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Solving intuitionistic fuzzy multi-objective linear programming problem and its application in supply chain management

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APPLICATIONS OF MATHEMATICS 2023年第3期68卷 269-287页

作者： Hassanpour, Hassan Hosseinzadeh, Elham Moodi, Mahsa Univ Birjand Dept Math Birjand *** Iran Kosar Univ Bojnord Imam Hassan Hosp Dept Math Arkan Rd Bojnord *** Iran

The aim of this paper is solving an intuitionistic fuzzy multi-objective linear programming problem containing intuitionistic fuzzy parameters, intuitionistic fuzzy maximization/minimization, and intuitionistic fuzzy constraints. To do this, a linear ranking function is used to convert the intuitionistic fuzzy parameters to crisp ones first. Then, linear membership and non-membership functions are used to manipulate intuitionistic fuzzy maximization/minimization and intuitionistic fuzzy constraints. Then, a multi-objective optimization problem is formulated containing maximization of membership functions and minimization of non-membership functions. To solve this problem, the minimax and weighted sum methods are used. Then, the described procedure is summarized as an algorithm to solve the problem, and a numerical example is solved by the proposed method. Finally, to investigate the capability and performance of the model, a supplier selection problem, which is one of the important applications in supply chain management, is solved by the proposed algorithm.

关键词： multi-objective linear programming intuitionistic fuzzy set accuracy function membership function non-membership function supplier selection

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A decentralized coordination algorithm for multi-objective linear programming with block angular structure

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ENGINEERING OPTIMIZATION 2021年第2期53卷 185-205页

作者： Okpoti, Evans Sowah Jeong, In-Jae Hanyang Univ Dept Ind Engn Seoul South Korea

This article considers linear multi-objective programming problems with block angular structure, which are analogous to multi-disciplinary optimization environments where disciplines must collaborate to achieve a common overall goal. In this decentralized environment, a mechanism to guide locally optimized decision makers' solutions to a Pareto-optimal solution without sharing the entire local information is developed. The mechanism is based on an augmented Lagrangian approach to generate a solution and is separated into two phases: phase I determines an ideal point for each of the single objectives and phase II searches for a compromise solution starting from a single ideal point. Theoretical results show that the algorithm converges and the solution generated is Pareto optimal. The algorithm's effectiveness is demonstrated via an illustrative example and a real-world bi-objective re-entrant flow-shop production planning problem. The real-world experimental results showed that the decentralized method had an average 50% better performance compared to other centralized methods.

关键词： Collaborative optimization decentralized coordination multi-objective linear programming block angular structure multi-agent

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Assignment model with multi-objective linear programming for allocating choice ranking using recurrent neural network

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RAIRO-OPERATIONS RESEARCH 2021年第5期55卷 3107-3119页

作者： Mirzazadeh, Zahra Sadat Hassan, Javad Bani Mansoori, Amin Ferdowsi Univ Mashhad Fac Sport Sci Mashhad Razavi Khorasan Iran Ferdowsi Univ Mashhad Dept Appl Math Mashhad Razavi Khorasan Iran

Classic linear assignment method is a multi-criteria decision-making approach in which criteria are weighted and each rank is assigned to a choice. In this study, to abandon the requirement of calculating the weight of criteria and use decision attributes prioritizing and also to be able to assign a rank to more than one choice, a multi-objective linear programming (MOLP) method is suggested. The objective function of MOLP is defined for each attribute and MOLP is solved based on absolute priority and comprehensive criteria methods. For solving the linear programming problems we apply a recurrent neural network (RNN). Indeed, the Lyapunov stability of the proposed model is proved. Results of comparing the proposed method with TOPSIS, VICOR, and MORA methods which are the most common multi-criteria decision schemes show that the proposed approach is more compatible with these methods.

关键词： linear assignment method multi-objective linear programming multi-attribute decision-making absolute prioritizing method recurrent neural networks stable in the sense of Lyapunov

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A multi-objective linear programming model for scheduling part families and designing a group layout in cellular manufacturing systems

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COMPUTERS & OPERATIONS RESEARCH 2023年 151卷

作者： Motahari, Rasool Alavifar, Zeinolabedin Andaryan, Abdullah Zareh Chipulu, Maxwell Saberi, Morteza Iran Univ Sci & Technol Sch Ind Engn Tehran Iran Iran Univ Sci & Technol Sch Railway Engn Tehran Iran Edinburgh Napier Univ Business Sch Edinburgh Midlothian Scotland Univ Technol Sydney Sch Comp Sci Sydney NSW Australia

Different industries compete to attract customers in different ways. In the field of production, group technology (GT) is defined by identifying and grouping similar parts based on their similarities in design and production. Cellular manufacturing (CM) is an application of GT to reconfigure the factory and job shop design. A manufacturing cell is a group of independent machines with different functions put together to produce a family of parts. Designing a cellular manufacturing system involves three major decisions: cell formation (CF), group layout (GL), and group scheduling (GS). Although these decisions are interrelated and can affect each other, they have been considered separately or sequentially in previous research. In this paper, CF, GL, and GS decisions are considered simultaneously. Accordingly, a multi-objective linear programming (MOLP) model is proposed to optimize weighted completion time, transportation cost, and machine idle time for a multi-product system. Finally, the model will be solved using the epsilon-constraint method, representing different scales solutions for decision-making. The proposed model is NP-hard. Therefore, a nondominated sorting genetic algorithm II (NSGA-II) is presented to solve it since GAMS software is unable to find optimal solutions for large-scale problems. Besides, to evaluate the performance of NSGA-II, the problem is solved by three metaheuristic algorithms.

