This paper introduces the Best-Worst PROMETHEE method, which avoids the rank reversal problem of other PROMETHEE methods. We use this new technique to rank schools in the Programme for International Student Assessment (PISA). We consider three separate outputs, provided by average student attainments in mathematics, language, and sciences. Our sample comprises 16,500 schools in 66 countries, and our results show significant differences between school performance both within and between countries. The top half of the ranking mainly comprises European and Asian countries, while the bottom half includes many North African, Middle Eastern, and South American countries. We find no strong association between inequality between schools and the country-level performance, suggesting the absence of a trade-off between equity and performance in education. The Best-Worst PROMETHEE is a generic method that can be used to support decisions in strategic sectors with multidimensional outcomes.