Fuzzy Bi-level Decision-Making Techniques: A Survey

© 2016 the authors. Bi-level decision-making techniques aim to deal with decentralized management problems that feature interactive decision entities distributed throughout a bi-level hierarchy. A challenge in handling bi-level decision problems is that various uncertainties naturally appear in decision-making process. Significant efforts have been devoted that fuzzy set techniques can be used to effectively deal with uncertain issues in bi-level decision-making, known as fuzzy bi-level decision-making techniques, and researchers have successfully gained experience in this area. It is thus vital that an instructive review of current trends in this area should be conducted, not only of the theoretical research but also the practical developments. This paper systematically reviews up-to-date fuzzy bi-level decisionmaking techniques, including models, approaches, algorithms and systems. It also clusters related technique developments into four main categories: basic fuzzy bi-level decision-making, fuzzy bi-level decision-making with multiple optima, fuzzy random bi-level decision-making, and the applications of bi-level decision-making techniques in different domains. By providing state-of-the-art knowledge, this survey paper will directly support researchers and practitioners in their understanding of developments in theoretical research results and applications in relation to fuzzy bi-level decision-making techniques

Fuzzy multilevel programming with a hybrid intelligent algorithm

AbstractIn order to model fuzzy decentralized decision-making problem, fuzzy expected value multilevel programming and chance-constrained multilevel programming are introduced. Furthermore, fuzzy simulation, neural network, and genetic algorithm are integrated to produce a hybrid intelligent algorithm for finding the Stackelberg-Nash equilibrium. Finally, two numerical examples are provided to illustrate the effectiveness of the hybrid intelligent algorithm

A compromise-based particle swarm optimization algorithm for solving Bi-level programming problems with fuzzy parameters

© 2015 IEEE. Bi-level programming has arisen to handle decentralized decision-making problems that feature interactive decision entities distributed throughout a bi-level hierarchy. Fuzzy parameters often appear in such a problem in applications and this is called a fuzzy bi-level programming problem. Since the existing approaches lack universality in solving such problems, this study aims to develop a particle swarm optimization (PSO) algorithm to solve fuzzy bi-level programming problems in the linear and nonlinear versions. In this paper, we first present a general fuzzy bi-level programming problem and discuss related theoretical properties based on a fuzzy number ranking method commonly used. A PSO algorithm is then developed to solve the fuzzy bi-level programming problem based on different compromised selections by decision entities on the feasible degree for constraint conditions under fuzziness. Lastly, an illustrative numerical example and two benchmark examples are adopted to state the effectiveness of the compromise-based PSO algorithm

Fuzzy multi-objective bilevel decision making by an approximation Kth-best approach

Many industrial decisions problems are decentralized in which decision makers are arranged at two levels, called bilevel decision problems. Bilevel decision making may involve uncertain parameters which appear either in the objective functions or constraints of the leader or the follower or both. Furthermore, the leader and the follower may have multiple conflict decision objectives that should be optimized simultaneously. This study proposes an approximation K th-best approach to solve the fuzzy multi-objective bilevel problem. Two case based examples further illustrate how to use the approach to solve industrial decision problems

Stochastic Multilevel Programming with a Hybrid Intelligent Algorithm

A framework of stochastic multilevel programming is proposed for modelling decentralized decision-making problem in stochastic environment. According to different decision criteria, the stochastic decentralized decision-making problem is formulated as expected value multilevel programming, and chanceconstrained multilevel programming. In order to solve the proposed stochastic multilevel programming models for the Stackelberg-Nash equilibriums, genetic algorithms, neural networks and stochastic simulation are integrated to produce a hybrid intelligent algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the hybrid intelligent algorithm

A λ-cut and goal-programming-based algorithm for fuzzy-linear multiple-objective bilevel optimization

