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A compromise programming approach for cross efficiency measurement in basic two-stage network system

EXPERT SYSTEMS WITH APPLICATIONS 2024年第PartA期252卷

作者： Hazhir, Maryam Masoumi Foroughi, Ali Asghar Univ Qom Dept Math Qom Iran

Data envelopment analysis (DEA) is a technique that allows each decision-making unit (DMU) to calculate efficiency using the most favorable weights for inputs and outputs. The resulting efficiency scores are incomparable and difficult to discriminate. Cross-efficiency is a concept for solving the problem of incomparability among the efficiencies of a set of DMUs that are calculated from different weights and is helpful for ranking. In basic DEA, several cross-efficiency evaluation methods with various secondary purposes have been presented, however, the internal mechanism of the DMUs in cross-efficiency evaluation is often neglected. In this study, we use the composition approach for a basic two-stage structure, so that the efficiencies of the divisions are estimated first, and then the overall efficiency of the system is obtained. To solve the linear bi-objective model in the combination approach, we consider a compromise programming problem to find the solution that is as close as possible to the ideal point. Finally, a secondary objective model is proposed to select a weight among the optimal weights of the compromise model, which also guarantees the efficiency of the optimal weight for the bi-objective problem. We use the optimal solution obtained from this model to evaluate cross-efficiency and rank DMUs for a series two-stage system. The proposed approach enables us to rank the DMUs by assessing the performance of each DMU and each of its separate divisions. The validity of the suggested network cross-efficiency evaluation is demonstrated by a numerical example from the literature.

关键词： Network DEA Cross-efficiency evaluation Composition approach multi-objective programming Compromise programming Two-stage system

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multi-choice conic goal programming model-based network data envelopment analysis

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RAIRO-OPERATIONS RESEARCH 2024年第4期58卷 3391-3416页

作者： Deliktas, Derya Ustun, Ozden Demirtas, Ezgi Aktar Arapoglu, Rifat Aykut Kutahya Dumlupinar Univ Fac Engn Dept Ind Engn Kutahya Turkiye Aksaray Univ Fac Engn Dept Ind Engn Aksaray Turkiye Eskisehir Osmangazi Univ Fac Engn Dept Ind Engn Eskisehir Turkiye

In multi-stage processes, classical Data Envelopment Analysis (DEA) acts like a black box and measures the efficiency of decision-making units (DMUs) without considering the internal structure of the system. Unlike classical DEA, recent studies have shown that the overall system efficiency scores are more meaningful if researched using the Network DEA (NDEA) methodology. NDEA performs simultaneous efficiency evaluations of sub-processes and the entire system. Recently, the composition method integrated with multi-objective programming (MOP) has been preferred by many authors to alleviate the drawbacks of earlier methods such as decomposition, slack-based measure (SBM) and the system-centric approach. This study proposes a novel approach incorporating multi-Choice Conic Goal programming into the NDEA (MCCGP-NDEA). It provides a more accurate representation of the Pareto front by revealing potential Pareto optimal solutions which are overlooked by the composition methods. Due to its ability to modify stage weights based on the decision makers' (DMs) preferences, it is likely to gather more samples from the Pareto surface. Computational results on available benchmark problems confirm that the proposed MCCGP-NDEA is a viable alternative to existing methods.

关键词： Data envelopment analysis network DEA multi-choice conic goal programming multi-objective programming

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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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Optimization of a quadratic programming problem over an integer efficient set

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2024年 441卷

作者： Prerna Sharma, Vikas TIET Sch Math Patiala Punjab India

multi-objective programming problem often contains numerous efficient solutions, which con-fuses the decision-maker. To assist in selecting the most desirable solution, optimizing a function over the efficient set becomes crucial. In this paper, we present a novel method for optimizing a general quadratic function over the efficient set of a multi-objective integer linear programming problem. To solve this problem, a ranking approach and efficiency test is utilized. The proposed methodology obtains a globally optimal solution by systematically scanning ranked solutions of an integer quadratic programming problem until the efficiency condition is satisfied. For generating ranked solutions, we construct a related integer linear programming problem. Then, ranked solutions of the integer linear programming problem are used for enumerating ranked solutions of the integer quadratic programming problem. The convergence of our algorithm is established theoretically, and its steps are illustrated using a numerical example. Aparticular case of the proposed method for optimizing a linear function over the efficient set of a multi-objective integer linear programming problem is also discussed. Further, extensive computational results demonstrate the effectiveness of our method for solving problems with large number of constraints, variables, and objective functions. Moreover, comparative analysis shows that the developed algorithm came out to be computationally more efficient as compared to the existing state-of-the-art algorithms.

