As the fast improvement of semiconductor manufacturing, today, IoT devices can acquire data in very high resolution and frequency. In many cases, the granularity is finer than required. More energy is consumed for the sensor data transmission via networks and storage in data centers. Data compression is a common approach to reduce the data size. In the literature, many methods based on Bounded-Error Piecewise Linear Approximation (BEPLA) have been proposed that use multiple straight lines to approximate the original data and maintain a tolerable error. Swing-RR first introduced the Resolution Reduction strategy, abbreviated as RR, where all line segment endpoints must be encoded by small integers, rather than floating point real numbers. Swing-RR is simple and has O(n) time complexity when the date size is n. The compression ratio is significantly better than other BELPA methods. However, it is not optimal in terms of number of line segments. In this paper, an optimal BEPLA algorithm with RR is presented, denoted as OBEPLA-RR. The experiments on public real world time series datasets show that the numbers of line segments generated by OBEPLA-RR are fewer than those by Swing-RR, and the compress ratios are significantly better than Swing-RR and other BEPLA methods.