In this paper, we consider the air-traffic conflict-resolution problem and develop an optimization model to identify the required heading and speed changes of aircraft to avoid conflict such that fuel costs are minimized. Nonconvex fuel functions in the optimization problem are modeled through tight linear approximations, which enable the formulation of the problem as a mixed-integer linear program. The significance of the developed model is that fuel-optimal conflict-resolution maneuvers can be identified in near real time, even for conflicts involving a large number of aircraft. Computational tests based on realistic air-traffic scenarios demonstrate that conflicts involving up to 15 aircraft can be solved in less than 10 s with an optimality gap of around 0.02%.