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A multi-objective Mixed Integer Linear programming Model for Energy Resource Allocation Problem: The Case of Turkey

GAZI UNIVERSITY JOURNAL OF SCIENCE 2014年第4期27卷 1157-1168页

作者： Ozcan, Evren Can Erol, Serpil Elect Generat Co TR-06520 Ankara Turkey Gazi Univ Ind Engn Dept TR-06570 Ankara Turkey

Energy is one of the most basic elements for raising social welfare, playing a fascinating role in economic and social progress of the countries and thus increasing the competitiveness of the countries in globalized world. Therefore, carrying out the sustainable energy policies which are based on social, economic and environmental factors and in this context, finding the local, sustainable, environmentally-friendly and economic resources and the optimal distribution of them have become a necessity in order to achieve the sustainable development thrusts. In this study, a multi-objective mixed integer linear programming (MOMILP) model which reflects the Turkey's realities and necessities and optimizes simultaneously the objectives of total cost minimization, CO2 emission minimization, energy import minimization, fossil resource usage minimization, employment maximization and social acceptance maximization is proposed. This model is solved by Minimum Deviation Method (MDM) considering the most basic energy resources (solar, wind, coal, natural gas, hydroelectric, nuclear etc.) used for the electricity generation all over the world and a 11-years electricity generation plan is obtained on the basis of resources for Turkey.

关键词： Energy resource allocation energy planning multi-objective programming minimum deviation method

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A fuzzy dependent-chance interval multi-objective stochastic expected value programming approach for irrigation water resources management under uncertainty

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DESALINATION AND WATER TREATMENT 2021年 212卷 17-30页

作者： Wang, Youzhi Li, Zhong Liu, Liu Guo, Ping China Agr Univ Ctr Agr Water Res China Beijing 100083 Peoples R China McMaster Univ Dept Civil Engn Hamilton ON L8S 4L8 Canada Minist Agr & Rural Affairs Wuwei Expt Stn Efficient Water Use Agr Wuwei 733000 Peoples R China

In this study, a fuzzy dependent-chance interval multi-objective stochastic expected value programming model is developed for irrigation water resources management under uncertainties. It incorporates fuzzy dependent-chance programming, stochastic expected value programming, interval programming into multi-objective programming. Compared with conventional programming methods, it can quantify the relationship between the expected values of stochastic variables and the fuzzy goals of expected values set by decision-makers through the satisfactory degrees, and trade-off the relationship amid multiple satisfactory degrees selected as objective functions. Besides, it can cope with uncertainties expressed as interval numbers, fuzzy numbers, and stochastic variables. Moreover, the fairness of water allocation constraints formulated by the GINI coefficient can achieve the interactions between fair water allocation and satisfactory degrees. The model is applied to a real case study of irrigation water resources management of different water types (i.e., surface water and groundwater) under different water flow levels (high, medium, and low flow levels) in the midstream region of the Heihe River basin, northwest China. The results reveal that: (1) maximum water demands of wheat and economic crop are satisfied while that of corn is not met under three flow levels;(2) the expected economic benefit and water shortages of crops have positive relationships with water allocation while the expected canal water loss has a negative relationship with water allocation;(3) the bigger expected economic benefit results in the higher satisfactory degree of the expected economic benefit while the lower expected water shortage and canal water loss lead to higher satisfactory degrees of expected water shortage and canal water loss. It shows that the developed model can overcome the disadvantages of the single-objective programming of putting attention to the satisfactory degree of a kind of ex

关键词： Irrigation water allocation Interval programming Stochastic expected value programming Fuzzy dependent-chance programming multi-objective programming Uncertainty

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A New Mean-Variance-Skewness Model for Portfolio Optimization Using Three-Part Zigzag Uncertain Variable

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PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES 2025年第1期95卷 55-70页

作者： Chhatri, Sanjoy Bhattacharya, Debasish Natl Inst Technol Agartala Dept Math Agartala 799046 Tripura India

A multi-objective portfolio selection problem involving newly introduced stocks has been studied here, and an innovative solution procedure for the same with a numerical illustration is also provided. The returns of these stocks are represented by a new uncertainty distribution, called the three-part zigzag uncertainty distribution, introduced in this paper. This newly defined uncertainty distribution function is regular and closer to an S-shaped curve than linear and zigzag uncertainty distribution functions. The properties of the three-part zigzag uncertainty distribution are studied, and the expression for the general order central moment of the distribution has been obtained. Using the expected value and the second, third order central moments, two maximizing objectives and one minimizing objective for the said optimization purpose are formed. Finally, using the "fmincon" function in Matlab 2018a, the constructed problem is solved. The solution obtained has been interpreted. The fact that it yields an efficient or Pareto optimal solution has also been *** Statement A three-objective portfolio selection problem in an uncertain situation has been constructed using a newly defined uncertainty distribution. An innovative solution procedure that elicits efficient solutions is suggested to solve the problem. The work done can be applied to solve real-life portfolio selection problems with better accuracy.