Bilevel-programming techniques are developed to handle decentralized problems with two-level decision makers, which are leaders and followers, who may have more than one objective to achieve. This paper proposes a λ-cut and goal-programming-based algorithm to solve fuzzy-linear multiple-objective bilevel (FLMOB) decision problems. First, based on the definition of a distance measure between two fuzzy vectors using λ-cut, a fuzzy-linear bilevel goal (FLBG) model is formatted, and related theorems are proved. Then, using a λ-cut for fuzzy coefficients and a goal-programming strategy for multiple objectives, a λ-cut and goal-programming-based algorithm to solve FLMOB decision problems is presented. A case study for a newsboy problem is adopted to illustrate the application and executing procedure of this algorithm. Finally, experiments are carried out to discuss and analyze the performance of this algorithm. © 2006 IEEE

Tri-level decision-making with multiple followers: Model, algorithm and case study

© 2015 Elsevier Inc. Tri-level decision-making arises to address compromises among interacting decision entities distributed throughout a three-level hierarchy; these entities are respectively termed the top-level leader, the middle-level follower and the bottom-level follower. This study considers an uncooperative situation where multiple followers at the same (middle or bottom) level make their individual decisions independently but consider the decision results of their counterparts as references through information exchanged among themselves. This situation is called a reference-based uncooperative multi-follower tri-level (MFTL) decision problem which appears in many real-world applications. To solve this problem, we need to find an optimal solution achieving both the Stackelberg equilibrium in the three-level vertical structure and the Nash equilibrium among multiple followers at the same horizontal level. In this paper, we first propose a general linear MFTL decision model for this situation. We then develop a MFTL Kth-Best algorithm to find an optimal solution to the model. Since the optimal solution means a compromised result in the uncooperative situation and it is often imprecise or ambiguous for decision entities to identify their related satisfaction, we use a fuzzy programming approach to characterize and evaluate the solution obtained. Lastly, a real-world case study on production-inventory planning illustrates the effectiveness of the proposed MFTL decision techniques

Multilevel decision-making: A survey

© 2016 Elsevier Inc. All rights reserved. Multilevel decision-making techniques aim to deal with decentralized management problems that feature interactive decision entities distributed throughout a multiple level hierarchy. Significant efforts have been devoted to understanding the fundamental concepts and developing diverse solution algorithms associated with multilevel decision-making by researchers in areas of both mathematics/computer science and business areas. Researchers have emphasized the importance of developing a range of multilevel decision-making techniques to handle a wide variety of management and optimization problems in real-world applications, and have successfully gained experience in this area. It is thus vital that a high quality, instructive review of current trends should be conducted, not only of the theoretical research results but also the practical developments in multilevel decision-making in business. This paper systematically reviews up-to-date multilevel decision-making techniques and clusters related technique developments into four main categories: bi-level decision-making (including multi-objective and multi-follower situations), tri-level decision-making, fuzzy multilevel decision-making, and the applications of these techniques in different domains. By providing state-of-the-art knowledge, this survey will directly support researchers and practical professionals in their understanding of developments in theoretical research results and applications in relation to multilevel decision-making techniques

Finding Optimal Strategies in a Multi-Period Multi-Leader-Follower Stackelberg Game Using an Evolutionary Algorithm

Stackelberg games are a classic example of bilevel optimization problems, which are often encountered in game theory and economics. These are complex problems with a hierarchical structure, where one optimization task is nested within the other. Despite a number of studies on handling bilevel optimization problems, these problems still remain a challenging territory, and existing methodologies are able to handle only simple problems with few variables under assumptions of continuity and differentiability. In this paper, we consider a special case of a multi-period multi-leader-follower Stackelberg competition model with non-linear cost and demand functions and discrete production variables. The model has potential applications, for instance in aircraft manufacturing industry, which is an oligopoly where a few giant firms enjoy a tremendous commitment power over the other smaller players. We solve cases with different number of leaders and followers, and show how the entrance or exit of a player affects the profits of the other players. In the presence of various model complexities, we use a computationally intensive nested evolutionary strategy to find an optimal solution for the model. The strategy is evaluated on a test-suite of bilevel problems, and it has been shown that the method is successful in handling difficult bilevel problems.Comment: To be published in Computers and Operations Researc