In the reordering buffer management problem, a sequence of requests must be executed by a service station, where a cost occurs for each pair of consecutive requests with different attributes. A reordering buffer management algorithm aims to permute the input sequence using the buffer to minimize the total cost. Reordering buffers has many potential applications in computer sciences and economics. In this article, we proved the minimum buffer length for the optimal solution to the reordering buffer management problem in the offline setting. With the assumption that color selection is always made when the buffer is full, selecting the most frequent color from the buffer given the smallest buffer size $k$ that satisfies either $o_1 < 2 \cdot \lceil \frac{k}σ \rceil$ OR $o_2 < \lceil \frac{k}σ \rceil$ guarantees the optimal solution, where $o_1$ and $o_2$ represent respectively the frequency of the most and the second most frequent colors in the input sequence $\mathcal{X}$, and $σ$ is the number of distinct colors appearing in $\mathcal{X}$. We proposed a new algorithm for the online setting of the problem that uses the results of the proof made on the minimum buffer length required for the optimal solution. Moreover, we presented the results of the first experimental setup that uses input sequences following discrete distributions to evaluate the performance of algorithms. Out of 432 cases, the new algorithm showed the best performance in 409 cases that is approximately $95\%$ of all cases.