Multi-follower tri-level decision making with uncooperative followers

© 2014 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. Multi-follower tri-level (MFTL) decision making addresses compromises among three interacting decision units within a hierarchical system of which multiple followers are involved in two lower-level units. The leader’s decision is affected not only by reactions of the followers but also by various relationships among them. The uncooperative relationship is the most basic situation in MFTL decision cases where multiple followers at the same level make individual decisions without any information exchange or share among them. To support such a MFTL decision, this paper firstly proposes a general model for the decision problem and then develops an extreme-point search algorithm based on bi-level Kth-Best approach to solve the model. Finally, a numerical experiment illustrates the decision model and procedures of the extreme-point search algorithm

A fuzzy tri-level decision making algorithm and its application in supply chain

In this paper, we develop a fuzzy tri-level decision making (FTLDM) model to deal with decentralized decision making problems with three levels of decision makers. Based on the -cut of fuzzy set, we transform an FTLDM problem into a multiobjective tri-level decision making problem. Based on the linear tri-level Kth-best algorithm, the global optimal solution can be obtained. A case study for third-party logistics decision making in supply chain is utilized to illustrate the effectiveness of the proposed algorithm. © 2013. The authors-Published by Atlantis Press

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

Olving tri-level linear programming problem by a novel hybrid algorithm

This paper presents a revised hybrid algorithm to solve a tri-level linear programming problem, a generalization of a bi-level one, involving three decision makers at the upper, middle, and lower levels. The decision-making priority is from top to bottom and the decision of each decision maker affects the decision space of others. A hybrid algorithm has been already proposed to solve this problem, but it does not ensure to converge whereas the proposed novel revised algorithm lacks this drawback and ensures convergence.Publisher's Versio

Solving tri-level programming problems using a particle swarm optimization algorithm

© 2015 IEEE. Tri-level programming, a special case of multilevel programming, arises to deal with decentralized decision-making problems that feature interacting decision entities distributed throughout three hierarchical levels. As tri-level programming problems are strongly NP-hard and the existing solution approaches lack universality in solving such problems, the purpose of this study is to propose an intelligence-based heuristic algorithm to solve tri-level programming problems involving linear and nonlinear versions. In this paper, we first propose a general tri-level programming problem and discuss related theoretical properties. A particle swarm optimization (PSO) algorithm is then developed to solve the tri-level programming problem. Lastly, a numerical example is adopted to illustrate the effectiveness of the proposed PSO algorithm

Synthesis, Interdiction, and Protection of Layered Networks

This research developed the foundation, theory, and framework for a set of analysis techniques to assist decision makers in analyzing questions regarding the synthesis, interdiction, and protection of infrastructure networks. This includes extension of traditional network interdiction to directly model nodal interdiction; new techniques to identify potential targets in social networks based on extensions of shortest path network interdiction; extension of traditional network interdiction to include layered network formulations; and develops models/techniques to design robust layered networks while considering trade-offs with cost. These approaches identify the maximum protection/disruption possible across layered networks with limited resources, find the most robust layered network design possible given the budget limitations while ensuring that the demands are met, include traditional social network analysis, and incorporate new techniques to model the interdiction of nodes and edges throughout the formulations. In addition, the importance and effects of multiple optimal solutions for these (and similar) models is investigated. All the models developed are demonstrated on notional examples and were tested on a range of sample problem sets

A solution to bi/tri-level programming problems using particle swarm optimization

© 2016 Elsevier Inc. Multilevel (including bi-level and tri-level) programming aims to solve decentralized decision-making problems that feature interactive decision entities distributed throughout a hierarchical organization. Since the multilevel programming problem is strongly NP-hard and traditional exact algorithmic approaches lack efficiency, heuristics-based particle swarm optimization (PSO) algorithms have been used to generate an alternative for solving such problems. However, the existing PSO algorithms are limited to solving linear or small-scale bi-level programming problems. This paper first develops a novel bi-level PSO algorithm to solve general bi-level programs involving nonlinear and large-scale problems. It then proposes a tri-level PSO algorithm for handling tri-level programming problems that are more challenging than bi-level programs and have not been well solved by existing algorithms. For the sake of exploring the algorithms' performance, the proposed bi/tri-level PSO algorithms are applied to solve 62 benchmark problems and 810 large-scale problems which are randomly constructed. The computational results and comparison with other algorithms clearly illustrate the effectiveness of the proposed PSO algorithms in solving bi-level and tri-level programming problems

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

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

A mixed-integer approximation of robust optimization problems with mixed-integer adjustments

In the present article we propose a mixed-integer approximation of adjustable-robust optimization (ARO) problems, that have both, continuous and discrete variables on the lowest level. As these trilevel problems are notoriously hard to solve, we restrict ourselves to weakly-connected instances. Our approach allows us to approximate, and in some cases exactly represent, the trilevel problem as a single-level mixed-integer problem. This allows us to leverage the computational efficiency of state-of-the-art mixed-integer programming solvers. We demonstrate the value of this approach by applying it to the optimization of power systems, particularly to the control of smart converters.Comment: 17 pages, 4 figure