关键词： Portfolio optimization Uncertain variable Efficient solution multi-objective programming 74PXX 90-XX

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Integrating reference point, Kuhn-Tucker conditions and neural network approach for multi-objective and multi-level programming problems

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OPSEARCH 2017年第4期54卷 663-683页

作者： Rizk-Allah, R. M. Abo-Sinna, Mahmoud A. Menoufia Univ Dept Basic Engn Sci Fac Engn Shibin Al Kawm Egypt Princess Nora Bent AbdulRahman Univ Dept Math Sci Fac Sci Riyadh Saudi Arabia

In this paper, a neural network approach is constructed to solve multi-objective programming problem (MOPP) and multi-level programming problem (MLPP). The main idea is to convert the MOPP and the MLPP into an equivalent convex optimization problem. A neural network approach is then constructed for solving the obtained convex programming problem. Based on employing Lyapunov theory, the proposed neural network approach is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the MOPP and the MLPP. The simulation results also demonstrate that the proposed neural network is feasible and efficient.

关键词： Karush-Kuhn-Tucker conditions multi-level programming multi-objective programming Neural network Asymptotic stability

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A multi-objective mean-variance mathematical programming approach to combined phase-out and clearance pricing strategy for seasonal products: case study of a Jeans retailer

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JOURNAL OF REVENUE AND PRICING MANAGEMENT 2020年第3期19卷 210-217页

作者： Nayeri, Mahmoud Dehghan Haghbin, Amir-Nader Mohammadi-Balani, Abdolkarim Bayat, Karim Tarbiat Modares Univ Fac Management & Econ Dept Ind Management Jalal Al Ahmad HighwayPOB 14115-111 Tehran *** Iran Tarbiat Modares Univ Jalal Al Ahmad HighwayPOB 14115-111 Tehran *** Iran

This paper presents a novel multi-objective mean-variance mathematical programming approach to the dynamic pricing problem for seasonal products. The basic pricing scheme is a combination of phase-out pricing that gradually lowers the price over time and clearance pricing in which the end-of-season inventory is sold altogether at a lower price to a wholesaler in order to make room for the next season's products. The model is then applied to a real-world case of a Jeans retailer in three different risk attitudes. Results show that the retailer should follow an almost fixed non-dynamic pricing strategy in the risk-taking attitudes, and a more flexible dynamic pricing strategy in risk-averse attitudes.

关键词： Dynamic pricing Seasonal products multi-objective programming Phase-out pricing Clearance pricing

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multi-objective Fuzzy Probabilistic programming Approach for Obtaining Optimum Crops Pattern with Water Replenishment

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International Journal of Applied and Computational Mathematics 2024年第4期10卷 1-21页

作者： Dutta, S. Sahoo, B.C. Bhanavi, S. Nethra, S. Department of Advanced Computing St. Joseph’s University Karnataka Bengaluru India Department of Soil and Water Conservation Engineering College of Agricultural Engineering and Technology Bhubaneswar India Department of Mathematics St. Joseph’s University Karnataka Bengaluru India

This research paper is concerned with the solution procedure of a multi-objective fuzzy probabilistic problem (MOFPP), taking different crop patterns as the objective functions and water requirements of crops as constraints, which is then solved using fuzzy programming technique. In order to handle fuzzy probabilistic constraints, a transformation technique is developed for fuzzy uniform distribution. As the study area receives less rainfall, the cultivation is mainly dependent on irrigation water. A continual use of underground water for irrigation led to a substantial decrease in the water level of the surrounding area. So, to uplift the underground water level, a proper selection of crops can play a vital role in the replenishment of underground water without compensating the farmer’s income. To illustrate the above technique, a case study is provided with the cultivated area of different crops as a decision variable. The two objective functions are taken as the yield of crops taken as fuzzy number and profit obtained by the farmers after selling the products. A comparison table is furnished in the result section for making better decisions. The study reveals that planting a combination of beans, bitter-gourd, and cabbages will yield maximum profit. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2024.

关键词： 60A86 60A86 97M40 Cropping pattern Fuzzy probabilistic programming multi-objective programming

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Uncertain programming model for designing multi-objective reverse logistics networks

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CLEANER LOGISTICS AND SUPPLY CHAIN 2024年 11卷

作者： Xia, Hanbing Chen, Zhiyuan Milisavljevic-Syed, Jelena Salonitis, Konstantinos Cranfield Univ Sustainable Mfg Syst Ctr Sch Aerosp Transport & Mfg Cranfield MK43 0AL England

Given the contradiction between the rapid growth of products and the modest recovery rate of end-of-life products, there is a pressing need to understand the societal significance of establishing a reverse logistics network for end-of-life products. This research constructs an open-loop five-tier reverse logistic network model encompassing customers, centres for collection, disassembly and inspection, remanufacturing, and disposal. A multi-objective mixed-integer nonlinear programming model under uncertainty has been developed. Unlike previous research, this model accounts for surrounding residents' disutility of facilities while simultaneously minimizing economic costs and environmental impact. Besides, uncertainty theory is introduced in solving the proposed model. More specifically, the formulated model converts all uncertain variables into uncertain distributions by implementing the uncertain multi-objective programming method. Furthermore, a customised non- dominated sorting genetic algorithm III (NSGA-III) is proposed and is employed for the first time to address facility selection and recycling volume distribution within the network. The model is then validated using a real- life case study focusing on end-of-life vehicles in Changchun, China. This research could assist decision-makers in both governmental and private sectors in achieving a balanced approach to the interests of the economy, environment, and local communities comprehensively when designing reverse supply chains.

