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INTERNATIONAL JOURNAL OF MATHEMATICAL ENGINEERING AND MANAGEMENT SCIENCES 2021年第6期6卷 1612-1628页

作者： Rani, Namrata Goyal, Vandana Gupta, Deepak Maharishi Markandeshwar Deemed Be Univ Dept Math Mullana Ambala India

This paper has been designed to introduce the method for solving the Bi-level Multi-objective (BL-MO) Fully Quadratic Fractional Optimization Model through fuzzy Goal programming (FGP) approach by utilising non-linear programming. In Fully Quadratic Fractional Optimization Model, the objective functions are in fractional form, having quadratic functions in both numerator and denominator subject to quadratic constraints set. The motive behind this paper is to provide a solution to solve the BL-MO optimization model in which number of decision-makers (DM) exists at two levels in the hierarchy. First, the fractional functions with fuzzy demand, which are in the form of fuzzy numbers, are converted into crisp models by applying the concept of alpha-cuts. After that, membership functions are developed which are corresponding to each decision-maker's objective and converted into simpler form to avoid complications due to calculations. Finally, the model is simplified by applying FGP approach, and a compromised solution to the initial model is obtained. An algorithm, flowchart and example are also given at the end to explain the study of the proposed model.

关键词： alpha-cut set BL-MO optimization model fuzzy programming Fully quadratic fractional programming

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Optimal platform design with modularity strategy under fuzzy environment

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SOFT COMPUTING 2019年第3期23卷 1059-1070页

作者： Song, Qinyu Ni, Yaodong Univ Int Business & Econ Sch Informat Technol & Management Beijing 100029 Peoples R China

Platform has been known as an effective strategy for trading off between product customization and economies of scale, and firms have paid more and more attention to designing an effective and efficient product platform. In platform designing, modularity strategy is usually adopted and new modules are introduced to maintain the variety of products and flexibility of the platform. However, production costs and failure rates of new modules are usually uncertain due to the lack of historical data. Besides, the values of some key parameters in platform design, such as cost saving from designing a modular platform and demand quantity of the products, are also often vague. In this paper, we study the problem of designing a product platform with modularity strategy under fuzzy environment. By characterizing the cost saving from designing a modular platform, the demand quantity of the products and the parameters representing economies of scale and product quality improvement as fuzzy variables, we formulate three fuzzy programming models. An efficient algorithm combining fuzzy simulation and simulated annealing is proposed to solve the models. Numerical experiments are conducted to show the performance of the algorithm.

关键词： Platform design Platform modularity Credibility theory fuzzy programming Simulated annealing

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Using mixed goal programming to optimize performance of extrusion process for multiple responses of irrigation pipes

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART E-JOURNAL OF PROCESS MECHANICAL ENGINEERING 2019年第2期233卷 412-424页

作者： Al-Refaie, Abbas Musallam, Ahmad Univ Jordan Dept Ind Engn Amman Jordan

The performance of the polyethylene extrusion process used in the plastic industry was optimized using mixed goal programming. Four responses, the roll weight, production cycle time, distance between emitters, and thickness, are crucial. After a combination of initial factor settings was determined, individual and moving range control charts were established for each response. Two-phase optimization was implemented using L-18 and L-9 arrays for conducting experiments. A two-phase fuzzy goal programming model was formulated and employed to determine the combination of optimal factor settings, which was used to perform experiments. The results showed a significant reduction in the average production time from 13.0 to 11.316 min. Moreover, the average respective relative percentages of variability reduction for the roll weight, production cycle time, distance between emitters, and thickness were 48.547%, 49.048%, 47.174%, and 63.704%, respectively, and the corresponding estimated process capability indices for the combination of initial (optimal) factor settings were 0.202 (1.440), 0.330 (0.914), and 0.460 (1.456). Such improvement results in significant reduction in quality costs.

关键词： fuzzy programming extrusion process process capability multiple responses

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Multi-objective multi-item fixed-charge solid transportation problem under twofold uncertainty

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NEURAL COMPUTING & APPLICATIONS 2019年第12期31卷 8593-8613页

作者： Roy, Sankar Kumar Midya, Sudipta Weber, Gerhard-Wilhelm Vidyasagar Univ Dept Appl Math Oceanol & Comp Programming Midnapore 721102 W Bengal India Middle East Tech Univ Inst Appl Math Ankara Turkey

In this paper, we investigate a multi-objective multi-item fixed-charge solid transportation problem (MOMIFCSTP) with fuzzy-rough variables as coefficients of the objective functions and of the constraints. The main focus of the paper is to analyze MOMIFCSTP under a fuzzy-rough environment for a transporting system. In practical situations, the parameters of a MOMIFCSTP are imprecise in nature, due to several uncontrollable factors. For these reasons, we introduce the fuzzy-rough variables in MOMIFCSTP to tackle vague data which are different from fuzziness and roughness. fuzzy-rough expected-value operator is employed to convert fuzzy-rough MOMIFCSTP into deterministic MOMIFCSTP. Thereafter, we develop a methodology to solve the deterministic MOMIFCSTP by technique for order preference by similarity to ideal solution (TOPSIS). Three distinct approaches, namely extended TOPSIS, weighted goal programming (WGP) and fuzzy programming, are used to derive Pareto-optimal solution from the suggested model. A comparison is drawn among the optimal solutions which are derived from different approaches. It is observed from the extracted results that TOPSIS provides a better optimal solution than WGP and fuzzy programming. TOPSIS also overcomes some difficulties which arise in WGP. Finally, a real-world (industrial) problem is incorporated to show the applicability and feasibility of the proposed problem.

