Since its introduction, mobile wireless communication has grown and changed substantially. This massive growth leads to different levels of complexity, mainly concerned with the assignment of different parameters to antennas or base stations. One parameter is the Root Sequence Index (RSI), related to the Physical Random Access Channel (PRACH) preambles, used to allocate uplink channels between the user equipment and the base station. The assignment of RSIs close-in-range to neighbor antennas may cause collisions, which are responsible for failures on service establishment, and therefore, performance degradation. Such allocation problems can be modeled as Graph Coloring Problems, including several additional constraints. However, few studies focus on RSI allocation and collisions from the optimization perspective. The objective of this study is to develop a method for allocating the RSI, trying to lessen the risk of collision and obeying other constraints. In this paper, we introduce an exact model for this problem alongside several instances extracted from a large carrier.