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Stochastic Fuzzy multi-level multi-objective Fractional programming Problem: A FGP Approach

OPSEARCH 2017年第4期54卷 816-840页

作者： Osman, M. S. Emam, O. E. El Sayed, M. A. El Asher Univ El Asher City Egypt Helwan Univ Fac Comp & Informat Dept Informat Syst POB 11795 Helwan Egypt Benha Univ Dept Basic Engn Sci Fac Engn Elqalyoubia Egypt

In this paper, a fuzzy goal programming (FGP) approach is considered for solving stochastic fuzzy multi-level multi-objective fractional programming (ML-MOFP) problem. In the developed stochastic fuzzy ML-MOFP model the fractional objective function coefficients and scalars are represented by fuzzy parameters. Moreover, in the constraints, the right-hand sides are independent random variable with known distribution function while both the left-hand side coefficients and the tolerance measures are considered to be fuzzy parameters. Therefore, the chance-constrained approach with dominance possibility criteria and the alpha-cut approach are utilized to transform the stochastic fuzzy ML-MOFP problem to its equivalent deterministic-crisp problem. Then, the membership functions for the defined fuzzy goals are setup. Also, in the proposed FGP model, a linearization procedures for the membership goals of the objective functions is developed. Hence, the FGP approach is used to achieve the highest degree of each of the membership goals by minimizing the sum of the negative deviational variables. Finally, an algorithm to clarify the developed FGP approach, as well as Illustrative numerical example, are presented.

关键词： multi-level programming Fractional programming Chance-constrained approach Fuzzy sets Fuzzy goal programming

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A multi-level method for groundwater remediation management accommodating non-competitive objectives

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JOURNAL OF HYDROLOGY 2019年 570卷 531-543页

作者： Lu, Hongwei Li, Jing Chen, Yizhong Lu, Jingzhao Hebei Normal Univ Coll Resource & Environm Sci Shijiazhuang 050024 Hebei Peoples R China Chinese Acad Sci Inst Geog Sci & Nat Resources Res Key Lab Water Cycle & Related Land Surface Proc Beijing 100101 Peoples R China North China Elect Power Univ Sch Renewable Energy Beijing 102206 Peoples R China

No attempts have been found on dealing with a set of non-competitive (or leader-follower-interactive) objectives when performing optimal groundwater remediation management. This study presents a multi-level nonlinear simulation-optimization (ML-NSO) model for groundwater remediation management when objectives should be satisfied at multiple levels. This model is formulated by integrating health-risk assessment (at the residential concern level), energy assessment (at the energy concern level) and contamination forecasting (at the environmental concern level) within a general framework. The capabilities and effectiveness of the developed model are illustrated through a real-world case located at Cantuar, Saskatchewan in Canada. Results facilitate (a) generating non-compromised solutions in association with the optimal strategies regarding groundwater injection and extraction, (b) displaying the distribution of contaminant concentration and carcinogenic risks for human health, and estimating the corresponding energy consumption, (c) resolving of conflicts and interactions among residential, energy, and environmental requirements. Moreover, the performance of ML-NSO model is enhanced by comparing with the single-level and multi-objective (SL-NSO and MO-NSO) models. Results show that ML-NSO model would assign higher priority on the residential and environmental concerns by tolerating a slight rise in energy cost The ML-NSO model would provide more comprehensive and systematic policies with considering the leader-follower relationship within system.

关键词： multi-level programming Groundwater remediation Optimization Health risks

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Planning water-energy-food nexus system management under multi-level and uncertainty

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JOURNAL OF CLEANER PRODUCTION 2020年 251卷 119658-000页

作者： Yu, L. Xiao, Y. Zeng, X. T. Li, Y. P. Fan, Y. R. Zhengzhou Univ Sch Water Conservancy Engn Zhengzhou 450001 Peoples R China Zhengzhou Key Lab Water Resource & Environm Zhengzhou 450001 Peoples R China Henan Key Lab Groundwater Pollut Prevent & Rehabi Zhengzhou 450001 Peoples R China Capital Univ Econ & Business Beijing 100070 Peoples R China Beijing Normal Univ Sch Environm Beijing 100875 Peoples R China Brunel Univ London Dept Civil & Environm Engn Uxbridge UB8 3PH Middx England

