Mobile cloud computing (MCC) has been proposed as a new approach to enhance mobile device performance via computation offloading. The growth in cloud computing energy consumption is placing pressure on both the environment and cloud operators. In this paper, we focus on energy-efficient resource management in MCC and aim to reduce cloud operators' energy consumption through resource management. We establish a deterministic resource management model by solving a combinatorial optimization problem with constraints. To obtain the resource management strategy in deterministic scenarios, we propose a deterministic strategy algorithm based on the adaptive group genetic algorithm (AGGA). Wireless networks are used to connect to the cloud in MCC, which causes uncertainty in resource management in MCC. Based on the deterministic model, we establish a stochastic model that involves a stochastic optimization problem with chance constraints. To solve this problem, we propose a stochastic strategy algorithm based on Monte Carlo simulation and AGGA. Experiments show that our deterministic strategy algorithm obtains approximate optimal solutions with low algorithmic complexity with respect to the problem size, and our stochastic strategy algorithm saves more energy than other algorithms while satisfying the chance constraints.