The integrated problem of handling equipment scheduling and storage space allocation in container terminals is an important mixed-integer programming problem in maritime logistics whose computational performance is strongly affected by the structure of the mathematical formulation. This study develops and compares two approaches for modeling precedence relationships: a general sequencing approach and an equipment-dependent sequencing approach. In the general sequencing formulation, sequencing variables are defined independently of handling equipment, whereas in the equipment-dependent sequencing formulation these variables are explicitly associated with operational equipment.
Structural analysis shows that although both formulations have a similar order of growth for constraints, their main difference lies in the number of variables. Specifically, the number of sequencing variables grows as O(├ 〖 |C|〗^2 ) in the general sequencing model and as O〖 |C|〗^2 (|Q|+|T|+|Y|) in the equipment-dependent sequencing model. Therefore, the equipment-dependent sequencing formulation depends not only on the number of containers but also on the number of operational equipment, resulting in a faster increase in model size as the number of equipment grows.
To evaluate computational performance, both formulations were implemented in CPLEX and tested on benchmark instances of different sizes. The results indicate that both models are capable of obtaining optimal solutions; however, as the problem size increases, the equipment-dependent sequencing formulation requires longer solution times due to the larger number of variables generated. These findings highlight the importance of structural formulation analysis for selecting suitable models and improving the scalability of integrated optimization problems.