A Functional Mathematical Optimization Algorithm for the Integration of the Tactical Berth, Quay Crane and Vehicle Scheduling

In this paper, the main problem considered is a tactical discrete berth allocation, including both the quay mobile crane scheduling and vehicle dispatching as sub-problems. Berths, cranes and yard vehicles are the most important resources used in container terminals. The objective is to reduce the vessel turnaround times with fewer resources. We assume that the vessel's stowage plan and yard templates or their estimates are given. We integrate using functional decomposition, where sub-problems are solved sequentially and in parallel, resulting in more modifiable and detailed parameters to the main problem. We have chosen the sub-problems and their solution algorithms primarily so that they are mathematically proven to be optimal or have proven properties. Different techniques are utilized: mixed integer linear programming, max plus algebra, greedy algorithms, dynamic programming written in functional language and general algebraic modeling system. In addition, we extend the features of the sub-problems. While allocating the cranes, we use the concept of the quay crane profile. We reformulate the crane scheduling problem so that the mobile cranes can be heterogeneous, and there can be both quay and mobile cranes. Some features are optional: for example, double cycling and yard remarshaling. Alternatively, we can reduce the number of vehicles by deciding how we unload or load stacks. The study is motivated by the practical needs of Finnish port operators.