关键词： Group technology Cell formation Group scheduling Group layout Cellular manufacturing system multi-objective linear programming

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A fuzzy approach for the intuitionistic multi-objective linear fractional programming problem using a bisection method

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2025年第2期49卷 1-24页

作者： Kara, Nurdan Kocken, Hale Gonce Akdemir, Hande Gunay Natl Def Univ TR-34334 Istanbul Turkiye Yildiz Tech Univ Dept Math Engn TR-34220 Istanbul Turkiye Giresun Univ Dept Math TR-28200 Giresun Turkiye

In this paper, intuitionistic fuzzy multi-objective linear fractional programming problems (IFMOLFPs) with several fractional criteria, including profit/cost, profit/time, or profitability ratio maximization, are considered. Moreover, all parameters, with the exception of the decision variables, are characterized as triangular intuitionistic fuzzy numbers. The component-wise optimization method is employed to transform IFMOLFP into an equivalent crisp multi-objective linear fractional problem. Then, we use an iterative fuzzy methodology that integrates linear programming with a bisection approach. The proposed approach addresses single-objective and real-life multi-objective organizational planning problems, which are approached using various methods in the literature. It is used for non-linear membership functions in solving these problems. Furthermore, the values obtained using the ranking function are compared. Ultimately, the decision-maker selects the most appropriate solution technique based on the weights of the objective functions.

关键词： multi-objective linear programming Fractional programming Fuzzy programming Intuitionistic fuzzy number Bisection method Membership function

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Electromagnetic Signal Classification Based on Class Exemplar Selection and multi-objective linear programming

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REMOTE SENSING 2022年第5期14卷 1177-1177页

作者： Zhou, Huaji Bai, Jing Niu, Linchun Xu, Jie Xiao, Zhu Zheng, Shilian Jiao, Licheng Yang, Xiaoniu Xidian Univ Sch Artificial Intelligence Xian 710071 Peoples R China Sci & Technol Commun Informat Secur Control Lab Jiaxing 314033 Peoples R China Hunan Univ Coll Comp Sci & Elect Engn Changsha 410082 Peoples R China

In the increasingly complex electromagnetic environment, a variety of new signal types are appearing;however, existing electromagnetic signal classification (ESC) models cannot handle new signal types. In this context, the emergence of class-incremental learning aims to incrementally update the classification model as new categories emerge. In this paper, an electromagnetic signal classification framework based on class exemplar selection and a multi-objective linear programming classifier (CES-MOLPC) is proposed in order to continuously learn new classes in an incremental manner. Specifically, our approach involves the adaptive selection of class exemplars considering normalized mutual information and a multi-objective linear programming classifier. The former is used to maintain the classification capability of the model for previous categories by selecting key samples, while the latter is used to allow the model to adapt quickly to new categories. Meanwhile, a weighted loss function based on cross-entropy and distillation loss is presented in order to fine-tune the model. We demonstrate the effectiveness of the proposed CES-MOLPC method through extensive experiments on the public RML2016.04c data set and the large-scale real-world ACARS signal data set. The results of the comparative experiments demonstrate that our method can achieve significant improvements over state-of-the-art methods.

关键词： class incremental learning electromagnetic signal classification deep learning multi-objective linear programming class exemplar selection normalized mutual information

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Optimization of hydraulic fracturing wastewater management alternatives: A hybrid multi-objective linear programming model

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JOURNAL OF CLEANER PRODUCTION 2021年 286卷 124950-124950页

作者： Shamloo, Nazila Bakhtavar, Ezzeddin Hewage, Kasun Sadiq, Rehan Univ British Columbia Sch Engn Okanagan Campus Kelowna BC V1V 1V7 Canada Urmia Univ Technol Fac Min & Mat Engn Band Rd Orumiyeh *** Iran

Production of high volumes of wastewater by hydraulic fracturing operations is a challenging issue in the unconventional gas industry in North America. A scheduling-based solution is required to optimally manage the produced wastewater. This study develops a novel, hybrid, multi-objective linear programming model to optimize hydraulic fracturing wastewater management alternatives. Minimizing overall wastewater treatment cost, environmental impacts, and undesirable deviations from different goals were simultaneously considered the main objectives of the system. The model used data from a case example operating for 31 weeks, and it determined the volume of wastewater and treated water over all periods. The results indicated that onsite treatment is the best possible alternative for reuse in subsequent fracking, in those weeks in which all constraints were satisfied. Offsite treatment was the second ranking alternative when the volume of wastewater was higher than the capacity of onsite treatment, and deep well injection was the result when no water was needed for subsequent fracking. A sensitivity analysis was conducted by weighting the objectives to express their importance levels. Compared to other objectives, environmental impact had greater effect on the selection of the optimal alternatives over each period. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Hydraulic fracturing Wastewater management Treatment multi-objective linear programming Goal programming