In this study, a multi-level interval fuzzy credibility-constrained programming (MIFCP) method is developed for planning the regional-scale water-energy-food nexus (WEFN) system. MIFCP can not only deal with uncertainties expressed as interval parameters and fuzzy sets, but also handle conflicts and hierarchical relationships among multiple decision departments. The MIFCP approach is then applied to planning the WEFN system of Henan Province, China. Solutions of three different decision targets in various hierarchy levels, five scenarios with different decision makers' objectives and five credibility levels toward different necessity degrees are examined. Several findings in association with various planting structures, water resources demand, energy consumption, fertilizer and pesticide utilizations and system benefits are achieved. Results reveal that the future total irrigation water can decrease by 1.49% from years 2020-2025. Results also disclose that the total cultivated area can change by 1.91% owing to the variation of fertilizer and pesticide change. Compared to single level programming (SLP) and bi-level programming (BP) approaches, the MIFCP-WEFN model can help decision-makers identify the optimal agricultural water resources management schemes by means of the leadership of water resources managers as well as the feedback of two diverse followers (i.e. energy managers and agricultural managers). (C) 2019 Elsevier Ltd. All rights reserved.

关键词： multi-level programming Planning Scenario analysis Uncertainty Water-energy-food nexus system

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A Novel Interactive Fuzzy programming Approach for Optimization of Allied Closed-Loop Supply Chains

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INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 2018年第1期11卷 672-691页

作者： Calik, Ahmet Pehlivan, Nimet Yapici Paksoy, Turan Weber, Gerhard Wilhelm KTO Karatay Univ Logist Management TR-42020 Konya Turkey Selcuk Univ Stat TR-42075 Konya Turkey Selcuk Univ Ind Engn TR-42075 Konya Turkey Middle East Tech Univ Dept Appl Math Ankara Turkey Poznan Univ Tech Fac Engn Management Chair Mkt & Econ Engn Ul Strzelecka 11 PL-60965 Poznan Poland

In recent years, the relationship between companies and suppliers has changed with the continuous rise in environmental awareness and customer expectations. In order to fulfill customers' needs, the actors in a Supply Chain (SC) network sometimes compete and sometimes cooperate with each other. In SC management, both competitive and collaborative strategies have become important and have required different points of view. In a collaborative environment, companies should strive for common targets with mutual relationship. After managers decided to share their resources, some positive effects have appeared on the companies and suppliers' performance such as profitability, flexibility and efficiency. Consequently, many companies are willing to cooperate with each other in a SC network because of these reasons. On the other hand, Closed-Loop Supply Chain (CLSC) management has been attracting a growing interest because of increased environmental issues, government regulations and customer pressures. Based on this initiative, our paper presents a novel allied CLSC network design model with two different SCs including common suppliers and common collection centers. First, a decentralized multi-level Mixed-Integer Linear programming (MILP) model that consists of two different levels of Decision Makers (DMs) is developed. The plants of common SCs comprise the upper-level DMs, common suppliers, common collection centers, and the logistics firm comprises the lower-level DMs. A novel Interactive Fuzzy programming (IFP) approach using Fuzzy Analytic Hierarchy Process (AHP) is proposed to obtain a preferred compromise solution for the developed model. Through use of Fuzzy AHP in the proposed IFP approach, the DMs can identify the importance of the lower-level DMs. In order to validate the developed model and the proposed IFP approach, a numerical example is implemented. According to the obtained results, our proposed IFP method outperforms Sakawa and Nishizaki's(1) and Calik et a

关键词： Closed-Loop Supply Chain Optimization Interactive Fuzzy programming Common Sources multi-level programming Preferred Compromise Solution

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A decentralized multi-level decision making model for solid transportation problem with uncertainty

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INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2018年第5期9卷 1022-1033页

作者： Jalil, Syed Aqib Javaid, Shakeel Muneeb, Syed Mohd Aligarh Muslim Univ Dept Stat & Operat Res Aligarh Uttar Pradesh India

In this paper, a multi-level model for the solid transportation problem having uncertain variables is presented. multi-level programming deals with the situation where more than one decision maker is available to model decentralized planning problem in any hierarchical system. In the model presented in this paper, all the parameters involved viz. transportation costs, supply availabilities, demands and conveyance capacities are considered as uncertain parameters. As the problem is based on uncertainty theory, the idea of minimizing (or maximizing) the expectation of objective functions under the set of chance constraints is followed to formulate the problem. A crisp model equivalent to the multi-level uncertain solid transportation problem is also given. A fuzzy based solution approach for solving multi-level programming problems is discussed to solve the presented model. Further, a numerical example of a three-level uncertain solid transportation problem with two conveyance options is given in order to understand the model more clearly.

