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SCALARIZATION IN VECTOR OPTIMIZATION

MATHEMATICAL programming 1984年第2期29卷 203-218页

作者： JAHN, J Fachbereich Mathematik TH Darmstadt 6100 Darmstadt Federal Republic Germany

In this paper some scalar optimization problems are presented whose optimal solutions are also solutions of a general vector optimization problem. This will be done for weakly minimal and minimal solutions, respective... 详细信息

关键词： Vector Optimization multi-objective programming Approximation

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Optimizing over the properly efficient set of convex multi-objective optimization problems

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ANNALS OF OPERATIONS RESEARCH 2020年第2期295卷 575-604页

作者： Ghazli, Kahina Gillis, Nicolas Moulai, Mustapha Fac Math USTHB LaROMad Algiers Algeria Univ Bejaia Bejaia Algeria Univ Mons Fac Polytech Dept Math & Operat Res Mons Belgium

Optimizing over the efficient set of a multi-objective optimization problem is among the difficult problems in global optimization because of its nonconvexity, even in the linear case. In this paper, we consider only properly efficient solutions which are characterized through weighted sum scalarization. We propose a numerical method to tackle this problem when the objective functions and the feasible set of the multi-objective optimization problem are convex. This algorithm penalizes progressively iterates that are not properly efficient and uses a sequence of convex nonlinear subproblems that can be solved efficiently. The proposed algorithm is shown to perform well on a set of standard problems from the literature, as it allows to obtain optimal solutions in all cases.

关键词： multi-objective programming Convex optimization Properly efficient set Penalty approach

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multi-criteria decision making approach for supplier selection and order allocation in a digital supply chain resilience

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ANNALS OF OPERATIONS RESEARCH 2024年 1-37页

作者： Fang, Jiaqi Zhou, Wenli Xiong, Lihui Wenzhou Univ Sch Business Wenzhou 325035 Zhejiang Peoples R China

The emergence of strong strategic sourcing and globalization has increased the sensitivity of supply chains to disruption, especially for technology companies. Supplier selection and order Allocation (SS-OA) has become a key strategic decision in high-quality supply chain planning and management. This paper builds a data-driven framework and, through a systematic literature review and interviews with management, establishes an evaluation system that integrates economic, resilience, and digital criteria. The adaptability and performance of suppliers were evaluated by AHP and TOPSIS. On this basis, a dual-objective order optimization model is established to optimize the value of flexible digital procurement and reduce related costs. Integrating the supplier selection criteria of the enterprise, the non-dominant sorting genetic algorithm in the meta-heuristic algorithm is used to solve the Pareto optimal solution set. This method provides decision support for supplier selection and order allocation in the supply chain, and promotes the sustainable development of enterprises.

关键词： Supply chain resilience multi-objective programming Supplier selection AHP TOPSIS NSGA-II

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A simulated multi-objective model for flexible job shop transportation scheduling

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ANNALS OF OPERATIONS RESEARCH 2022年第2期311卷 899-920页

作者： Xu, Yiyi Sahnoun, M'hammed Ben Abdelaziz, Fouad Baudry, David CESI LINEACT Lab 80 Rue Edmund Halley Rouen Madrillet Innovat F-76800 St Etienne Du Rouvray France Neoma Business Sch 1 Rue Marchal Juin F-76130 Mont St Aignan France

This paper proposes a new dynamic algorithm based on simulation approach and multi-objective optimization to solve the FJSP with transportation assignment. The objectives considered in scheduling jobs and transportation tasks in a flexible job shop manufacturing system include makespan, robot travel distance, time difference with due date and critical waiting time. The results obtained from the computational experiments have shown that the proposed approach is efficient and competitive.

关键词： Flexible job shop scheduling multi-objective programming Simulation multi-agent systems Transportation

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A class of generalized invex functions and vector variational-like inequalities

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2017年第1期2017卷 70页

作者： Li, Ru Yu, Guolin Beifang Univ Nationalities Inst Appl Math Ningxia 750021 Yinchuan Peoples R China

In this paper, a class of generalized invex functions, called (a,.,.)-invex functions, is introduced, and some examples are presented to illustrate their existence. Then we consider the relationships of solutions between two types of vector variational-like inequalities and multi-objective programming problem. Finally, the existence results for the discussed variational-like inequalities are proposed by using the KKM-Fan theorem.

