In this paper, we consider a cooperative network, where relays are capable of simultaneous wireless information and power transfer with a power splitting scheme, and study the optimal design for power splitting ratio at each relay, downlink power allocation, channel assignment, as well as relay association to maximize the weighted sum rate with both amplify-and-forward and decode-and-forward protocols. In essence, such a resource allocation problem is a mashup of continuous-variable optimization and combinatorial optimization. To solve such a challenging problem, we first investigate the optimal solution for power-split ratio in single-user cooperative communication, based on which we propose a dynamic programming solution by exploiting the optimal substructure property of the original problem. To further reduce computational complexity, we propose a polynomial-time heuristic algorithm by leveraging local search strategy, which decomposes the original problem into three subproblems (i.e., downlink power allocation, channel assignment, and relay association) and alternately solves each one given the other two such that the weighted sum rate can be iteratively improved. Simulation results show that the proposed resource allocation scheme outperforms a baseline scheme based on max-sum criterion. Moreover, the proposed local search solution is fairly close in performance to the dynamic programming solution under various parameter settings while the computational complexity is significantly reduced.