关键词： Reverse logistics network multi-objective programming Uncertainty theory End-of-life products Non-dominated sorting genetic algorithm III

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Convergence of Random to Power-Law Networks Using a multi-objective Non-linear programming Model

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JOURNAL OF multi-CRITERIA DECISION ANALYSIS 2015年第5-6期22卷 232-243页

作者： Petridis, Nikolaos Aristotle Univ Thessaloniki Fac Econ & Polit Sci Sch Econ Thessaloniki 54124 Greece

Networks are a powerful and useful tool for analysing complex systems. Three main types of networks have been proposed in the relative literature in order to interpret adequately evolving or stationary phenomena. In this research, two network structures are analysed;the first type is the random network, which was initially introduced by Erdos and Renyi. Random networks properties remain the same over time, and they do not exhibit high degree of clustering, whereas the second structure studied, the power-law network that have been examined by Albert and Barabasi, can incorporate attributes that are observed in natural networks (i.e. the World Wide Web and the authors' collaboration). In this study, an attempt is made to investigate the conditions under which random network and power law (or scale free) converge into one at a given time point. Three main metrics are used in order to examine the proximity between the studied structures: (i) clustering coefficient, (ii) average path length and (iii) degree distribution. Considering the difference of the corresponding metrics of each network type as an objective function, a multi-objective discontinuous non-linear programming model is employed using the weighted sum model as a solution approach. A statistical meta-analysis is performed using a multivariate logit model in order to assess the effect of each network's specific variables on the objective function. Copyright (C) 2015 John Wiley & Sons, Ltd.

关键词： random networks power-law networks multi-objective programming weighted sum model logit model

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An interactive weighted fuzzy goal programming technique to solve multi-objective reliability optimization problem

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Journal of Industrial Engineering International 2019年第1-Sup期15卷 95-104页

作者： Kundu, Tanmay Islam, Sahidul Department of Mathematics University of Kalyani Kalyani 741235 West Bengal India

This paper presents an application of interactive fuzzy goal programming to the nonlinear multi-objective reliability optimization problem considering system reliability and cost of the system as objective functions. As the decision maker always have an intention to produce highly reliable system with minimum cost, therefore, we introduce the interactive method to design a high productivity system here. This method plays an important role to maximize the worst lower bound to obtain the preferred compromise solution which is close to the best upper bound of each objective functions. Until the preferred compromise solution is reached, new lower bounds corresponding to each objective functions will be determined based on the present solution to develop the updated membership functions as well as aspiration levels to resolve the proposed problem. Considering judgmental vagueness of decision maker, here we consider the resources as trapezoidal fuzzy numbers and apply total integral value of fuzzy number to transform into crisp one. To illustrate the methodology and performance of this approach, numerical examples are presented and evaluated by comparing with the other method at the end of this paper. © 2019, The Author(s).

关键词： Fuzzy programming Goal programming Interactive methods multi-objective programming Reliability

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Fuzzy Efficient Interactive Goal programming Approach for multi-objective Transportation Problems

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International Journal of Applied and Computational Mathematics 2017年第2期3卷 505-525页

作者： Singh, Pitam Kumari, Saru Singh, Priyamvada Department of Mathematics Motilal Nehru National Institute of Technology Allahabad Allahabad India Department of Mathematics C.C.S University Campus Meerut India Department of Earth and Planetary Sciences University of Allahabad Allahabad India

multi-objective transportation problem (MOTP) is a special case of vector minimization linear optimization problem with equality constraints and the objectives are conflicting in nature. Due to the conflicting nature of objectives, no method is available to find single optimal solution for MOTP. All the methods can find only the compromise solution. This paper presents an efficient method for solving MOTP to find fuzzy efficient and compromise solution using the qualities of three well known approaches i.e. (i) fuzzy programming, (ii) goal programming, (iii) interactive programming. In this approach, fuzzy goals are decided by the decision maker (DM) for each objectives and membership functions are constructed for each objective. Then the method is developed using fuzzy set theory and the best quality of the developed method is that the decision maker is focussed only in the part of evaluation of the solution at each step using the acceptable terms and conditions. The present method is the extension of Waeil and Lee (Omega 34:158–166, 2006). To measure the efficiency of the method, some distance metric functions are used and it is verified by two numerical examples. The results are compared with previous reported work for the same numerical problems. © 2016, Springer India Pvt. Ltd.

关键词： Fuzzy goal programming Fuzzy multi-objective transportation programming Interactive programming multi-objective programming multi-objective transportation problem

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