关键词： Efficient set multi-objective programming Quadratic programming Integer programming

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An improved bi-level programming model for water resources allocation under multiple uncertainties

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JOURNAL OF ENVIRONMENTAL MANAGEMENT 2023年第1期345卷 118882页

作者： Ren, Chongfeng Wang, Yashi Yu, Linghui Zhang, Hongbo Xie, Zhishuai Changan Univ Sch Water & Environm Xian Peoples R China Changan Univ Key Lab Ecohydrol & Water Secur Arid & Semiarid Re Minist Water Resources Xian Peoples R China Changan Univ Key Lab subsurface Hydrol & Ecol Effect Arid Reg Minist Educ Xian Peoples R China Changan Univ Sch Water & Environm Yantastr 126 Xian 710054 Shaanxi Peoples R China

Nowadays, with the scarcity of water resources, competition for water resources among different levels and water sectors is growing increasingly fierce. Furthermore, uncertainties are unavoidable in the water resources system. To address the aforementioned issues, a fuzzy max-min decision bi-level multi-objective interval programming model was proposed, which can not only focus on water conflicts at the same level or between different levels, but also pay attention to optimal allocation of water resources under uncertainty. The developed model was then applied to a case study in Wuwei City, Gansu Province, China, which selected fairness of water distribution and agricultural economic benefits as planning objectives. Based on the developed model, different water resources optimal allocation schemes under different representative hydrological years were provided. From the result, as representative hydrological years changed from wet (P = 25%) to dry (P = 75%), agricultural economic benefit and Gini coefficient of agriculture would vary from [35.19, 37.78] x 108 yuan to [31.12, 31.99] x 108 yuan and from [0.468, 0.429] to [0.505, 0.503], which indicates that as available water resources decrease, agricultural economic benefit would decrease and fairness of water distribution would also decrease. And the water distribution fairness of the upper bound water allocation scheme is higher than that of the lower bound water allocation scheme when in the same representative hydrological year. In addition, no matter what representative hydrological year, the results of the established bi-level programming model are always in the middle of the results of the upper and lower level individual objective, which means that the developed bi-level programming model has great advantage to deal with water competing conflict among different levels. Furthermore, based on the results of developed model, the reasonable water resources optimization schemes can be determined by the decision-ma

关键词： Water resources optimal allocation Bi-level programming multi-objective programming multiple uncertainties

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A multi-objective programming approach, integrated into the TOPSIS method, in order to optimize product design;in three-dimensional concurrent engineering

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COMPUTERS & INDUSTRIAL ENGINEERING 2013年第4期64卷 875-885页

作者： Shidpour, H. Shahrokhi, M. Bernard, A. Univ Kurdistan Dept Engn Sanandaj Iran Ecole Cent Nantes F-44321 Nantes 3 France

This paper proposes a new method to address a three-dimensional concurrent engineering (3D-CE) approach. It uses a multi-objective Linear programming (MOLP) model integrated to the TOPSIS method in order to determine the best configuration product design, assembly process and suppliers of components. This method is able to involve various supply chain strategies by considering qualitative and quantitative criteria in the early stages of the new product development (NPD) process. It also applies the Fuzzy Analytic Hierarchy Process (FAHP) method to determine the relative importance of criteria defined to evaluate configurations of design alternatives, assembly processes and suppliers of components. A sensitivity analysis from different parameters in the model that affect the selection of the best design alternative is performed by creating a computer program using visual studio. A numerical example is used to demonstrate method efficacy and finally, the paper suggests some areas for future research. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： New product development TOPSIS 3D-CE Qualitative and quantitative parameters multi-objective programming FAHP

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Development of a New Municipal Solid Waste Management System: multi-objective programming for a Merged Metropolis

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ENVIRONMENTAL ENGINEERING SCIENCE 2013年第4期30卷 153-160页

作者： Wu, Edward Ming-Yang Tsai, Chia-Cheng Lin, Chitsan Kuo, Shu-Lung Kang, Zhi-Bo I Shou Univ Dept Civil & Ecol Engn Kaohsiung Taiwan Natl Kaohsiung Marine Univ Dept Marine Environm Engn Kaohsiung 811 Taiwan Natl Univ Kaohsiung Gen Educ Ctr Kaohsiung Taiwan

On December 25, 2010, two administrative regions with entirely different administrative status, resources, and areas of development, Kaohsiung City and Kaohsiung County, were required by a long-term national land reform program in Taiwan to merge into one administrative entity. A new plan for managing solid wastes had to be quickly implemented to provide services of equal quality to all residents. The government of the new administrative region is required to initiate a new plan at the top level to provide a platform for planning sublevel solid waste collection and disposal systems. To address the issue, this study used an urban planning approach and multi-objective mathematical programming to reconcile conflicting objectives within the system, which must be built and maintained at minimum cost and provide maximum equity. Because the second objective of maximum equity is difficult to express quantitatively, this study initiated an indicator for this variable, that is, to minimize the total metric ton-kilometers of waste being transported. Furthermore, a constraint method was introduced to simplify the two objectives into a single objective function. Additionally, this model pioneered the inclusion of time as a variable. This made possible a time-dependent dynamic annual solution for each year of the 10-year study period. Hence, the model reflected the actual solid waste complexity in the newly merged region and provided valuable information for top-down planning of future subsystems projects.

