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

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

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

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

Multi-objective, multi-level, multi-stakeholder considerations for airport slot allocation

Airport slot scheduling has attracted the attention of researchers as a capacity management tool at congested airports. In an attempt to better grasp the demands of the problem, recent research work has employed multi-objective optimisation (MOO) approaches. However, the multiple stakeholders (e.g. airlines, coordinators, aviation and local authorities), their numerous or even conflicting objectives and the complexity of the decision-process (rules and slot priorities), have rendered the holistic modelling of the slot allocation problem a demanding and yet incomplete task. Through a rigorous review of the policy rules and the identification of the modelling gaps in the ΜΟΟ airport slot allocation literature, this study aims to contribute to the field by proposing novel modelling considerations and solution approaches which accommodate additional characteristics of the real-world decision context. In detail, by building on previous research efforts, we propose a tri-objective slot allocation model (TOSAM), which jointly considers schedule delays, maximum displacement and demand-based fairness. We further proved that multi-level, game-theoretic-based considerations are suitable to capture the interactions among the different slot priorities, leading to enhanced airport slot schedules. To address the incurring complexity, we introduced the notion of inter-level tolerance and solved the TOSAM with systematic multi-level interactions for a medium sized airport. Our computational results suggest that by tolerating small objective function sacrifices at the upper decision levels, the resulting Pareto frontiers are of greater cardinality and quality in comparison to existing solution methods. Finally, we propose and illustrate two alternative bi-stage solution methods that exemplify the potential synergies between the MOO and multi-attribute decision-making literature

EVALUATING WATER MANAGEMENT POLICY IN SAUDI ARABIA USING A BILEVEL, MULTI-OBJECTIVE, MULTI-FOLLOWER PROGRAMMING APPROACH

Over the past five decades, the Saudi government has adopted many agricultural policies aimed to: achieve self-sufficiency of food, increase the participation of the agricultural sector in the economy, and reduce the consumption of irrigation water. Due to conflicts among government objectives and the incompatibility of farmers\u27 objectives with those of some agricultural policies, the government has not been able to fully achieve its objectives. To accomplish its goals the government, or decision maker needs to understand the farmer, or follower, reaction when s/he adopts a new decision. The dissertation aims to build a model that achieves government goals of minimizing the total irrigation water used while improving the total revenue from agricultural production, while incorporating farmers’ objective of maximizing their profit. To do this, linear programming and bi-level multi-objective multi-follower models are developed and applied to six regions of Saudi Arabia, which account for around 70 percent of cropland and consume about 13.131 BCM of irrigation water per year. The result of the linear programming model applied to the Riyadh region shows there is an unobserved factor effect on the farmers’ decisions, including irrigation water demand that comes from the presence of indirect subsidies. On the other hand, the bi-level multi-objective, multi-follower model shows there is the possibility to minimize irrigation water consumption while maintaining current total revenue from crop production through reallocating irrigation water among regions, while applying a variety of crop specific tax and subsidy policies among the regions to alter planting decisions

Risk Hedging Strategies in New Energy Markets

In recent years, two typical developments have been witnessed in the energy market. On the one hand, the penetration of renewable generations has gradually replaced parts of the traditional ways to generate energy. The intermittent nature of renewable generation can lead to energy supply uncertainty, which might exacerbate the imbalance between energy supply and demand. As a result, the problem of energy price risks might occur. On the other hand, with the introduction of distributed energy resources (DERs), new categories of markets besides traditional wholesale and retail markets are emerging. The main benefits of the penetration of DERs are threefold. First, DERs can increase power system reliability. Second, the cost of transmission can be reduced. Third, end users can directly participate in some of these new types of markets according to their energy demand, excess energy, and cost function without third-party intervention. However, energy market participants might encounter various types of uncertainties. Therefore, it is necessary to develop proper risk-hedging strategies for different energy market participants in emerging new markets. Thus, we propose risk-hedging strategies that can be used to guide various market participants to hedge risks and enhance utilities in the new energy market. These participants can be categorized into the supply side and demand side. Regarding the wide range of hedging tools analyzed in this thesis, four main types of hedging strategies are developed, including the application of ESS, financial tools, DR management, and pricing strategy. Several benchmark test systems have been applied to demonstrate the effectiveness of the proposed risk-hedging strategies. Comparative studies of existing risk hedging approaches in the literature, where applicable, have also been conducted. The real applicability of the proposed approach has been verified by simulation results

Multifollower trilevel decision making models and system

In a trilevel hierarchical decision problem, the objectives and variables of each decision entity at one level are controlled, in part, by the decision entities at other levels. The choice of values for the decision variables at each level may influence the decisions made at other levels, and may thereby improve/reduce the objective for each level. When multiple decision entities are involved at the middle and bottom levels of a trilevel decision problem, the top-level entity's decision will be affected, not only by these followers' individual reactions, but also by the relationships between them. We call this problem a multifollower trilevel (MFTL) decision. This paper firstly defines and analyzes various kinds of relationships between decision entities in an MFTL decision problem. We then propose an MFTL decision making framework, in which 64 standard MFTL decision situations and their possible combinations are identified. To model these MFTL decision situations, we developed an innovative decision entity-relationship diagram (DERD) approach. We also established a general model for MFTL decision making and a set of standard MFTL decision models using trilevel programming. A trilevel decision support system (TLDSS) software has also been developed to transfer a DERD into a programming model. Finally, a case study illustrates typical MFTL decision making models and their development, using both DERD and programming approaches. © 2012 IEEE