Clinical trials have traditionally followed a fixed design, in which patient allocation to treatments is fixed throughout the trial and specified in the protocol. The primary goal of this static design is to learn about the efficacy of treatments. Response-adaptive designs, where assignment to treatments evolves as patient outcomes are observed, are gaining in popularity due to potential for improvements in cost and efficiency over traditional designs. Such designs can be modeled as a Bayesian adaptive Markov decision process (BAMDP). Given the forward-looking nature of the underlying algorithms which solve BAMDP, the problem size grows as the trial becomes larger or more complex, often exponentially, making it computationally challenging to find an optimal solution. In this study, we propose grid-based approximation to reduce the computational burden. The proposed methods also open the possibility of implementing adaptive designs to large clinical trials. Further, we use numerical examples to demonstrate the effectiveness of our approach, including the effects of changing the number of observations and the grid resolution.