Many complex grid workflow processes often have only one global fixed-time constraint at the last activity. Since grid workflow execution normally lasts a long time, local control is very important to ensure the overall temporal correctness. With only one global fixed-time constraint, we cannot control grid workflow execution locally in terms of time. As a result, for any temporal violations, we must handle them globally with the consideration of all activities. This would impact the overall cost-effectiveness of grid workflow execution. Therefore, in this paper, we investigate how to assign local fixed-time constraints within the global one so that we can control grid workflow execution locally. Corresponding assigning and verification methods are developed. With local fixed-time constraints, we can achieve better cost-effectiveness.