关键词： vector variational-like inequality multi-objective programming invex function KKM-Fan theorem

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Solving multi-objective integer indefinite quadratic fractional programs

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ANNALS OF OPERATIONS RESEARCH 2021年第1-2期296卷 821-840页

作者： Mekhilef, Amal Moulai, Mustapha Drici, Wassila USTHB Fac Math Dept Operat Res BP 32 Algiers 16111 Algeria USTHB Fac Math LaROMaD Lab BP 32 Algiers 16111 Algeria

In this paper, we describe an exact algorithm for solving a multi-objective integer indefinite quadratic fractional maximization problem. The algorithm generates the whole set of efficient solutions of the above mentioned problem. We optimize at first one of the objective functions in the original feasible region;in an iterative way and through the introduction of auxiliary constraints (efficient cut or branching constraint), the same objective function is optimized over progressively restricted or separated parts of the original feasible region, each time we get a candidate solution for non dominated solution, the efficient set is updated, the process ends when there is no unexplored parts of the original domain. The proposed method is based on an efficient cut which allows to reduce the feasible set avoiding non efficient solutions, the simplex like algorithm to solve a mono objective quadratic fractional maximization problem, and the classical branch and bound technique for integer decision variables. We establish theoretical results which prove the effectiveness of this new exact method, for illustration, numerical experiments are reported.

关键词： multi-objective programming Integer programming Quadratic programming Fractional programming Efficient cut Branch and cut

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Applying Nonlinear MODM Model to Supply Chain Management with Quantity Discount Policy under Complex Fuzzy Environment

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JOURNAL OF INDUSTRIAL ENGINEERING AND MANAGEMENT-JIEM 2014年第3期7卷 660-680页

作者： Zhang, Zhe Xu, Jiuping Nanjing Univ Sci & Technol Sch Econ & Management Nanjing Jiangsu Peoples R China Sichuan Univ Uncertainty Decis Making Lab Chengdu Sichuan Peoples R China

Purpose: The aim of this paper is to deal with the supply chain management (SCM) with quantity discount policy under the complex fuzzy environment, which is characterized as the bifuzzy variables. By taking into account the strategy and the process of decision making, a bifuzzy nonlinear multiple objective decision making (MODM) model is presented to solve the proposed problem. Design/methodology/approach: The bi-fuzzy variables in the MODM model are transformed into the trapezoidal fuzzy variables by the DMs's degree of optimism a 1 and a 2, which are de-fuzzified by the expected value index subsequently. For solving the complex nonlinear model, a multi-objective adaptive particle swarm optimization algorithm (MO-APSO) is designed as the solution method. Findings: The proposed model and algorithm are applied to a typical example of SCM problem to illustrate the effectiveness. Based on the sensitivity analysis of the results, the bifuzzy nonlinear MODM SCM model is proved to be sensitive to the possibility level alpha(1). Practical implications: The study focuses on the SCM under complex fuzzy environment in SCM, which has a great practical significance. Therefore, the bi-fuzzy MODM model and MO-APSO can be further applied in SCM problem with quantity discount policy. Originality/value: The bi-fuzzy variable is employed in the nonlinear MODM model of SCM to characterize the hybrid uncertain environment, and this work is original. In addition, the hybrid crisp approach is proposed to transferred to model to an equivalent crisp one by the DMs's degree of optimism and the expected value index. Since the MODM model consider the bi-fuzzy environment and quantity discount policy, so this paper has a great practical significance.

关键词： bi-fuzzy variable nonlinear multi-objective programming sensitivity analysis particle swarm optimization

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Integrated blood supply chain planning for disaster relief

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INTERNATIONAL JOURNAL OF DISASTER RISK REDUCTION 2018年 27卷 168-188页

作者： Samani, Mohammad Reza Ghatreh Torabi, S. Ali Hosseini-Motlagh, Seyyed-Mandi Iran Univ Sci & Technol Sch Ind Engn Univ Ave Tehran 16846 Iran Univ Tehran Sch Ind Engn Coll Engn Tehran Iran

