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

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

Tri-level Multi-follower Decision Making

© Springer-Verlag Berlin Heidelberg 2015. In a tri-level hierarchical decision problem, each decision entity at one level has its objective, constraints and decision variables affected in part by the decision entities at the other two levels. The choice of values for its variables may allow it to influence the decisions made at other levels, and thereby improve its own objective. We called this a tri-level decision problem. When multiple decision entities are involved at the middle and bottom levels, the top-level entity’s decision will be affected not only by these followers’ individual reactions but also by the relationships among the followers. We call this problem a tri-level multi-follower (TLMF) decision

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 for supply chain management

University of Technology Sydney. Faculty of Engineering and Information Technology.Multilevel decision-making techniques aim to handle decentralized decision problems that feature multiple decision entities distributed throughout a hierarchical organization. Decision entities at the upper level and the lower level are respectively termed the leader and the follower. Three challenges have appeared in the current developments in multilevel decision-making: (1) large-scale - multilevel decision problems become large-scale owing to high-dimensional decision variables; (2) uncertainty - uncertain information makes related decision parameters and conditions imprecisely or ambiguously known to decision entities; (3) diversification – multiple decision entities that have a variety of relationships with one another may exist at each decision level. However, existing decision models or solution approaches cannot completely and effectively handle these large-scale, uncertain and diversified multilevel decision problems. To overcome these three challenges, this thesis addresses theoretical techniques for handling three categories of unsolved multilevel decision problems and applies the proposed techniques to deal with real-world problems in supply chain management (SCM). First, the thesis presents a heuristics-based particle swarm optimization (PSO) algorithm for solving large-scale nonlinear bi-level decision problems and then extends the bi-level PSO algorithm to solve tri-level decision problems. Second, based on a commonly used fuzzy number ranking method, the thesis develops a compromise-based PSO algorithm for solving fuzzy nonlinear bi-level decision problems. Third, to handle tri-level decision problems with multiple followers at the middle and bottom levels, the thesis provides different tri-level multi-follower (TLMF) decision models to describe various relationships between multiple followers and develops a TLMF Kth-Best algorithm; moreover, an evaluation method based on fuzzy programming is proposed to assess the satisfaction of decision entities towards the obtained solution. Lastly, these proposed multilevel decision-making techniques are applied to handle decentralized production and inventory operational problems in SCM

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

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

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

Multi-parametric programming : novel theory and algorithmic developments

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