Game theoretic optimisation in process and energy systems engineering: A review

Game theory is a framework that has been used by various research fields in order to represent dynamic correlation among stakeholders. Traditionally, research within the process and energy systems engineering community has focused on the development of centralised decision making schemes. In the recent years, decentralised decision-making schemes have attracted increasing attention due to their ability to capture multi-stakeholder dynamics in a more accurate manner. In this article, we survey how centralised and decentralised decision making has been facilitated by game theoretic approaches. We focus on the deployment of such methods in process systems engineering problems and review applications related to supply chain optimisation problems, design and operations, and energy systems optimisation. Finally, we analyse different game structures based on the degree of cooperation and how fairness criteria can be employed to find fair payoff allocations

Multi-parametric programming : novel theory and algorithmic developments

Imperial Users onl

Bilevel optimisation with embedded neural networks: Application to scheduling and control integration

Scheduling problems requires to explicitly account for control considerations in their optimisation. The literature proposes two traditional ways to solve this integrated problem: hierarchical and monolithic. The monolithic approach ignores the control level's objective and incorporates it as a constraint into the upper level at the cost of suboptimality. The hierarchical approach requires solving a mathematically complex bilevel problem with the scheduling acting as the leader and control as the follower. The linking variables between both levels belong to a small subset of scheduling and control decision variables. For this subset of variables, data-driven surrogate models have been used to learn follower responses to different leader decisions. In this work, we propose to use ReLU neural networks for the control level. Consequently, the bilevel problem is collapsed into a single-level MILP that is still able to account for the control level's objective. This single-level MILP reformulation is compared with the monolithic approach and benchmarked against embedding a nonlinear expression of the neural networks into the optimisation. Moreover, a neural network is used to predict control level feasibility. The case studies involve batch reactor and sequential batch process scheduling problems. The proposed methodology finds optimal solutions while largely outperforming both approaches in terms of computational time. Additionally, due to well-developed MILP solvers, adding ReLU neural networks in a MILP form marginally impacts the computational time. The solution's error due to prediction accuracy is correlated with the neural network training error. Overall, we expose how - by using an existing big-M reformulation and being careful about integrating machine learning and optimisation pipelines - we can more efficiently solve the bilevel scheduling-control problem with high accuracy.Comment: 18 page

A reformulation strategy for mixed-integer linear bi-level programming problems

Bi-level programming has been used widely to model interactions between hierarchical decision-making problems, and their solution is challenging, especially when the lower-level problem contains discrete decisions. The solution of such mixed-integer linear bi-level problems typically need decomposition, approximation or heuristic-based strategies which either require high computational effort or cannot guarantee a global optimal solution. To overcome these issues, this paper proposes a two-step reformulation strategy in which the first part consists of reformulating the inner mixed-integer problem into a nonlinear one, while in the second step the well-known Karush-Kuhn-Tucker conditions for the nonlinear problem are formulated. This results in a mixed-integer nonlinear problem that can be solved with a global optimiser. The computational and numerical benefits of the proposed reformulation strategy are demonstrated by solving five examples from the literature

Modeling and Robust Design of Networks under Risk: The Case of Information Infrastructure

Study of network risks allows to develop insights into the methods of building robust networks, which are also critical elements of infrastructures that are of a paramount importance for the modern society. In this paper we show how the modern quantitative modeling methodologies can be employed for analysis of network risks and for design of robust networks under uncertainty. This is done on the example of important problem arising in the process of building of the information infrastructure: provision of advanced mobile data services. We show how portfolio theory developed in the modern finance can be used for design of robust provision network comprising of independent agents. After this the modeling frameworks of Bayesian nets andMarkov fields are used for the study of several problems fundamental for the process of service adoption such as the sensitivity of networks, the direction of improvements, and the propagation of user attitudes on social networks

Management, Technology and Learning for Individuals, Organisations and Society in Turbulent Environments