This paper proposes a multi-objective mixed integer linear programming model for the design of an integrated blood supply chain network for disaster relief. The developed model accounts for all the special aspects of blood supply chains involving uncertain demand of blood products and their irregular supply, perishability of blood products and shortage avoidance. It also provides a trade-off analysis between the cost efficiency (via minimizing the total costs), responsiveness (through minimizing the maximum unsatisfied demand) and effectiveness of the designed network (by minimizing the time span between blood production in regional blood centers and consumption in demand zones so that their freshness is preserved). A hybrid framework based on the two-stage stochastic programming and possibilistic programming approaches is devised to deal with a mixture of random and epistemic uncertainties. Some numerical experiments are conducted to validate the proposed model and its solution approach. Also, a real case study is presented to demonstrate the practicality of the proposed model. Helpful managerial insights are also provided through conducting a number of sensitivity analyses.

关键词： Blood supply chain Disaster relief multi-objective programming Two-stage stochastic programming Possibilistic programming

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Fuzzy multi-objective vendor selection under lean procurement

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2012年第2期219卷 305-311页

作者： Yu, Min-Chun Goh, Mark Lin, Hung-Chung Natl Kaohsiung Univ Appl Sci Dept Business Adm Kaohsiung 807 Taiwan Natl Univ Singapore Dept Decis Sci Singapore 117548 Singapore Univ S Australia Sch Management Adelaide SA 5001 Australia

This paper investigates a fuzzy multi-objective vendor selection program under lean procurement based on cost minimization, delivery schedule violation minimization, and maximizing the quality level of the purchased quantity. Specifically, the paper incorporates the vendor production capacity uncertainty into the model to identify an appropriate selection policy for vendors under practical operating conditions. The use of a soft time-window mechanism for the vendor selection model enables decision makers to further incorporate a time based performance metric for vendor evaluation, based on the degree of urgency or need for a part. A solution algorithm using fuzzy AHP is proposed. The results of a numerical example suggest that decision makers prefer vendors who can promise tighter delivery schedules rather than on cost or quality. A sensitivity analysis of the soft time-window on the achievement of the lean procurement objectives is also conducted. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Vendor selection Lean procurement Fuzzy multi-objective programming Soft time window

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Vehicle routing problem with fuzzy time windows

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FUZZY SETS AND SYSTEMS 2009年第5期160卷 683-695页

作者： Tang, Jiafu Pan, Zhendong Fung, Richard Y. K. Lau, Henry Northeastern Univ Dept Syst Engn Key Lab Integrated Automat Proc Ind MOE Shenyang 110004 Peoples R China City Univ Hong Kong Dept Mfg Engn & Engn Management Kowloon Hong Kong Peoples R China Hong Kong Polytech Univ Dept Ind & Syst Engn Kowloon Hong Kong Peoples R China

In this paper, a vehicle routing problem with fuzzy time windows (VRPFTW) is proposed and solved. In the transportation business, time windows are not always strictly obeyed and the deviation of service time from the customer-specific time window determines the customer's satisfaction level, which can also be regarded as the Supplier's service level. This paper applies fuzzy membership functions to characterize the service level issues associated with time window violation in a vehicle routing problem and propose VRPFTW. VRPFTW is formulated as a multi-objective model with two goals: (I) to minimize the travel distance and (2) to maximize the service level of the supplier to customers. To solve this multi-objective model, a two stage algorithm is developed to obtain a Pareto solution for VRPFTW. Using the two-stage algorithm, VRPFTW is decomposed into two subproblems, namely a traditional vehicle routing problem with time windows (VRPTW-alpha) and a service improvement problem,and each of the objective, is sequentially solved. The service improvement problem is solved under two different scenarios. When the fuzzy membership function is linear, it is shown that the service improvement problem can be solved by the cutting plane algorithm within finite iterations, and when the fuzzy membership function is concave, the service improvement problem can be solved by a subgradient-based algorithm. Moreover, an alternative formulation of VRPFTW is also proposed and analyzed. Experiments are conducted to compare different models of vehicle routing problems with time windows in situations where violation of time windows is allowed, and the results show that the VRPFTW model can achieve considerable cost-savings, while at the same time maintaining an acceptable service level. Published by Elsevier B.V.

关键词： Vehicle routing problem (VRP) Time windows Service level Fuzzy constraints multi-objective programming

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