The sensor resource management problem in a multi-object tracking scenario is considered. In order to solve it, a dynamic budget balancing algorithm is proposed which models the different sensor tasks as partially observable Markov decision processes. Those are being solved by applying a combination of Lagrangian relaxation and policy rollout. The algorithm converges to a solution which is close to the optimal steady-state solution. This is shown through simulations of a two-dimensional tracking scenario. Moreover, it is demonstrated how the algorithm allocates the sensor time budgets dynamically to a changing environment and takes predictions of the future situation into account.