关键词： Fixed-charge solid transportation problem Multi-objective programming fuzzy-rough variable Twofold uncertainty TOPSIS fuzzy programming Weighted goal programming

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A bi-level multi-objective data envelopment analysis model for estimating profit and operational efficiency of bank branches

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RAIRO-OPERATIONS RESEARCH 2019年第5期53卷 1633-1648页

作者： Omrani, Hashem Mohammadi, Setareh Emrouznejad, Ali Urmia Univ Technol Fac Ind Engn Orumiyeh Iran Aston Univ Aston Business Sch Birmingham W Midlands England

Data Envelopment Analysis (DEA) is a powerful method for analyzing the performance of decision making units (DMUs). Traditionally, DEA is applied for estimating the performance of a set of DMUs through measuring a single perspective of efficiency. However, in recent years, due to increasing competition in various industries, modern enterprises focus on enhancing their performance by measuring efficiencies in different aspects, separately or simultaneously. This paper proposes a bi-level multi-objective DEA (BLMO DEA) model which is able to assess the performance of DMUs in two different hierarchical dimensions, simultaneously. In the proposed model, we define two level efficiency scores for each DMU. The aim is to maximize these two efficiencies, simultaneously, for each DMU. Since the objective functions at both levels are fractional, a fuzzy fractional goal programming (FGP) methodology is used to solve the proposed BLMO DEA model. The capability of the proposed model is illustrated by a numerical example. Finally, to practically validate the proposed model, a real case study from 45 bank's branches is applied. The results show that the proposed model can provide a more comprehensive measure for efficiency of each bank's branch based on simultaneous measuring of two different efficiencies, profit and operational efficiencies, and by considering the level of their importance.

关键词： Data envelopment analysis (DEA) bi-level programming fuzzy programming bank efficiency

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A novel meta-heuristic approach to solve fuzzy multi-objective straight and U-shaped assembly line balancing problems

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SOFT COMPUTING 2019年第17期23卷 8217-8245页

作者： Babazadeh, Hossein Javadian, Nikbakhsh Univ Sci & Technol Dept Ind Engn Tehran Iran Mazandaran Univ Sci & Technol Dept Ind Engn Babol Sar Iran

The consideration of this study is devoted to deal with the straight and U-shaped assembly line balancing problems (ALBPs). The ALBP involves allocation of required tasks to a set of workstations, so that objective functions being optimized are subjected to set of constraint. While many efforts have been dedicated in the literature to develop deterministic model of the assembly line, the attention is not considerably paid to those in uncertain circumstances. In this paper, along with proposing a novel fuzzy model for ALBP, triangular fuzzy numbers are deployed with to respect vagueness and uncertainty subjected to the task processing times. For this purpose, two conflicting objectives are considered simultaneously with regard to set of constraints, so that the efficiency of the line has to be maximized. To solve the problem, a modified NSGA-II, which utilized a new repairing mechanism, is proposed in response to the need of appropriate method treating such complicated problems. The validity of the proposed model and algorithm is evaluated and proved though a benchmark test problem. The obtained results reveal that in contrast to benchmark that applied an exact solution procedure, the proposed algorithm is capable of delivering the astonishing solutions in a more effective procedure. Along with the use of NSGA-II, in this study, three well-known meta-heuristic algorithms, namely PESA-II, NSACO and NPGA-II, are also employed for solving the problem in order to evaluate the effectiveness of the proposed algorithm, so that the results demonstrate the high performance for the NSGA-II over them. Finally, in light of the obtained results, this study offers an efficient framework enabling the decision maker to handle uncertainty in ALBPs along with the use of an efficient algorithm to solve them.

关键词： Multi-objective optimization Assembly line balancing fuzzy programming NSGA-II algorithm Repairing mechanism

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Generalized fuzzy linear programming for decision making under uncertainty: Feasibility of fuzzy solutions and solving approach

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INFORMATION SCIENCES 2013年 241卷 12-27页

作者： Fan, Y. R. Huang, G. H. Yang, A. L. Univ Regina Fac Engn Regina SK S4S 0A2 Canada North China Elect Power Univ SC Resources & Environm Res Acad MOE Key Lab Reg Energy Syst Optimizat Beijing 102206 Peoples R China

