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Type-2 fuzzy multi-objective DEA model: An application to sustainable supplier evaluation

APPLIED SOFT COMPUTING 2016年 46卷 424-440页

作者： Zhou, Xiaoyang Pedrycz, Witold Kuang, Yunxin Zhang, Zhe Shaanxi Normal Univ Int Business Sch Xian Peoples R China Univ Alberta Dept Elect & Comp Engn Edmonton AB T6R 2V4 Canada King Abdulaziz Univ Fac Engn Dept Elect & Comp Engn Jeddah 21589 Saudi Arabia Polish Acad Sci Syst Res Inst PL-01447 Warsaw Poland Dongbei Univ Finance & Econ Sch Management Sci & Engn Dalian Peoples R China Nanjing Univ Sci & Technol Sch Econ & Management Nanjing Jiangsu Peoples R China

In the last 10 years, sustainable supply chain management (SSCM) has become one of the important topics in business and academe. Sustainable supplier performance evaluation and selection play a significant role in establishing an effective SSCM. One of the techniques that can be used for evaluating sustainable supplier performance is data envelopment analysis (DEA). The conventional DEA methods require accurate measurement of both input and output variables present in the problem. In practice, the observed values of the input and output data present in real-world problems are often imprecise. To cope with this situation, fuzzy DEA models were constructed for expressing relative fuzzy efficiencies of decision-making units (DMUs). However, fuzzy DEA is still limited to fuzzy input/output data while some inputs and outputs might be affected by various factors of uncertainty and information granularity, meaning that they could be better modeled in terms of fuzzy sets of type-2. In this paper, we develop a multi-objective DEA model in a setting of type-2 fuzzy modeling to evaluate and select the most appropriate sustainable suppliers. In the proposed model, both efficiency and effectiveness are considered to describe the integrated productivity of suppliers. In sequel, chance constrained programming, critical value-based reduction methods and equivalent transformations are considered to solve the problem. A detailed case study is employed to show the advantages of the proposed model in terms of measuring effectiveness, efficiency and productivity in an uncertain environment expressed at different confidence levels. At the same time, the results demonstrate that the model is capable of helping decision makers to balance economic, social, and environmental factors when selecting sustainable suppliers. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Sustainable supplier evaluation Multi-objective DEA Productivity Type-2 fuzzy variables chance constrained programming

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Green supply chain network design considering chain-to-chain competition on price and carbon emission

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COMPUTERS & INDUSTRIAL ENGINEERING 2020年 145卷

作者： Wang, Jian Wan, Qian Yu, Mingzhu Huazhong Univ Sci & Technol Key Lab Image Proc & Intelligent Control Sch Artificial Intelligence & Automat Educ Wuhan 430074 Peoples R China Shenzhen Univ Coll Management Inst Big Data Intelligent Management & Decis Shenzhen 518060 Peoples R China

In this paper, we study the competitive and sustainable supply chain network design problem. We consider the chain-to-chain competition between two supply chains. The problem is divided into two stages. The retail price and carbon emission equilibrium at the competition stage are studied. Then, the equilibrium results of the competition stage are substituted into the network design stage as constraints. To address the computational complexity of large-scale problems, a Benders decomposition algorithm is proposed. Through computational studies we find that (1) considering carbon emission competition in the supply chain lowers both the total optimized cost and carbon emission;(2) the carbon emissions of the total supply chain network increases with the probability of capacity satisfaction;(3) the proposed Benders decomposition algorithm outperforms CPLEX for large scale problems.

关键词： Supply chain network design Carbon emission Competition chance constrained programming Benders decomposition algorithm

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PoBO: A Polynomial Bounding Method for chance-constrained Yield-Aware Optimization of Photonic ICs

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IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS 2022年第11期41卷 4915-4926页

作者： He, Zichang Zhang, Zheng Univ Calif Santa Barbara Dept Elect & Comp Engn Santa Barbara CA 93106 USA

Conventional yield optimization algorithms try to maximize the success rate of a circuit under process variations. These methods often obtain a high yield but reach a design performance that is far from the optimal value. This article investigates an alternative yield-aware optimization for photonic ICs: we will optimize the circuit design performance while ensuring a high yield requirement. This problem was recently formulated as a chance-constrained optimization, and the chance constraint was converted to a stronger constraint with statistical moments. Such a conversion reduces the feasible set and sometimes leads to an over-conservative design. To address this fundamental challenge, this article proposes a carefully designed polynomial function, called optimal polynomial kinship function, to bound the chance constraint more accurately. We modify existing kinship functions via relaxing the independence and convexity requirements, which fits our more general uncertainty modeling and tightens the bounding functions. The proposed method enables a global optimum search for the design variables via polynomial optimization. We validate this method with a synthetic function and two photonic IC design benchmarks, showing that our method can obtain better design performance while meeting a prespecified yield requirement. Many other advanced problems of yield-aware optimization and more general safety-critical design/control can be solved based on this work in the future.

