This paper considers the generic problem of a central authority selecting an appropriate subset of operators in order to perform a process (i.e. mission or task) in an optimized manner. The subset is selected from a given and usually large set of 'n' candidate operators, with each operator having a certain resource availability and capability. This general mission performance optimization problem is considered in terms of Unmanned Aerial Vehicles (UAVs) acting as firefighting operators in a fire extinguishing mission and from a deterministic and a stochastic algorithmic point of view. Thus the applicability and performance of certain computationally efficient stochastic multistage optimization schemes is examined and compared to that produced by corresponding deterministic schemes. The simulation results show acceptable accuracy as well as useful computational efficiency of the proposed schemes when applied to the time critical resource allocation optimization problem. Distinguishing features of this work include development of a comprehensive UAV firefighting mission framework, development of deterministic as well as stochastic resource allocation optimization techniques for the mission and development of time-efficient search schemes. The work presented here is also useful for other UAV applications such as health care, surveillance and security operations as well as for other areas involving resource allocation such as wireless communications and smart grid.