  The paper presents a two-stage stochastic program to model a routing problem
involving an Unmanned Aerial Vehicle (UAV) in the context of patrolling
missions. In particular, given a set of targets and a set of supplemental
targets corresponding to each target, the first stage decisions involve finding
the sequence in which the vehicle has to visit the set of targets. Upon
reaching each target, the UAV collects information and if the operator of the
UAV deems that the information collected is not of sufficient fidelity, then
the UAV has to visit all the supplemental targets corresponding to that target
to collect additional information before proceeding to visit the next target.
The problem is solved using a progressive hedging algorithm and extensive
computational results corroborating the effectiveness of the proposed model and
the solution methodology is presented.
