This paper introduces a novel machine learning model called multiple instance ranking (MIRank) that enables ranking to be performed in a multiple instance learning setting. The motivation for MIRank stems from the hydrogen abstraction problem in computational chemistry, that of predicting the grouping of hydrogen atoms from which a hydrogen is abstracted (removed) during metabolism. The model predicts the preferred hydrogen grouping within a molecule by ranking the groups, with the ambiguity of not knowing which hydrogen within the preferred grouping is actually abstracted. This paper formulates MIRank in its general context and proposes an algorithm for solving MIRank problems using successive linear programming. The method outperforms multiple instance classification models on several real and synthetic datasets.