With the rapid development of e-commerce, warehousing and logistics systems are facing the dual challenges of increasing order processing demand and green and low-carbon transformation. Traditional manual and single-robot scheduling methods are not only limited in efficiency, but will also make it difficult to meet the strategic needs of sustainable development due to their high energy consumption and resource redundancy. Therefore, in order to respond to the sustainable development goals of green logistics and resource optimization, this paper replaces the traditional mobile handling robot in warehousing and logistics with a composite robot composed of a mobile chassis and a robotic arm, which reduces energy consumption and labor costs by reducing manual intervention and improving the level of automation. Based on the traditional contract net protocol framework, a distributed task allocation strategy optimization method based on an improved genetic algorithm is proposed. This framework achieves real-time optimization of the robot task list and enhances the rationality of the task allocation strategy. By combining the improved genetic algorithm with the contract net protocol, multi-robot multi-task allocation is realized. The experimental results show that the improvement strategy can effectively support the transformation of the warehousing and logistics system to a low-carbon and intelligent sustainable development mode while improving the rationality of task allocation.