Intelligent mobile robots play an important role in the green and efficient operation of warehouses and have a significant impact on the natural environment and the economy. Path planning technology is one of the key technologies to achieve intelligent mobile robots. In order to improve the pickup efficiency and to reduce the resource waste and carbon emissions in logistics, we investigate the robot path optimization problem. Under the guidance of the sustainable development theory, we aim to achieve the goal of environmental social governance by shortening and smoothing robot paths. To improve the robot’s ability to avoid dynamic obstacles and to quickly solve shorter and smoother robot paths, we propose a fusion algorithm based on the improved genetic algorithm and the dynamic window approach. By doing so, we can improve the efficiency of warehouse operations and reduce logistics costs, whilst also contributing to the realization of a green supply chain. In this paper, we implement an improved fusion algorithm for mobile robot path planning and illustrate the superiority of our algorithm through comparative experiments. The authors’ findings and conclusions emphasize the importance of using advanced algorithms to optimize robot paths and suggest potential avenues for future research.