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Uncertain random multilevel programming with application to production control problem

SOFT COMPUTING 2015年第6期19卷 1739-1746页

作者： Ke, Hua Su, Taoyong Ni, Yaodong Tongji Univ Sch Econ & Management Shanghai 200092 Peoples R China Univ Int Business & Econ Sch Informat Technol & Management Beijing 100029 Peoples R China

For modeling decentralized decision-making problems with uncertain random parameters, an uncertain random multilevel programming is proposed. For some special case, an equivalent crisp mathematical programming to the established uncertain random programming is presented. A searching method by integrating uncertain random simulations, neural network, and genetic algorithm is produced to search the quasi-optimal solution under some decision-making criterion. Finally, the proposed uncertain random multilevel programming is applied to a production control problem.

关键词： multilevel programming Uncertain random programming Uncertain programming Uncertainty theory

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Interactive multilevel programming approaches in neutrosophic environments

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JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING 2022年第4期13卷 2143-2159页

作者： Luo, Suizhi Pedrycz, Witold Xing, Lining Natl Univ Def Technol Coll Syst Engn Changsha 410073 Peoples R China Univ Alberta Dept Elect & Comp Engn Edmonton AB T6R 2G7 Canada

multilevel programming is a mathematical programming problem with hierarchical structure. A typical feature of multilevel programming is that the upper level exhibits a priority over the lower level. However, the solutions obtained by most existing programming methods either violate this rule or ignore the participants' desire for a win-win outcome. The objective of this study is to propose new multilevel programming approaches for obtaining desirable solutions. First, three types of membership functions in neutrosophic set are defined to comprehensively describe fuzzy cognition of decision makers. Then, considering dissimilar intentions of experts, three different interactive approaches are proposed to solve multilevel programming problems. To demonstrate the feasibility of the proposed approaches, a case of pricing decision-making of data products is investigated and the impacts of four key parameters are discussed. Finally, several numerical examples are studied by using the proposed approaches and other existing methods. Two evaluation indexes, the equilibrium coefficient and distance measure, are utilized to appraise the performance of the developed programming methods. The results demonstrate that the proposed approaches can obtain sound solutions which obey the rule of multilevel programming, realize the mutual benefits of participants, and can provide guidelines for the pricing of satellite image data products.

关键词： Interactive approach multilevel programming Neutrosophic set theory Pricing decision-making

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Interactive intuitionistic fuzzy methods for multilevel programming problems

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EXPERT SYSTEMS WITH APPLICATIONS 2017年 72卷 258-268页

作者： Zhao, Xiaoke Zheng, Yue Wan, Zhongping Wuhan Univ Sch Math & Stat Wuhan 430072 Peoples R China Huaibei Normal Univ Sch Management Huaibei 235000 Peoples R China Wuhan Univ Computat Sci Hubei Key Lab Wuhan 430072 Peoples R China

multilevel programming problems model a decision-making process with a hierarchy structure. Traditional solution methods including vertex enumeration algorithms and penalty function methods are not only inefficient,to obtain the solution of the multilevel programming problems, but also lead to a paradox that the follower's decision power dominates the leader's. In this paper, both multilevel programming and intuitionistic fuzzy set are used to model problems in hierarchy expert and intelligent systems. We first present a score function to objectively depict the satisfactory degrees of decision makers by virtue of the intuitionistic fuzzy set for solving multilevel programming problems. Then we develop three optimization models and three interactive intuitionistic fuzzy methods to consider different satisfactory solutions for the requirements of expert decision makers. Furthermore, a new distance function is proposed to measure the merits of a satisfactory solution. Finally, a case study for cloud computing pricing problems and several numerical examples are given to verify the applicability and the effectiveness of the proposed models and methods. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： multilevel programming Interactive intuitionistic fuzzy method Satisfactory solution Decision making

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Optimality conditions and geometric properties of a linear multilevel programming problem with dominated objective functions

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2004年第2期123卷 409-429页

作者： Ruan, GZ Wang, SY Yamamoto, Y Zhu, SS Xiangtan Univ Dept Math Xiangtan Hunan Peoples R China Chinese Acad Sci Inst Syst Sci Acad Math & Syst Sci Beijing Peoples R China Hunan Univ Sch Business Adm Changsha Hunan Peoples R China Univ Tsukuba Inst Policy & Planning Sci Tsukuba Ibaraki 305 Japan Fudan Univ Sch Management Dept Management Sci Shanghai 200433 Peoples R China

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD( l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD( l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems.

