Wiley & Sons, Ltd.

关键词： stochastic optimization downside risk retailer multi-objective programming

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Robustness analysis methodology for multi-objective combinatorial optimization problems and application to project selection

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2015年 52卷 142-155页

作者： Mavrotas, George Figueira, Jose Rui Siskos, Eleftherios Natl Tech Univ Athens Sch Chem Engn Lab Ind & Energy Econ Athens 15780 Greece Univ Lisbon Inst Super Tecn CEG IST P-1049001 Lisbon Portugal Natl Tech Univ Athens Sch Elect & Comp Engn Decis Support Syst Lab Athens 15780 Greece

multi-objective combinatorial optimization (MOCO) problems, apart from being notoriously difficult and complex to solve in reasonable computational time, they also exhibit high levels of instability in their results in case of uncertainty, which often deviate far from optimality. In this work we propose an integrated methodology to measure and analyze the robustness of MOCO problems, and more specifically multi-objective integer programming ones, given the imperfect knowledge of their parameters. We propose measures to assess the robustness of each specific Pareto optimal solution (POS), as well as the robustness of the entire Pareto set (PS) as a whole. The approach builds upon a synergy of Monte Carlo simulation and multi-objective optimization, using the augmented epsilon-constraint method to generate the exact PS for the MOCO problems under examination. The usability of the proposed framework is justified through the identification of the most robust areas of the Pareto front, and the characterization of every POS with a robustness index. This index indicates a degree of certainty that a specific POS sustains its efficiency. The proposed methodology communicates in an illustrative way the robustness information to managers/decision makers and provides them with an additional supplement/tool to guide and support their final decision. Numerical examples focusing on a multi-objective knapsack problem and an application to academic capital budgeting problem for project selection, are provided to verify the efficacy and added value of the methodology. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Robustness analysis multi-criteria Combinatorial optimization multi-objective programming Monte Carlo simulation Visualization

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Improving Fairness in Staff Assignment: An Approach for Lexicographic Goal programming

Improving Fairness in Staff Assignment: An Approach for Lexi...

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IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)

作者： Rihm, Tom Baumann, Philipp Univ Bern Dept Business Adm Bern Switzerland Univ Calif Berkeley Dept Ind Engn & Operat Res Berkeley CA USA

ISBN: (纸本)9781467380669

In many staff-assignment problems, a large variety of requirements has to be considered when assigning employees to work shifts. As the importance of the requirements is often described in a hierarchical manner, lexicographic goal programming has been used to minimize the number of requirement violations. The resulting schedules are in general of high quality with respect to requirement violations but may lack acceptance by employees because of an unfair distribution of the violations. We introduce a novel approach for lexicographic goal programming that allows to improve an existing schedule in terms of fairness without deteriorating its quality with regard to requirement violations. The effectiveness of the proposed approach is demonstrated for a test set derived from real-world data.

关键词： Staff Assignment Fairness multi-objective programming Mixed-Integer Linear programming

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Optimal water allocation through a multi-objective compromise between environmental, social, and economic preferences

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ENVIRONMENTAL MODELLING & SOFTWARE 2015年 64卷 18-30页

作者： Roozbahani, Reza Schreider, Sergei Abbasi, Babak RMIT Univ Sch Math & Geospatial Sci Melbourne Vic 3001 Australia

Raising water demands and insufficient freshwater resources are the main reasons of water conflicts in transboundary watersheds. Sustainable water allocation can be a resolution for water disputes as it addresses simultaneously economic, social and environmental benefits. In this paper, a multi-objective model is introduced, which leads to sustainable water allocation of transboundary watersheds taking into account all these three aspects. Five water allocation objectives are proposed for this model in which three of them address the social factors and others represent the economic and environmental preferences. The Compromise programming technique is employed to solve the applied model to the Sefidrud Basin, Iran and several water allocation schemes are provided based on various weights combinations. The results of the model elucidate that the proposed model can allocate 83 percent of the Basin's water resources, to its stakeholders in a sustainable way while the environmental demand is satisfied. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Water allocation multi-objective programming Compromise programming Water allocation objectives

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An integrated technology pushing and requirement pulling model for weapon system portfolio selection in defence acquisition and manufacturing

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART B-JOURNAL OF ENGINEERING MANUFACTURE 2015年第6期229卷 1046-1067页

作者： Dou, Yajie Zhang, Pengle Ge, Bingfeng Jiang, Jiang Chen, Yingwu Natl Univ Def Technol Coll Informat Syst & Management Dept Management Changsha 410073 Hunan Peoples R China

