Tracking targets in undersea warfare requires successful detection by an active search asset. Maximizing detection likelihood requires strategic placement and routing of the search assets in the search region over the planning horizon. We develop a two-stage stochastic integer programming model that maximizes the expected total reward for target detections under uncertainty in target motion and sensor detection performance, where time-dependent rewards allow decision-makers to prioritize early detections. Leveraging the problem structure, we derive a closed-form solution for the second-stage subproblem, enabling efficient solution of large-scale instances via Benders decomposition. Computational experiments demonstrate the scalability of the decomposition approach and the quality of solutions obtained through sample average approximation.