This book presents the collection of fifty papers which were presented in the Second International Conference on BUSINESS SUSTAINABILITY 2011 - Management, Technology and Learning for Individuals, Organisations and Society in Turbulent Environments , held in Póvoa de Varzim, Portugal, from 22ndto 24thof June, 2011.The main motive of the meeting was growing awareness of the importance of the sustainability issue. This importance had emerged from the growing uncertainty of the market behaviour that leads to the characterization of the market, i.e. environment, as turbulent. Actually, the characterization of the environment as uncertain and turbulent reflects the fact that the traditional technocratic and/or socio-technical approaches cannot effectively and efficiently lead with the present situation. In other words, the rise of the sustainability issue means the quest for new instruments to deal with uncertainty and/or turbulence. The sustainability issue has a complex nature and solutions are sought in a wide range of domains and instruments to achieve and manage it. The domains range from environmental sustainability (referring to natural environment) through organisational and business sustainability towards social sustainability. Concerning the instruments for sustainability, they range from traditional engineering and management methodologies towards “soft” instruments such as knowledge, learning, and creativity. The papers in this book address virtually whole sustainability problems space in a greater or lesser extent. However, although the uncertainty and/or turbulence, or in other words the dynamic properties, come from coupling of management, technology, learning, individuals, organisations and society, meaning that everything is at the same time effect and cause, we wanted to put the emphasis on business with the intention to address primarily companies and their businesses. Due to this reason, the main title of the book is “Business Sustainability 2.0” but with the approach of coupling Management, Technology and Learning for individuals, organisations and society in Turbulent Environments. Also, the notation“2.0” is to promote the publication as a step further from our previous publication – “Business Sustainability I” – as would be for a new version of software. Concerning the Second International Conference on BUSINESS SUSTAINABILITY, its particularity was that it had served primarily as a learning environment in which the papers published in this book were the ground for further individual and collective growth in understanding and perception of sustainability and capacity for building new instruments for business sustainability. In that respect, the methodology of the conference work was basically dialogical, meaning promoting dialog on the papers, but also including formal paper presentations. In this way, the conference presented a rich space for satisfying different authors’ and participants’ needs. Additionally, promoting the widest and global learning environment and participation, in accordance with the Conference's assumed mission to promote Proactive Generative Collaborative Learning, the Conference Organisation shares/puts open to the community the papers presented in this book, as well as the papers presented on the previous Conference(s). These papers can be accessed from the conference webpage (http://labve.dps.uminho.pt/bs11). In these terms, this book could also be understood as a complementary instrument to the Conference authors’ and participants’, but also to the wider readerships’ interested in the sustainability issues. The book brought together 107 authors from 11 countries, namely from Australia, Belgium, Brazil, Canada, France, Germany, Italy, Portugal, Serbia, Switzerland, and United States of America. The authors “ranged” from senior and renowned scientists to young researchers providing a rich and learning environment. At the end, the editors hope, and would like, that this book to be useful, meeting the expectation of the authors and wider readership and serving for enhancing the individual and collective learning, and to incentive further scientific development and creation of new papers. Also, the editors would use this opportunity to announce the intention to continue with new editions of the conference and subsequent editions of accompanying books on the subject of BUSINESS SUSTAINABILITY, the third of which is planned for year 2013.info:eu-repo/semantics/publishedVersio

Inventory control in supply chains: Alternative approaches to a two-stage lot-sizing problem

The principal challenge of inventory control in supply chains is that the interacting autonomous enterprises have to plan their production and logistics under information asymmetry, driven by different, often conflicting objectives. In this paper, four different computational approaches are investigated to cope with this challenge: decomposition, integration, coordination, and bilevel programming. The four approaches are applied to solving the same two-stage economic lot-sizing problem, and compared in computational experiments. The prerequisites of the approaches are analyzed, and it is shown that the profits realized and the costs incurred at the different parties largely depend on the solution approach applied. This research also resulted in a novel coordination mechanism, as well as a new algorithm for the bilevel optimization approach to the investigated lot-sizing problem. A specific goal of this study is to highlight the so far less recognized application potential of the coordination and the bilevel optimization approaches for controlling inventories in a supply chain. © 2012 Elsevier B.V. All rights reserved

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