An integrated technology pushing and requirement pulling model is presented to address the problem of selecting a suitable portfolio from several candidate multi-function weapon systems in the defence acquisition and manufacturing process. The optimal weapon system portfolios both satisfy the technical effects and compound capability requirements with relative acquisition and manufacturing constraints. In the first stage, multiple criteria analysis is employed to build a portfolio value hierarchal structure from two main perspectives: a five-level set of technology pushing measures and a two-level set of requirement pulling measures. The developmental maturity level of a technology, its functionality, systems, capability, and portfolio are all captured by technology pushing measures, based on an additive multiple criteria model. The requirement satisfaction level of a system or portfolio is obtained by requirement pulling measures based on linear programming optimization and the first-ignorance model, which is founded on expert opinion, using pairwise comparisons. In the second stage, by means of manufacturing cost consumption and capability requirement constraint assumptions, the dominance structure of the portfolios is designed and all the technology and requirement portfolios are generated as a set of Pareto-optimal solutions, through multi-objective integer programming. An illustrative case study is presented to validate the efficiency of the proposed model, and the computational results are further analysed and discussed.

关键词： Weapon system portfolio selection technology pushing and requirement pulling model portfolio value analysis multi-objective programming

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An Optimization-Simulation Approach for Groundwater Abstraction under Recharge Uncertainty

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WATER RESOURCES MANAGEMENT 2015年第10期29卷 3681-3695页

作者： Zekri, Slim Triki, Chefi Al-Maktoumi, Ali Bazargan-Lari, Mohammad Reza Sultan Qaboos Univ Dept Nat Resource Econ Al Khoud 123 Oman Sultan Qaboos Univ Dept Mech & Ind Engn Al Khoud 123 Oman Univ Salento Dept Engn Innovat I-73100 Lecce Italy Sultan Qaboos Univ Dept Soil & Water & Agr Engn Al Khoud 123 Oman Islamic Azad Univ Dept Civil Engn Tehran Iran

Droughts and climate variability cause uncertainties on water supply especially in arid regions and coastal aquifers' over-exploitation causes seawater intrusion. Since the rate and extent of aquifer recharge is often very uncertain, determining the optimal groundwater abstraction is a challenging task. In this paper a framework is proposed for estimating the optimal abstraction of groundwater for urban supply under uncertainty and under complex conditions of water table fluctuations and seawater intrusion. It is based on a combination of several models: (i) a Monte-Carlo Simulation (MCS) to incorporate the uncertainties in groundwater recharge, (ii) a numerical groundwater flow model, MODFLOW to simulate the effects of abstractions on the water table fluctuations and seawater intrusion and (iii) a multi-objective optimization model to generate the set of Pareto optimal solutions for each recharging scenario. Maximizing the benefit to the water utility, minimizing the average groundwater table level fluctuations and minimizing the seawater intrusion are the objectives of the model. A fast multi-objective evolutionary algorithm is used to obtain the Pareto efficient solutions for each recharging scenario. Compromise programming (CP) is then used to select the closest solutions to the ideal. Finally, the amount of optimal reliable groundwater abstraction is estimated using a cumulative distribution function. The proposed methodology is applied to a coastal aquifer in the western part of Muscat metropolitan area, Oman. The results have shown that annual groundwater abstraction volume may range from 12.7 to 18.8 Mm(3) compared to 6.8 Mm(3) currently pumped. This would result in an economic benefit of $10.5 million to $15.4 million/year. On the other hand the aquifer's maximum annual mean drawdown would range from 0.7 to 0.9 m.

关键词： Managed aquifer recharge Uncertainty Seawater intrusion Groundwater simulation Dynamic optimization multi-objective programming

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Establishment of Supply And Demand Match Indicators for Taxi Resource

Establishment of Supply And Demand Match Indicators for Taxi...

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2016 2nd Workshop on Advanced Research and Technology in Industry Applications(WARTIA 2016)

作者： Yilin Song School of Energy Power and Mechanical EngineeringNorth China Electric Power University

With the coming of "Internet +" era,drops a taxi,Uber and other companies rely on mobile Internet software to establish a taxi service platform,and achieve information exchange between the passengers and the *** at this phenomenon,based on in the history data in a certain period at designated observation point of Beijing to analyze the taxi resources match and the difficulty of taking a *** the sky drops and quick smart travel platform,this paper extracts 11 sample locations in Beijing such as Jianguomen,Fuxingmen of taxi distribution and demand in 22 sample time from September 6th to May 7th,2015,taking the number of people using the drops one million and drops penetration in the taxi industry,to estimate Beijing's taxi operations(supply and demand).In order to establish a reasonable target,we should analyze the match level of supply and demand of different space-time taxi *** establish the related matching degree of the taxi demand supply indicators(defined as the difference rate),this paper uses control variables to analyze taxi resource matching degree of sample locations and sample time in *** cluster analysis method to get the conclusion of 11 observation points:The matching degree in Fuxingmen,Xizhimen and Zhongguancun is low,and that of Jianguomen,Dongzhimen and Xisanqi is *** matching degree of weekend daytime and weekday evening peak(7:00-10:00,17:00-20:00) is lower compared with other periods.

关键词： Internet + cluster analysis multi-objective programming

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