Due to new legislation, a lot of research is done in the development of a Collision Avoidance Systems (CAS) for surface mines. Almost all CASs studied in literature are decentralized and developed for passenger vehicles or aviation applications. That makes them unsuitable for the mining environment. A centralized system can ensure optimal control, which means scenarios like intersections can be managed much better. This results in a decreased impact on production. It also increases acceptance, which means operators will be less inclined to turn off the CAS. For this reason, a centralized CAS for mining vehicles was developed. Literature shows that c{MILP} can create relatively accurate models that can be solved very fast. Since only linear constraints can be used, a new geometric model was formulated using four squares that are equally spaced on the longitudinal axis of the vehicle. The vehicle dynamics are described using a linear model. When the optimization problem becomes infeasible, no control is issued to the vehicle. The construction of three different operation modes for the vehicle allow the algorithm to deal with the non linear event of a collision which would otherwise result in an infeasible problem. Weight can be assigned to individual vehicles to determine which vehicle should be prioritized or to model traffic situations. Simulations of six scenarios commonly encountered in mines, involving two vehicles, show that the system is able to avoid all collisions. When a third vehicle is added, collisions are still avoided but solution times increase exponentially. As simulation results were promising, the system was implemented on two test vehicles. Quantitative tests show that the optimization runs as fast using noisy real world data as it does using clean, artificially created data.