Spectrum sharing between different technologies has become a necessity as the RF spectrum has become more congested than ever due to the increasing number of connected devices and applications all wishing to access the spectrum simultaneously. Vehicular networks are one of many scenarios of spectrum sharing as vehicles are expected to share the same spectrum for radar sensing and communication purposes. Channel assignment among radar sensors and communication transceivers in automotive systems is crucial for the success of future vehicular networks. This paper proposes an optimization framework for the channel assignment to multiple automotive radars and communication transceivers aiming at maximizing the number of served vehicles under hard quality of service requirements. The channel assignment problem is formulated as an integer linear optimization with binary variables. A heuristic solution that is based on ordered sequential channel assignment (OSCA) is proposed and is shown to achieve at least 92% of the solution obtained from branch-and-cut based techniques with much less computational complexity and run-time; at most 2% of the run-time of branch-and-cut.