This paper describes methods for optimizing the task allocation problem for a fleet of unmanned aerial vehicles (UAVs) with tightly coupled tasks and rigid relative timing constraints. The overall objective is to minimize the mission completion time for the fleet, and the task assignment must account for differing UAV capabilities and no-fly zones. Loitering times are included as extra degrees of freedom in the problem to help meet the timing constraints. The overall problem is formulated using mixed-integer linear programming (MILP), which gives the globally optimal solution. An approximate decomposition solution method is also used to overcome the computational issues that arise when using MILP for larger problems. The problem is also posed in a way that can be solved using Tabu search. This approach is demonstrated to provide good solutions in reasonable computation times for large problems that are very difficult to solve using the exact or approximate decomposition methods.