The quality of faculty scholarship and productivity is one of the primary measures for faculty evaluation in most academic institutions. Due to the diversity and interdisciplinary nature of modern academic research fields, it is increasingly important to use journal quality lists, with journal ratings, that offer credible measures of the worth of faculty scholarship. Despite the existence of such metrics, journal lists, by their very nature, exclude some well‐recognized journals. Consequently, academic institutions expend inordinate resources to assess the quality of unrated journals appropriately and equitably across disciplines. The current research proposes mathematical programming models as a path to determining unknown ratings of multiple journal quality lists, using only their known rating information. The objective of the models is to minimize the total number of instances where two journals are rated in opposite order by two different journal quality lists. Computational results based on journal quality list data in https://harzing.com/ indicate that the proposed methods outperform existing imputation algorithms with most realistic test data sets in terms of accuracy, root mean square error, and mean absolute deviation.