关键词： Solid transportation problem multi-level programming Uncertainty theory Uncertain variable

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Life cycle assessment of greenhouse gas emissions and water-energy optimization for shale gas supply chain planning based on multi-level approach: Case study in Barnett, Marcellus, Fayetteville, and Haynesville shales

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ENERGY CONVERSION AND MANAGEMENT 2017年 134卷 382-398页

作者： Chen, Yizhong He, Li Guan, Yanlong Lu, Hongwei Li, Jing North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewabl Beijing 102206 Peoples R China North China Elect Power Univ Sch Renewable Energy Beijing 102206 Peoples R China

This study develops a multi-level programming model from a life cycle perspective for performing shale gas supply chain system. A set of leader-follower-interactive objectives with emphases of environmental, economic and energy concerns are incorporated into the synergistic optimization process, named MGUMEM-MWL model. The upper-level model quantitatively investigates the life-cycle greenhouse gas (GHG) emissions as controlled by the environmental sector. The middl-level one focuses exclusively on system benefits as determined by the energy sector. The lower-level one aims to recycle water to minimize the life-cycle water supply as required by the enterprises. The capabilities and effectiveness of the developed model are illustrated through real-world case studies of the Barnett, Marcellus, Fayetteville, and Haynesville Shales in the US. An improved multi-level interactive solution algorithm based on satisfactory degree is then presented to improve computational efficiency. Results indicate that: (a) the end use phase (i.e., gas utilization for electricity generation) would not only dominate the life-cycle GHG emissions, but also account for 76.1% of the life-cycle system profits;(b) operations associated with well hydraulic fracturing would be the largest contributor to the life-cycle freshwater consumption when gas use is not considered, and a majority of freshwater withdrawal would be supplied by surface water;(c) nearly 95% of flowback water would be recycled for hydraulic fracturing activities and only about 5% of flowback water would be treated via CWT facilities in the Marcellus, while most of the wastewater generated from the drilling, fracturing and production operations would be treated via underground injection control wells in the other shale plays. Moreover, the performance of the MGU-MEM-MWL model is enhanced by comparing with the three bi-level programs and the multi-objective approach. Results demonstrate that the MGU-MEM-MWL decisions would provide

关键词： multi-level programming Life cycle Shale gas Greenhouse gas Energy Water supply

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A Decentralized Model for Allied Closed-Loop Supply Chains: Comparative Analysis of Interactive Fuzzy programming Approaches

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INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 2017年第2期19卷 367-382页

作者： Calik, Ahmet Paksoy, Turan Yildizbasi, Abdullah Pehlivan, Nimet Yapici Selcuk Univ Dept Stat Konya Turkey Selcuk Univ Dept Ind Engn Konya Turkey Yildirim Beyazit Univ Dept Ind Engn Ankara Turkey

The supply chain network design problem addresses various factors that maximize customers' demand and minimizes the sum of strategic, tactical, and operational costs. Companies with common activities in their supply chains have started to cooperate with each other to achieve better service levels. Based on this initiative, a multi-level mixed-integer linear programming model is developed that includes two allied supply chains with different decision makers (DM) at two different decision-making levels. The primary aim of this study is to design an allied closed-loop supply chain (CLSC) network that uses some of the same facilities. The secondary aim of this study is to examine this allied CLSC model simultaneously and analyse the impact of the DMs' objectives based on satisfaction degrees. Various interactive fuzzy programming (IFP) approaches were utilized to examine the presented multi-level CLSC model. A novel IFP approach which is based on the fuzzy analytic hierarchy process (AHP) is proposed. The effectiveness of the proposed IFP approach on the CLSC model is investigated with hypothetical data. The computational results show that the proposed approach obtains higher satisfaction degrees for upper-level DMs than the other approaches.

