Development of a method to identify problems of a bilevel nature within different engineering applications

Abstract

Problems of bilevel nature are inextricably linked to decentralized problems involving multiple decision-making typically with multiple objectives, as are those characterized by Nash equilibrium and variations of the Pareto optimization. These problems are to be found within a wide array of seemingly disparate engineering topics ranging from multi-disciplinary complex system design to multi-echelon decentralized inventory planning. Due to the potential for different forms of decision-making (i.e. cooperative, non-cooperative or sequential) to manifest within problems of decentralized settings, there exists regardless of the field of interest a need to determine the exact nature of such problems with respect to the type of decision-making present. This thesis enquires into the issues associated with identifying the form of decision-making that is in line with the bilevel nature and subsequently describes a method to potentially identify such problems within the decentralized setting. To formally define the identification process of a bilevel nature unfettered to any particular field of interest, a general approach based on complex systems was adopted. Four topics in engineering where bilevel problems have been clearly established, as evident from literature review, namely: i) the multi-disciplinary complex system design, ii) the transport network design, iii) the decentralized capacitated plant selection and, iv) the multi-echelon decentralized inventory planning problems were scrutinized to form the bulk of the area of study. In order to consolidate different events of bilevel problems across the different areas of interest, characteristics defined within the framework of complex systems that are unique to the decision-making process (i.e. Pareto, Nash and Stackelberg/bilevel) were identified. These then form the basis for the method developed to identify the bilevel problem.