An extended kth-best approach for referential-uncooperative bilevel multi-follower decision making

Bilevel decision techniques have been mainly developed for solving decentralized management problems with decision makers in a hierarchical organization. When multiple followers are involved in a bilevel decision problem, called a bilevel multi-follower (BLMF) decision problem, the leader's decision will be affected, not only by the reactions of these followers, but also by the relationships among these followers. The referential-uncooperative situation is one of the popular cases of BLMF decision problems where these multiple followers don't share decision variables with each other but may take others' decisions as references to their decisions. This paper presents a model for the referential-uncooperative BLMF decision problem. As the kth-best approach is one of the most successful approaches in dealing with normal bilevel decision problems, this paper then proposes an extended kth-best approach to solve the referential-uncooperative BLMF problem. Finally an example of logistics planning illustrates the application of the proposed extended kth-best approach

An analytics-based heuristic decomposition of a bilevel multiple-follower cutting stock problem

This paper presents a new class of multiple-follower bilevel problems and a heuristic approach to solving them. In this new class of problems, the followers may be nonlinear, do not share constraints or variables, and are at most weakly constrained. This allows the leader variables to be partitioned among the followers. We show that current approaches for solving multiple-follower problems are unsuitable for our new class of problems and instead we propose a novel analytics-based heuristic decomposition approach. This approach uses Monte Carlo simulation and k-medoids clustering to reduce the bilevel problem to a single level, which can then be solved using integer programming techniques. The examples presented show that our approach produces better solutions and scales up better than the other approaches in the literature. Furthermore, for large problems, we combine our approach with the use of self-organising maps in place of k-medoids clustering, which significantly reduces the clustering times. Finally, we apply our approach to a real-life cutting stock problem. Here a forest harvesting problem is reformulated as a multiple-follower bilevel problem and solved using our approachThis publication has emanated from research conducted with the financial support of Science Foundation Ireland (SFI) under Grant Number SFI/12/RC/228

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

Big data based intelligent decision support system for sustainable regional development

Timely intelligent decision making is increasingly important for modern society. With the availability of big data and advanced artificial intelligence in decision making, more objective and evidence-based quantitative smart decisions can be made in a timely manner. This research proposed a big data based intelligent decision support system (B-IDSS) for sustainable business development. The system can be used by both the government agencies and corporate business (e.g. farms. mining) in advanced planning, collaboration and management. This paper also addresses the performance optimization as bilevel decision-making problem with one leader and multiple followers. An extended Kuhn-Tucker approach is introduced as one of the algorithms that can be adapted in the system

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

A bi-level decision model for customer churn analysis

This paper develops a bi-level decision model and a solution approach to optimizing service features for a company to reduce its customer churn rate. First, a bi-level decision model, together with its modeling approach, are developed to describe the gaming relationship between decision makers in a company (service provider) and its customers. Then, a practical solution approach to reaching solutions for the bi-level-modeled customer churn problem is developed. Finally, experiments and case studies are conducted to illustrate the bi-level decision model and the solution approach. © 2013 Wiley Periodicals, Inc

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

An extended branch and bound algorithm for bilevel multi-follower decision making in a referential-uncooperative situation

Within the framework of any bilevel decision problem, a leader's decision at the upper level is influenced by the reaction of their follower at the lower level. When multiple followers are involved in a bilevel decision problem, the leader's decision will not only be affected by the reactions of those followers, but also by the relationships among those followers. One of the popular situations within this framework is where these followers are uncooperatively making decisions while having cross reference of decision information, called a referential-uncooperative situation in this paper. The well-known branch and bound algorithm has been successfully applied to a one-leader-and-one-follower linear bilevel decision problem. This paper extends this algorithm to deal with the abovementioned linear bilevel multi-follower decision problem by means of a linear referential-uncooperative bilevel multi-follower decision model. It then proposes an extended branch and bound algorithm to solve this problem with a set of illustrative examples in a referential-uncooperative situation. © World Scientific Publishing Company