Uplink resource allocation in OFDMA cellular networks enhanced with two-hop fixed relays is studied in this paper. A resource optimization problem that maximizes sum uplink throughput of all users is formulated under path selection and PHY/MAC constraints. The dual decomposition method is adopted to solve the problem efficiently and optimally. Dual problem of the primal problem is decoupled into N pertone subproblems, which can be efficiently solved by an exhaustive search when optimal power allocation is determined by KKT conditions for given user and its uplink path. Per-tone subproblems interact through dual variables. The numerical results show that the proposed optimal method can significantly improve the total capacity compared with existing suboptimal method.