In this study, a generalized fuzzy linear programming (GFLP) method is developed for dealing with uncertainties expressed as fuzzy sets. The feasibility of fuzzy solutions of the GFLP problem is investigated. A stepwise interactive algorithm (SIA) based on the idea of design of experiment is then advanced to solve the GFLP problem. This SIA method was implemented through (i) discretizing membership grade of fuzzy parameters into a finite number of alpha-cut levels, (ii) converting the GFLP model into an interval linear programming (ILP) submodel under every alpha-cut level, (iii) solving the ILP submodels through an interactive algorithm and obtaining the associated interval solutions, (iv) acquiring the membership functions of fuzzy solutions through statistical regression methods. A simple numerical example is then proposed to illustrate the solution process of the GFLP model through SIA. A comparison between the solutions obtained though SIA and Monte Carlo method is finally conducted to demonstrate the robustness of the SIA method. The results indicate that the membership functions for decision variables and objective function are reasonable and robust. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Decision making fuzzy programming fuzzy sets Optimization Monte Carlo Uncertainty

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A fuzzy Logic Based Approach to Solve Interval Multiobjective Nonlinear Transportation Problem

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PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES 2019年第2期89卷 279-289页

作者： Dalman, Hasan Sivri, Mustafa Istanbul Gelisim Univ Dept Comp Engn Istanbul Turkey Yildiz Tech Univ Dept Math Engn Istanbul Turkey

This paper presents the solution procedure of multiobjective nonlinear transportation problem (MNOTP) where the cost coefficients of the objective functions, and the supply and the unknown demand parameters have been formulated as interval numbers by the decision maker. This problem has been converted into a conventional MNOTP where to minimize the interval nonlinear objective functions, the order relations that define the choice between intervals have been determined by the interval arithmetic. Also, the constraints with interval supply and unknown demand parameters have been transformed into its deterministic forms. Then the deterministic problems have been solved by two compromise programming methods. Finally, a numerical example is presented to illustrate the efficiency of the proposed procedure as well.

关键词： fuzzy programming Interval numbers Transportation problem Multiobjective programming Nonlinear programming

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A multi-objective robust possibilistic model for technology portfolio optimization considering social impact and different types of financing

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APPLIED SOFT COMPUTING 2020年 86卷

作者： Shaverdi, Marzieh Yaghoubi, Saeed Ensafian, Hamidreza Iran Univ Sci & Technol Sch Progress Engn Tehran Iran Iran Univ Sci & Technol Sch Ind Engn Tehran Iran

With respect to limited financial resources, prioritization of technology fields in order to be supported financially is a matter of paramount significance that governmental organizations, such as "Technology Development Funds (TDFs)", face with. Innovation and technology development, as the cornerstone of the economic development of countries, requires making decisions in terms of assigning the best-suited form of financial resources mainly by governments. Accordingly, this study addresses a multi-objective portfolio optimization problem in a multi-period setting with the aim of maximizing the created jobs - as a key factor in social welfare - as well as intended profit while minimizing the risk of inappropriate portfolio selection. To formulate the proposed mathematical model, different financing methods, technology readiness levels (TRL), and return on investment (ROI) associated with each technological project are taken into account. Afterward, to deal with the uncertainty arisen from fuzzy parameters, the Multi-Objective Robust Possibilistic programming approach (MORPP) is applied, the performance of which is examined under several computational tests. Finally, to illustrate the performance of the proposed model and its applicability in practice, the computational results are shown through a real case study in Iran Innovation & Prosperity Fund (IIPF). The results show that selecting small and medium-sized enterprises (SMEs) for being financed, is the best option when increasing job creation is considered in portfolio optimization. Furthermore, the comparison of the MORPP model results with the deterministic model shows that the solutions obtained from the robust possibilistic approach outweighed the deterministic model. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Technology portfolio selection Financial resource allocation Multi-objective robust possibilistic programming fuzzy programming Augmented epsilon-constraint

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Uncertain location-allocation decisions for a bi-objective two-stage supply chain network design problem with environmental impacts

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EXPERT SYSTEMS 2020年第5期37卷 e12558-e12558页

作者： Mahmoodirad, Ali Niroomand, Sadegh Islamic Azad Univ Masjed Soleiman Branch Dept Math Masjed Soleiman Iran Firouzabad Inst Higher Educ Dept Ind Engn Firuzabad Fars Iran

In the cases that the historical data of an uncertain event is not available, belief degree-based uncertainty theory is a useful tool to reflect such uncertainty. This study focuses on uncertain bi-objective supply chain network design problem with cost and environmental impacts under uncertainty. As such network may be designed for the first time in a geographical region, this problem is modelled by the concepts of belief degree-based uncertainty theory. This article is almost the first study on belief degree-based uncertain supply chain network design problem with environmental impacts. Two approaches such as expected value model and chance-constrained model are applied to convert the proposed uncertain problem to its crisp form. The obtained crisp forms are solved by some multi-objective optimization approaches of the literature such as TH, Niroomand, MMNV. A deep computational study with several test problems are performed to study the performance of the crisp models and the solution approaches. According to the results, the obtained crisp formulations are highly sensitive to the changes in the value of the cost parameters. On the other hand, Niroomand and MMNV solution approaches perform better than other solution approaches from the solution quality point of view.

关键词： environmental impact fuzzy programming multi-objective optimization supply chain network design problem uncertainty theory

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