In wireless sensor networks, many sensors face energy constraints and can switch among different work modes to save energy. How to properly schedule work modes is important for network utility maximization (NUM) in the long run. This paper proposes multiperiod scheduling to maximize total network utility by considering energy constraints and periodic sensing requirements. This NUM problem presents challenging mixed-integer programming, and it is difficult to solve by using a centralized approach under complete information. Thus, we first simplify the multiperiod problem to an equivalent single-period problem, and then further reduce it to a pure-integer programming problem, which can be solved easily in a centralized way. As for the cases without a centralized coordinator among all sensors, we propose an average consensus-based distributed algorithm (ACDA) to distributively schedule the work modes of all sensors using only local information. We prove that ACDA converges exponentially fast and reaches global optimum as long as the energy consumption of running the algorithm is ignorable. The proposed distributed solution is also robust against packet drop, node failures, and the changes of communication topology. Extensive simulation results have also shown the effectiveness of the proposed distributed algorithms. © 1991-2012 IEEE.