The Multi-Agent Pickup and Delivery (MAPD) problem has received significant academic attention, resulting in a variety of solution techniques that both assigns tasks to agents and finds a conflict-free routing plan for all agents in the system. However, limited research is done to investigate the added value of an integrated MAPD solving technique for real-world problems in which task allocation and path planning are performed simultaneously. The integration of the assignment and routing problem is relevant for the minimization of ground delay when implementing tug-enabled taxiing operations at airports to reduce the environmental impact of aircraft ground movements. In this work, a novel algorithmic framework is introduced that minimizes ground delay for tug-enabled taxiing compared to conventional taxiing operations by combining the Temporal Sequential Single-Item (TeSSI) allocation algorithm with Priority Based Search (PBS) and Safe-Interval Path Planning (SIPP) for path planning. Experiments were conducted to assess the performance of a coupled approach, where the assignment and routing problem are solved together, in comparison to a decoupled approach, where they are solved separately. The evaluation focused on ground delay for different towing fleet sizes. The findings indicate that the coupled approach does not offer significant advantages compared to a decoupled approach in the domain of aircraft engine-off towing operations: the decrease in total ground delay for a few specific cases was minimal, while the computational run times significantly increased across all scenarios. Key operational results highlight that, when tugs are limited, the primary contributor to the total ground delay per departing flight is the ramp delay caused by tug unavailability. Furthermore, the relationship between ramp delay and fleet size is not linear but exhibits exponential growth only after reducing the fleet size below a certain threshold of available tugs. These practical observations provide relevant insights for airports considering implementation of tug-enabled taxiing operations.