关键词： Optimization Integrated circuit modeling Photonics Uncertainty Yield estimation Measurement Design automation chance constrained programming photonic design automation process variation uncertainty quantification yield-aware optimization

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Two-storage inventory model with lot-size dependent fuzzy lead-time under possibility constraints via genetic algorithm

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第2期179卷 352-371页

作者： Maiti, Manas Kumar Maiti, Manoranjan Mahishadal Raj Coll Dept Math Mahishadal 721628 Purba Medinipur India Vidyasagar Univ Dept Math Midnapore 721102 India

Multi-item inventory models with stock dependent demand and two storage facilities are developed in a fuzzy environment where processing time of each unit is fuzzy and the processing time of a lot is correlated with its size. These are order-quantity reorder-point models with back-ordering if required. Here possibility and crisp constraints on investment and capacity of the small storehouse respectively are considered. The models are formulated as fuzzy chance constrained programming problem and is solved via generalized reduced gradient (GRG) technique when crisp equivalent of the constraints are available. A genetic algorithm (GA) is developed based on fuzzy simulation and entropy where region of search space gradually decreases to a small neighborhood of the optima and it is used to solve the models whenever the equivalent crisp form of the constraint is not available. The models are illustrated with some numerical examples and some sensitivity analyses have been done. For some particular cases results observed via GRG and GA are compared. (c) 2006 Elsevier B.V. All rights reserved.

关键词： region reducing genetic algorithm chance constrained programming fuzzy lead time two-storage inventory

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Assessing the effect of wind power peaking characteristics on the maximum penetration level of wind power

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IET GENERATION TRANSMISSION & DISTRIBUTION 2015年第16期9卷 2466-2473页

作者： Jiang, Xin Chen, Hongkun Xiang, Tieyuan Wuhan Univ Dept Elect Engn Wuhan 430072 Peoples R China

A probabilistic approach with considering the peaking characteristics of wind power is proposed to determine the maximum wind power penetration level (WPPL). To evaluate the effect wind peaking characteristics brought to the hosting capacity of systems, a detailed simulation of wind speed/load distributions over a long period is required. Thus, taking an hour as the time scale, the time-sharing peaking characteristics of wind power are discussed by describing the hourly distribution of wind output and load. Based on the chance constrained programming, a WPPL model is established in this study. The optimisation process is achieved using the improved particle swarm optimisation algorithm based on Monte-Carlo simulation. This proposed approach has been applied to an actual power system in central China. Simulation results show that the WPPL would be too optimistic without considering the anti-peaking characteristics of wind power. Besides various sensitivity analyses are performed to assess the effect of other parameters on the maximum penetration level.

关键词： wind power particle swarm optimisation Monte Carlo methods load distribution wind power plants load distribution wind speed power system Monte Carlo simulation improved particle swarm optimisation algorithm WPPL chance constrained programming time scale maximum wind power penetration level wind power peaking characteristics effect

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Multi-objective optimal planning of wind distributed generation considering uncertainty and different penetration level of plug-in electric vehicles

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SUSTAINABLE CITIES AND SOCIETY 2020年 62卷

作者： Zeynali, Saeed Rostami, Naghi Feyzi, M. R. Mohammadi-ivatloo, Behnam Univ Tabriz Fac Elect & Comp Engn Tabriz Iran

Despite the many challenges related to the simultaneous surge in wind-based distributed generation (WDGs) and plug-in electric vehicles (PEVs) in modern power systems, they will be a great help in reducing greenhouse gas emissions. Nonetheless, the associated problems such as uncertainty in production-load sides, voltage instability, and power loss augmentation should be reanalyzed. These predicaments can be dealt to some extent with proper siting and sizing of WDGs together with capacitor banks (CBs) as a conventional voltage regulator and reactive power compensator. However, the sizing and siting problem consists of various objectives, such as voltage stability improvement, emission reduction, and cost reduction. It is a great challenge to optimize these contradictory objectives altogether. Hence, to overcome all these struggles, this paper proposes a tri-objective optimization formulation for optimal planning of WDGs and CBs in the power system, considering uncertainties derived from PEVs' load demand, wind speed, and conventional load. The objectives to be optimized are, namely, voltage stability index, total cost, and greenhouse gas emissions. Moreover, this study assimilates an unaccustomed type of point estimate method (PEM) into strength Pareto multi-objective differential evolution algorithm, which is not only computationally light but also reasonably accurate. Moreover, chance-constrained programming is integrated into the PEM using a maximum entropy method to deal with smooth constraints. The accuracy of the proposed method is evaluated by the Monte-Carlo simulation. Eventually, the proposed algorithm is compared with other standard multi-objective metaheuristic optimization algorithms.