关键词： Allied supply chains Decentralized closed-loop supply chain Interactive fuzzy programming multi-level programming

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Identifying the shared metabolic objectives of glycerol bioconversion in Klebsiella pneumoniae under different culture conditions

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JOURNAL OF BIOTECHNOLOGY 2017年 248卷 59-68页

作者： Xu, Gongxian Li, Caixia Bohai Univ Dept Math Jinzhou 121013 Peoples R China

This paper addresses the problem of identifying the shared metabolic objectives of glycerol bioconversion in Klebsiella pneumoniae for production of 1,3-propanediol (1,3-PD) under different culture conditions. To achieve this goal, we propose a multi-level programming model. This model includes three optimization problems, where the constraint region of the first level problem is implicitly determined by the other two optimization problems. The optimized objectives of the first and second level problems are to minimize the set of fluxes that are of major importance to glycerol metabolism and the difference between the observed fluxes and those computed by the model, respectively. The third level problem in the proposed multi-level programming simultaneously solves a set of flux balance analysis (FBA) models. A method is proposed to solve efficiently the presented multi-level programming problem. In this method, we first transform the proposed multi-level problem into a bi-level problem by applying the dual theory of linear programming to the FBA models of the third level. Next, the optimal solution of the above bi-level problem is obtained by iteratively solving a sequence of mixed integer programming problems. Optimization results reveal that the proposed method can identify the shared metabolic objectives of glycerol bioconversion in Klebsiella pneumoniae under three groups of experimental data. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Flux balance analysis Metabolic objective identification multi-level programming Optimization 1,3-propanediol Klebsiella pneumoniae

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Finding the nucleoli of large cooperative games

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2016年第3期248卷 1078-1092页

作者： Nguyen, Tr-Dung Thomas, Lyn Univ Southampton Math Sci & Business Sch Southampton SO17 1BJ Hants England Univ Southampton Sch Business Southampton SO17 1BJ Hants England

The nucleolus is one of the most important solution concepts in cooperative game theory as a result of its attractive properties - it always exists (if the imputation is non-empty), is unique, and is always in the core (if the core is non-empty). However, computing the nucleolus is very challenging because it involves the lexicographical minimization of an exponentially large number of excess values. We present a method for computing the nucleoli of large games, including some structured games with more than 50 players, using nested linear programs (LP). Although different variations of the nested LP formulation have been documented in the literature, they have not been used for large games because of the large size and number of LPs involved. In addition, subtle issues such as how to deal with multiple optimal solutions and with tight constraint sets need to be resolved in each LP in order to formulate and solve the subsequent ones. Unfortunately, this technical issue has been largely overlooked in the literature. We treat these issues rigorously and provide a new nested LP formulation that is smaller in terms of the number of large LPs and their sizes. We provide numerical tests for several games, including the general flow games, the coalitional skill games and the weighted voting games, with up to 100 players. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

关键词： Nucleolus Cooperative game multi-level programming Payoff distribution Constraint generation Lexicographical minimization

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A multi-level approach to active distribution system planning for efficient renewable energy harvesting in a deregulated environment

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ENERGY 2016年 96卷 614-624页

作者： Zeng, Bo Wen, Junqiang Shi, Jinyue Zhang, Jianhua Zhang, Yuying North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewabl Beijing 102206 Peoples R China

Increasing penetration of renewable distributed generation accentuates the need of active distribution system. However, under the unbundling environment, the conflicting interests between different market participants create hurdles for efficient exploitation of renewable energy sources. To address this issue, we develop a multi-level optimization approach for active distribution system planning, with the purpose of best coordinating the target of renewable energy harvest with the benefits of individuals. The proposed model considers the decision-making of utility under the constraints by the reaction of distributed generation owner as well as the system operational characteristics. It collectively determines the optimal solution concerning network reinforcement, reserve and renewable generation deployment. Furthermore, demand response has been considered as an additional active network management scheme in this work and the uncertainties of renewable generation and load responsiveness are also accounted for. Numerical results based on a 33-bus distribution system verify the effectiveness of the proposed method. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Active distribution system Renewable distributed generation Active network management multi-level programming Deregulated market

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