It is shown that the Clar number of a benzenoid hydrocarbon H (defined as the number of circles in a Clar formula, or equivalently as the maximum number of mutually resonant hexagons of H) can be determined by mixed-integer programming. Moreover, linear programming appears to suffice in practice to find in moderate computing time the Clar number of pericondensed hydrocarbons with more than a thousand hexagons.