关键词： Plug-in electric vehicle Wind distributed generation Point estimate method Sizing and siting Multi-objective optimization chance constrained programming

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Studies on stochastic unit commitment formulation with flexible generating units

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ELECTRIC POWER SYSTEMS RESEARCH 2010年第1期80卷 130-141页

作者： Ding, Xiaoying Lee, Wei-Jen Wang Jianxue Liu, Lin Univ Texas Arlington Energy Syst Res Ctr Arlington TX 76019 USA Xi An Jiao Tong Univ Xian 710049 Peoples R China State Key Lab Elect Insulat & Power Equipment Xian 710049 Peoples R China

In recent years, restructured power system has emerged and renewable energy generation technology has developed. More and more different unit characteristics and stochastic factors make the unit commitment (UC) more difficult than before. A novel stochastic UC formulation which covered the usual thermal units, flexible generating units and wind generation units is proposed to meet the need of energy-savings and environment protection. By introducing a UC risk constraint (UCRC), many stochastic factors such as demand fluctuations, unit force Outages. variety of energy price, even the stochastic characteristics of wind generation can be dealt with. Based on the theory of chance constrained programming (CCP), the UCRC, a probabilistic constraint is changed into a determinate constraint, and then the presented formulation can be solved by usual optimization algorithms. Numerical simulations on 4 test systems with different scales show that different UC schedules can be determined according to different stochastic factors and its calculation time is acceptable in the view of practical engineer. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Stochastic unit commitment Flexible generating units Wind generation chance constrained programming

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Optimization of Industrial Structure Considering the Uncertainty of Water Resources

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WATER RESOURCES MANAGEMENT 2013年第11期27卷 3885-3898页

作者： Ren, C. F. Guo, P. Li, M. Gu, J. J. China Agr Univ Ctr Agr Water Res Beijing 100083 Peoples R China Hefei Univ Technol Coll Architecture & Art Hefei 230009 Peoples R China

This paper developed a stochastic linear fractional programming model for industry optimization allocation base on the uncertainty of water resources incorporating chance constrained programming and fractional programming. In this paper, the stochastic linear fractional programming is used in the real word. The development SLFP has the following advantages: (1) The model can compare the two aspects of the targets;(2) The model can reflect the system efficiency intuitively;(3) The model can deal with uncertain issues with probability distribution;(4) The model can give different optimal plans under different risk conditions. The model has a significant value for the industry optimization allocation under uncertainty in local and areas to achieve the maximum economic benefits and the full use of the water resources.

关键词： chance constrained programming Water resources optimal allocation Stochastic linear fractional programming Industrial optimization Uncertainty

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A Characterization of the Subdifferential of Singular Gaussian Distribution Functions

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SET-VALUED AND VARIATIONAL ANALYSIS 2015年第3期23卷 465-483页

作者： van Ackooij, W. Minoux, M. OSIRIS EDF R&D F-92141 Paris France Univ Paris 06 LIP6 F-75000 Paris France

For optimization problems involving probabilistic constraints it is important to be able to compute gradients of these constraints efficiently. For distribution functions of Gaussian random variables with positive definite covariance matrices, computing gradients can be done efficiently. Indeed, a formula, linking components of the partial derivative and other regular Gaussian distribution functions exists and has been frequently employed by Pr,kopa. Recently, Henrion and Moller provided not only sufficient conditions under which singular Gaussian distribution functions are differentiable, but also a formula akin to the regular case. The sufficient conditions, rule out a set of points having zero (Lebesgue) measure. We show here that in these points, the sub-differential (in the sense of Clarke) of a Gaussian distribution function can be fully characterized. We moreover provide sufficient and necessary conditions under which these distribution functions are differentiable.

关键词： chance constrained programming Probabilistic constraints Stochastic programming Gradients

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A simultaneous inventory control and facility location model with stochastic capacity constraints

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NETWORKS & SPATIAL ECONOMICS 2006年第1期6卷 39-53页

作者： Miranda, Pablo A. Garrido, Rodrigo A. Pontificia Univ Catolica Chile Dept Transport Engn Santiago Chile

Traditionally, logistics analysts divide decisions levels into strategic, tactical and operational. Often these levels are considered separately for modeling purposes. The latter may conduce to make non-optimal decisions, since in reality there is interaction between the different levels. In this research, a cross-level model is derived to analyze decisions about inventory control and facility location, specially suited to urban settings, where the storage space is scarce and the vehicles' capacity is usually restricted. Both conditions, on the one hand make the problem difficult to solve optimally but on the other hand make it more realistic and useful in practice. This paper presents a simultaneous nonlinear-mixed-integer model of inventory control and facility location decisions, which considers two novel capacity constraints. The first constraint states a maximum lot size for the incoming orders to each warehouse, and the second constraint is a stochastic bound to inventory capacity. This model is NP-Hard and presents nonlinear terms in the objective function and a nonlinear constraint. A heuristic solution approach is introduced, based on Lagrangian relaxation and the subgradient method. Numerical experiments were designed and applied. The solution procedure presented good performance in terms of the objective function. One of the key conclusions of the proposed modeling approach is the fact that a reduction of the inventory capacity does not necessarily imply an increase in the number of installed warehouses. In fact, reducing the order size allows the optimal allocation 66 of customers (those with higher variances) into different warehouses, reducing the total system's cost. (C) Springer Science + Business Media, LLC 2006.

关键词： inventory facilities location chance constrained programming Lagrangian relaxation

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