This paper studies a variation of the pickup and delivery formulation with time windows which is applied to air cargo export operations. The formulation is extended using three factors. 1) Pickup nodes are positioned at freight forwarders. Delivery nodes are located at ground handlers. Trucks can only visit one freight forwarder. 2) Dock capacity of the ground handlers is implemented in the model. Each dock can only be occupied by one truck at a time. 3) A multi stack loading approach is introduced for the trucks. To be consistent with practice, a Last-in First-out (LIFO) approach is considered when delivering shipments. Three model variants are introduced in this paper with respect to the LIFO strategy with different nuances. i) All LIFO constraints are relaxed. This is also referred to as the ‘no-LIFO’ (NL) model variant. ii) Only direct accessibility in the stacks is allowed. This is also referred to as the ‘strict-LIFO’ (SL) model variant. iii) Side-accessible unloading from an adjacent stack is also allowed. This is also referred to as the ‘side-accessible’ (SA) model variant. For each model variant, an exact model is presented and solved with the branch-and-bound approach. In addition to that, a meta-heuristic is developed that is based on a large neighborhood search to solve large data instances. Two objective functions are used. First of all, a cost-based objective function where a fixed penalty per truck is introduced. The second objective function is time-based, where only the total time duration of the routes of all trucks is minimized. It is concluded that the meta-heuristic model gives good results in terms of solution quality, computational time and stableness. It is also concluded that the SA model variant benefits over the SL model variant. The relative benefit depends on the data instance, capacity of a stack and the used objective function. For small data instances, a maximum benefit of 15.0% was observed for the SA model variant using the exact and meta-heuristic model. For larger data instances, a maximum benefit of 14.1% was observed using the meta-heuristic model. Given the current trends towards more shipment standardization in logistics and more collaboration among stakeholders, we believe many supply chains can potentially benefit from this scheduling model that incorporates both paradigms.