An exact method for storage space assignment at airport cargo terminal: A temporal-spatial packing problem

With the spiking volume of non-stackable cargos, such as cargo pallets or unit loading devices, to be transported by airplanes, the ground space at airport cargo terminals becomes tight and requires precise management regarding storage space assignment, making it a temporal-spatial packing problem. The problem is first formulated as a mixed-integer linear programming model, adhering to a time-dependent storage principle, to minimize wasted space and maximize the dispersion effectiveness of the assignment decisions, and subsequently, the logic-based Benders decomposition (LBBD) approach is proposed. Two enhancement methods are developed, where effective constraints and corresponding cuts are applied to the master problem, and the Lagrangian relaxation method is adopted in the subproblem, converting the original LBBD into a bi-level decomposition structure. An extensive analysis highlights the superiority of the bi-level LBBD approach, augmented with corresponding enhancement methods, over other decomposition-based approaches. Specifically, our approach successfully solves 50% of complex instances, compared to other approaches which solve only a single instance or fail to find any optimal solution. Compared to an empirical approach, our approach shows particularly effective in handling instances with 150 cargos, successfully placing all items within the storage space while also delivering superior dispersion performance.