Automatic guided vehicles (AGVs) have become an important transport resources in modern job shops, yet their deployment introduces new scheduling challenges, such as AGV assignment, power constraints, and fleet size limitations. To address the green scheduling problem of job shops considering AGV charging requirements, this study develops a multi-objective optimization model that minimizes makespan and energy consumption while accounting for AGV power levels and charging behavior. An improved genetic algorithm is proposed to solve the model. It employs dual-segment chromosome encoding for job sequencing and AGV allocation, and local search strategies and dedicated genetic operators for each chromosome segment. A decoding mechanism considering AGV power and charging constraints is also designed. Through orthogonal simulation experiments using the FT06 benchmark case, the influence of AGV fleet size and battery capacity on scheduling performance are analyzed via range and variance methods. Simulation results demonstrate the effectiveness of the proposed model and algorithm.