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Inverse optimization for multi-objective linear programming

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OPTIMIZATION LETTERS 2019年第2期13卷 281-294页

作者： Naghavi, Mostafa Foroughi, Ali Asghar Zarepisheh, Masoud Univ Qom Dept Math Qom Iran Mem Sloan Kettering Canc Ctr Dept Med Phys New York NY 10021 USA

This paper generalizes inverse optimization for multi-objective linear programming where we are looking for the least problem modifications to make a given feasible solution a weak efficient solution. This is a natural extension of inverse optimization for single-objective linear programming with regular optimality replaced by the Pareto optimality. This extension, however, leads to a non-convex optimization problem. We prove some special characteristics of the problem, allowing us to solve the non-convex problem by solving a series of convex problems.

关键词： multi-objective linear programming linear programming Inverse optimization Efficiency

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A novel grey multi-objective binary linear programming model for risk assessment in supply chain management

Supply Chain Analytics

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Supply Chain Analytics 2023年 2卷

作者： Vafadarnikjoo, Amin Moktadir, Md. Abdul Paul, Sanjoy Kumar Ali, Syed Mithun Sheffield University Management School The University of Sheffield Conduit Rd Sheffield S10 1FL United Kingdom Institute of Leather Engineering and Technology University of Dhaka Dhaka Bangladesh UTS Business School University of Technology Sydney Sydney Australia Department of Industrial and Production Engineering Bangladesh University of Engineering and Technology Dhaka 1000 Bangladesh

Robust and resilient agri-food supply chain management (AFSCM) is paramount to agribusinesses, given the many challenges and risks that this increased demand will bring in the coming decades. Interruptions caused by various risks to this crucial supply chain network, particularly in emerging economies, can put the lives of millions in danger, not to mention creating devastating impacts on the economy and the environment. Even so, there are only a limited number of quantitative risk management studies in the AFSCM literature. In this study, an integrated modified risk mitigation matrix (M-RMM) is developed to analyze the mitigation strategies for dealing with various risks in the context of the agri-food supply chain. The M-RMM is integrated with the grey multi-objective binary linear programming (GMOBLP) model to obtain the optimal risk mitigation strategies related to the three objective functions of risk, cost, and time minimization. The proposed model is a useful tool for formulating sustainable business policies and reducing food waste, and acquiring a context-specific (i.e., a developing economy), sector-specific (i.e., the agri-food processing sector), and multi-product (i.e., fresh and non-perishable) approach. The findings reveal that continuous training and development and vulnerability analysis of IT systems are the most effective risk mitigation strategies to lessen the impacts of lack of skilled personnel, sub-standard leadership, failure in IT systems, insufficient capacity to produce quality products, and poor customer relationships. The findings assist practitioners in managing risks in supply chains. © 2023 The Authors

关键词： Agri-food supply chain Best-worst method Grey theory multi-objective linear programming Risk mitigation Supply chain management

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Grey-fuzzy solution for multi-objective linear programming with interval coefficients

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GREY SYSTEMS-THEORY AND APPLICATION 2018年第3期8卷 312-327页

作者： Mahmoudi, Amin Feylizadeh, Mohammad Reza Darvishi, Davood Liu, Sifeng Islamic Azad Univ Shiraz Branch Dept Ind Engn Shiraz Iran Payame Noor Univ Dept Basic Sci Math Tehran Iran Nanjing Univ Aeronaut & Astronaut Inst Grey Syst Studies Nanjing Jiangsu Peoples R China

Purpose The purpose of this paper is to propose a method for solving multi-objective linear programming (MOLP) with interval coefficients using positioned programming and interactive fuzzy programming approaches. Design/methodology/approach In the proposed algorithm, first, lower and upper bounds of each objective function in its feasible region will be determined. Afterwards using fuzzy approach, considering a membership function for each objective function and finally using grey linear programming, the solution for this problem will be obtained. Findings According to the presented example, in this paper, the proposed method is both simple in use and suitable for solving different problems. In the numerical example mentioned in this paper, the proposed method provides an acceptable solution for such problems. Practical implications As in most real-world situations, the coefficients of decision models are not known and exact. In this paper, the authors consider the model of MOLP with interval data, since one of the solutions to cover uncertainty is using interval theory. Originality/value Based on using grey theory and interactive fuzzy programming approaches, an appropriate method has been presented for solving MOLP problems with interval coefficients. The proposed method, against the complex methods, has less effort and offers acceptable solutions.

关键词： Grey linear programming Grey system Interactive fuzzy programming approach Interval coefficient multi-objective linear programming

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