• air cargo;
  • logistics;
  • scheduling;
  • Lagrangian relaxation

We consider the scheduling of truck arrivals at an air cargo terminal. By coordinating arrivals of cargo delivery trucks with outbound flight departure schedules, some of the shipments can be transferred directly to the departing flights, while others will be stored at the terminal's storage facility and incur extra handling and storage costs. The objective is to obtain a feasible schedule so as to minimize the total cost of operations. We formulate the problem as a time-indexed integer program and show that, even with limited number of unloading docks at the terminal, the problem is non-trivial (NP-hard in the strong sense). Our solution method includes an exact solution procedure to determine an optimal unloading sequence for the shipments carried by each truck, together with a Lagrangian relaxation-based heuristic for assigning trucks to truck docks and determining truck arrival times. We conducted computational experiments to test the performance of our solution method. Computational results show that our method can generate near-optimal solutions efficiently. Our simulation results indicate that the scheduling approach proposed in this paper has the potential to generate significant cost savings over a first-come, first-served approach currently used at the air cargo terminal that we observed.