关键词： bilevel programming multilevel programming upper semicontinuity connectedness

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ON THE STRUCTURE AND PROPERTIES OF A LINEAR multilevel programming PROBLEM

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1989年第3期60卷 353-373页

作者： BENSON, HP College of Business Administration University of Florida Gainesville

Many decision-making situations involve multiple planners with different, and sometimes conflicting, objective functions. One type of model that has been suggested to represent such situations is the linear multilevel programming problem. However, it appears that theoretical and algorithmic results for linear multilevel programming have been limited, to date, to the bounded case or the case of when only two levels exist. In this paper, we investigate the structure and properties of a linear multilevel programming problem that may be unbounded. We study the geometry of the problem and its feasible region. We also give necessary and sufficient conditions for the problem to be unbounded, and we show how the problem is related to a certain parametric concave minimization problem. The algorithmic implications of the results are also discussed.

关键词： linear multilevel programming multilevel programming multiple-criteria decision making multistage optimization

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Derivation of A Mathematical Structure for Market-Based Transmission Augmentation in Oligopoly Electricity Markets using multilevel programming

Derivation of A Mathematical Structure for Market-Based Tran...

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General Meeting of the IEEE-Power-and-Energy-Society

作者： Hesamzadeh, M. R. Biggar, D. Hosseinzadeh, N. Wolfs, P. J. Swinburne Univ Technol Melbourne Vic Australia Cent Queensland Univ Fac Sci & Engn Rockhampton Qld 4702 Australia Australian Compitit & Consumer Comiss Canberra ACT Australia Australian Energy Regulator Melbourne Vic Australia

ISBN: (纸本)9781424442409

In this paper, we derive and evaluate a new mathematical structure for market-based augmentation of the transmission system. The closed-form mathematical structure can capture both the efficiency benefit and competition benefit of the transmission capacity. The Nash solution concept is employed to model the price-quantity game among GenCos. The multiple Nash equilibria of the game are located through a characterisation of the problem in terms of minima of the R function. The worst Nash equilibrium is used in the mechanism of transmission augmentation. The worst Nash equilibrium is defined as the one which maximises the social cost, total generation cost + total value of lost load. Thorough analysis of a simple three-node network is presented to clearly highlight the mechanism of the derived mathematical structure from different perspectives.

关键词： Transmission Augmentation Oligopoly Electricity Market multilevel programming

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A Fuzzy Goal programming Technique for Quadratic Multiobjective multilevel programming

A Fuzzy Goal Programming Technique for Quadratic Multiobject...

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IEEE International Conference on Fuzzy Systems (FUZZ)

作者： Biswas, Animesh Bose, Koushik Univ Kalyani Dept Math Kalyani 741235 W Bengal India

ISBN: (纸本)9781479900206

The purpose of this paper is to develop a fuzzy goal programming methodology for solving quadratic multiobjective multilevel programming problems in a hierarchical decision making environment. In the proposed procedure, the tolerance membership functions in fuzzy set theory are defined first for measuring the degree of satisfactions of the objectives of each decision maker at each level. Then a nonlinear fuzzy goal programming model is formulated to achieve highest degree of each of the defined membership goals at each level to the extent possible on the basis of priorities of importance of optimizing the objectives. Afterwards the nonlinear fuzzy goals are converted into linear forms by applying a linear approximation technique. The model is then solved for measuring the degree of satisfaction of the objectives of decision makers at each level by arriving at a compromise decision regarding the optimality of the sets of decision variables controlled individually by each of them. To illustrate the proposed methodology a numerical example is solved and compared the solution with existing approaches.