关键词： cost minimization deterministic status modeling of equity multi-objective programming municipal solid waste management superior plan

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Optimizing the industrial structure of a watershed in association with economic-environmental consideration: an inexact fuzzy multi-objective programming model

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JOURNAL OF CLEANER PRODUCTION 2013年 42卷 116-131页

作者： Zhou, M. Chen, Q. Cai, Y. L. Peking Univ Coll Urban & Environm Sci Beijing 100871 Peoples R China Qinghai Normal Univ Coll Life & Geog Sci Xining 810008 Qinghai Peoples R China

An inexact fuzzy multi-objective programming model (IFMOP) is developed in this study for dealing with industrial structure optimization problems under uncertainty. The IFMOP model is formulated based on integration of an inexact linear programming (ILP), fuzzy flexible optimization (FFO), and multi-objective programming (MOP). It improves upon the existing industrial structure optimization model with advantages in uncertainty reflection, model coupling, data availability and computational requirement. The model can deal with uncertainties expressed as discrete intervals and fuzzy sets. Therefore, it can effectively reflect dynamic, interactive complex, and uncertain characteristics of industrial system without unrealistic simplification. Moreover, the model can be used for supporting temporal and spatial optimization of industrial structure under a variety of environmental and socio-economic conditions. The developed model is first applied to a real case of planning industrial structure of South Four Lake watershed in Shandong province, China. Results demonstrated that the model could help decision makers generate stable and balanced industrial structure patterns, gain in-depth insights into effects of the uncertainties, and analyze trade-offs among economical objective, environmental protection and social demand. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Inexact linear programming Fuzzy flexible programming multi-objective programming Hybrid uncertain model Industrial structure optimization

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Fuzzy goal programming technique for multi-objective indefinite quadratic bilevel programming problem

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ARCHIVES OF CONTROL SCIENCES 2020年第4期30卷 683-699页

作者： Arora, R. Gupta, K. Univ Delhi Dept Math Keshav Mahavidyalaya Delhi India Univ Delhi Kirori Mal Coll Dept Math Delhi India

Bilevel programming problem is a non-convex two stage decision making process in which the constraint region of upper level is determined by the lower level problem. In this paper, a multi-objective indefinite quadratic bilevel programming problem (MOIQBP) is presented. The defined problem (MOIQBP) has multi-objective functions at both the levels. The followers are independent at the lower level. A fuzzy goal programming methodology is employed which minimizes the sum of the negative deviational variables of both the levels to obtain highest membership value of each of the fuzzy goal. The membership function for the objective functions at each level is defined. As these membership functions are quadratic they are linearized by Taylor series approximation. The membership function for the decision variables at both levels is also determined. The individual optimal solution of objective functions at each level is used for formulating an integrated pay-off matrix. The aspiration levels for the decision makers are ascertained from this matrix. An algorithm is developed to obtain a compromise optimal solution for (MOIQBP). A numerical example is exhibited to evince the algorithm. The computing software LINGO 17.0 has been used for solving this problem.

关键词： bilevel programming indefinite quadratic programming multi-objective programming pay-off matrix Taylor series approximation LINGO 17.0

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SDG-oriented multi-scenario sustainable land-use simulation under the background of urban expansion

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ENVIRONMENTAL SCIENCE AND POLLUTION RESEARCH 2022年第48期29卷 72797-72818页

作者： Zhou, Min Ma, Yuxiang Tu, Jiating Wang, Mengcheng Huazhong Univ Sci & Technol Coll Publ Adm 1037 Luoyu Rd Wuhan Peoples R China

With the continuous improvement of urbanization level and the continuous expansion of city scale, there are some unreasonable land development and utilization problems, which will make the contradiction between people and land more prominent and the risk of ecological environment deterioration more serious. It hinders the sustainable land use (SLU) and then affects the realization of regional Sustainable Development Goals (SDGs). SDGs have become a programmatic document for all countries in the world to implement sustainable development. It provides a guideline and direction for the sustainable urban expansion. The sustainable urban expansion promotes the realization of SDGs worldwide. By combining the SDGs with the urban SLU, this paper obtains the optimized future land-use demand of the multi-scenario city and the urban expansion simulation scenario to the SDGs under the multi-scenario through the uncertain mathematical model (MIFCCP) and the spatial simulation model (PLUS). We find that firstly, the net profit of land use (LNB) reaches the highest value under the economic development scenario (ED), when the probability of environmental constraint violation p = 0.01 and p = 0.15, LNB = [2625.48, 3244.98] x 10(9) CNY, and [2646.95, 3271.51] x 10(9) CNY. Ecosystem service value (ESV) reached the highest value under the sustainable development scenario (SD), when p = 0.01 and p = 0.15, ESV = [75.34, 93.12] x 10(9) CNY, and [72.62, 95.56] x 10(9) CNY. The net carbon emissions from land use (LNC) reached the minimum value in SD scenario, and when p = 0.01 and p = 0.15, the LNC reached [57.46, 71.02] x 10(6) ton and [56.12, 76.04] x 10(6) ton. Secondly, the contribution degree of 15 driving factors to the change of local types is excavated, among which, the driving factors of traffic stations have the highest contribution degree to the change of construction land and cultivated land, and the third-class roads have the highest contribution degree to the change of wetland

关键词： Sustainable land use SDGs multi-objective programming Uncertain model Patch-generating simulation Land use simulation

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