Retransmission-based broadcasting scheme is one of ways for enhancing broadcast reliability. This paper deals with the issue about how much we can improve the broadcast reliability for the deadline-constrained one-hop broadcasting based on the slotted-Aloha with retransmission. The successful delivery probability (SDP) is derived and then the optimal access probability maximizing the SDP is provided. A simple, but sub-optimal access probability, which achieves the SDP close to the optimal value, is also proposed. Further, we find the optimal number of retransmissions maximizing the SDP while satisfying a given throughput requirement.