This study presents a robust optimization algorithm for automated highway merge. The merging scenario is one of the challenging scenes in automated driving, because it requires adjusting ego vehicle's speed to match other vehicles before reaching the end point. Then, we model the speed planning problem as a deterministic Markov decision process. The proposed scheme is able to compute each state value of the process and reliably derive the optimal sequence of actions. In our approach, we adopt jerk as the action of the process to prevent a sudden change of acceleration. However, since this expands the state space, we also consider ways to achieve a real-time operation. We compared our scheme with a simple algorithm with the Intelligent Driver Model. We not only evaluated the scheme in a simulation environment but also conduct a real world testing.