This paper addresses the joint base station (BS) assignment and power control problem in a hybrid energy supply wireless network, where an energy harvesting BS and a grid-powered BS coordinate to serve a mobile user. In order to minimize the grid energy consumption while maximizing the number of transmitted data packets, we introduce the total service cost over an N-block frame as the performance metric, which is the weighted sum of the grid energy cost and the packet drop cost. With non-causal side information (SI) available at the BSs, including energy SI and channel SI, a Greedy Assignment algorithm with low complexity and near optimal performance is proposed. For the causal SI setting, the design problem is formulated as a discrete Markov decision problem. Interesting solution structures are derived, which help develop an efficient monotone backward induction algorithm. To further reduce the complexity, a heuristic online policy is also proposed. Simulation results shall validate the effectiveness of the proposed policies and demonstrate a unique tradeoff in such networks, i.e., the tradeoff between the grid energy consumption and the provided quality of service.