Bilevel optimization in maritime and port logistics: A review

Bilevel optimization is well-suited for modeling hierarchical decision processes involving two levels of decision-making. At the upper level, a leader controls a subset of variables that influence the lower-level problem, which is associated with a follower seeking to optimize their own objective function. Consequently, the follower's decisions affect the outcomes of the leader's problem. Given the involvement of numerous stakeholders in global trade, hierarchical planning decisions in the maritime and port industry can be effectively addressed using a bilevel optimization approach. This article reviews bilevel optimization problems in maritime and port logistics, focusing on three subcategories within maritime logistics (maritime freight transport, inland ports & waterways, and hinterland freight transport) and three subcategories within port logistics (seaside, yard, and landside). We identify research gaps and challenges in the existing literature and discuss promising avenues for further research. Key findings indicate a growing number of publications in recent years, reflecting the approach's ability to capture hierarchical and complex decision-making processes. However, more research is needed, especially in port logistics, where fewer contributions were found. Promising research avenues include the incorporation of multiple conflicting objectives, the development of tailored mathematical programming approaches, and the integration of uncertainty and resilience into optimization models. Research focused on sustainability, particularly on environmental goals and policy mechanisms for the reduction of emissions and the adoption of renewable fuels, remains essential, as do social considerations, which are currently underrepresented. Furthermore, more practical applications are needed to capture real-world operational characteristics and the complex interactions between hierarchical decision makers with conflicting objectives.