Recent supply chain disruptions and crisis response policies (e.g., the COVID-19 pandemic and the Red Sea crisis) have highlighted the role of container terminals as crucial and scarce resources in the global economy. To tackle these challenges, the industry increasingly aims for advanced operational collaboration among multiple stakeholders, as demonstrated by the ambitions of the recently founded Gemini alliance. Nonetheless, collaborative planning models often disregard the requirements and incentives of stakeholders or simply solve idealized small instances. Motivated by the above, we design novel and effective collaboration mechanisms among terminal operators that share the resources (berths and quay cranes). We first define the collaborative berth allocation problem and propose a mixed integer linear programming (MILP) model to minimize the total cost of all terminals, referred to as the coalitional costs. We adopt the core and the nucleolus concepts from cooperative game theory to allocate the coalitional costs such that stakeholders have stable incentives to collaborate. To obtain solutions for realistic instance sizes, we propose two exact row-generation-based core and nucleolus algorithms that are versatile and can be used for various combinatorial optimization problems. To the best of our knowledge, the proposed row-generation approach for the nucleolus is the first of its kind for combinatorial optimization problems. Extensive experiments demonstrate that the collaborative berth allocation approach achieves up to 28.44% of cost savings, increasing the solution space in disruptive situations, while the proposed core and nucleolus solutions guarantee the collaboration incentives for individual terminals.

Berth allocation is fundamental to port-related operations in maritime shipping. Port managers have to deal with the increasing demands either by expanding the terminals or by improving efficiency to maintain competitiveness. Port expansion is a long-term project, and it requires much capital investment. Thus, the question of how to enhance the efficiency of berth allocation has received much research interest. Research on the Berth Allocation Problem (BAP) in container ports is quite advanced. However, only limited research focuses on BAP in bulk ports, although some similarities exist. Contributing to Operations Research approaches on the BAP, this paper develops a hybrid BAP mixed-integer optimization model dedicated to bulk ports. In addition to considering the handling characteristics of bulk ports, we also incorporate more practical factors such as unavailability and stock levels. The objective of the proposed model is to minimize the demurrage fee for all vessels under consideration of unavailability and stock constraints. We use the commercial software CPLEX to obtain the optimal solutions for a set of distinct instances, explicitly considering the situation of multiple cargo types on one vessel, which provides a better fit for the loading or discharging operations in real-world bulk ports. This is the first study to our knowledge that dedicates itself to the BAP in bulk ports and considers unavailability and stock constraints simultaneously. Our solutions can provide timely and effective decision support to bulk port managers.