关键词： multilevel programming Quadratic programming Goal programming Fuzzy programming Fuzzy Goal programming Linear Approximation Technique

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Using Genetic Algorithm for Solving Linear multilevel programming Problems via Fuzzy Goal programming

Using Genetic Algorithm for Solving Linear Multilevel Progra...

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1st International Conference on Logic, Information, Control and Computation

作者： Pal, Bijay Baran Chakraborti, Debjani Biswas, Papun Univ Kalyani Dept Math Kalyani 741235 W Bengal India Narula Inst Technol Dept Math Kolkata 700109 W Bengal India JIS Coll Engn Dept Elect Engn Kalyani 741235 W Bengal India

ISBN: (纸本)9783642192623

This article presents a fuzzy goal programming (FGP) procedure for modeling and solving multilevel programming (MLP) problems by using genetic algorithm (GA) in a large hierarchical decision making system. In the proposed approach, an GA scheme is introduced first for searching of solutions at different stages and thereby solving the problem and making decision in the order of hierarchy of execution of decision powers of the decision makers (DMs) located at different hierarchical levels. In the proposed GA scheme, Roulette-wheel selection scheme, single point crossover and random mutation are adopted to search a satisfactory solution in the hierarchical decision system. To illustrate the potential use of the approach, a numerical example is solved.

关键词： multilevel programming Fuzzy programming Fuzzy Goal programming Goal programming Genetic Algorithm Membership Function

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On the Quasiconcave multilevel programming Problems

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2022年第3期39卷

作者： Sadeghi, H. Esmaeili, M. Shahid Chamran Univ Ahvaz Fac Math Sci & Comp Dept Math Ahvaz Iran

multilevel programming appears in many decision-making situations. Investigation of the main properties of quasiconcave multilevel programming (QCMP) problems, to date, is limited to bilevel programming (only two levels). In this paper, first, we present an extension of the properties of quasiconcave bilevel programming (QCBP) problems for the case when three levels exist. Then, by induction on n (the number of levels), we prove the existence of an extreme point of the polyhedral constraint region that solves the QCMP problem under given conditions. Ultimately, a number of numerical examples are illustrated to verify the results.

关键词： Extreme points trilevel programming multilevel programming quasiconcave functions optimal solutions

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Solving Multi-Objective multilevel programming problems using two-phase Intuitionistic Fuzzy Goal programming method

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JOURNAL OF COMPUTATIONAL SCIENCE 2022年 63卷

作者： Mollalign, Demmelash Mushi, Allen Guta, Berhanu Addis Ababa Univ Dept Appl Math Addis Ababa Ethiopia Univ Dares Salaam Dept Math Dar Es Salaam Tanzania

This paper presents a two-phase intuitionistic fuzzy goal programming (two-phase IFGP) algorithm to solve Multi-Objective multilevel programming (MO-MLP) problems. The coefficient of each objective and constraint function is assumed to be triangular intuitionistic fuzzy parameters and the crisp MO-MLP problems are obtained using the accuracy function method. To avoid decision lock, the top levels set tolerance limits for decision variables to control the lower levels. The problem is modeled in the intuitionistic fuzzy environment using membership and non-membership functions for each objective function at all levels and decision variables controlled by the top levels. Then, we proposed an IFGP algorithm to achieve the highest degree of each membership and non-membership goal by minimizing unwanted deviational variables and generating compensatory solutions for all decision-makers at all levels. Moreover, in the proposed approach, two-phase IFGP is modeled to yield a compromise solution that satisfies both the MN-Pareto optimal solution and the Pareto optimal solution at each level. Also, verification of the proposed method is discussed with numerical examples.

关键词： Multi-objective programming multilevel programming Intuitionistic fuzzy goal programming Intuitionistic fuzzy decision set Two-phase model

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