Motivated by crowd-sourcing applications, we consider a model where we have partial observations from an isotonic or bi-isotonic n x d matrix. with an unknown permutation pi^* acting on its rows. Focusing on the twin problems of recovering the permutation pi^* and estimating the unknown matrix, we introduce a polynomial-time procedure achieving the minimax risk for these two problems and for both the isotonic and bi-isotonic settings. The minimax risk is shown up to polylogarithmic factors for all possible values of n, d and all sampling efforts.