Bilevel integer linear models for ranking items and sets

Item and set orderings help with data management. Depending on the context, it is just as important to order a list of items (customers from different provinces, companies from different sectors, players from different teams) as it is to order a list of sets of these items (provinces, sectors, teams). It is evident that the order that is chosen for the items is not independent of the order that is chosen for the sets. It is possible that several set orders are sensible for the same item order and vice versa, that several item orders are sensible for the same set order. In this work, we propose a bilevel model to calculate an adequate order of items when an order of sets is available and another bilevel model to calculate an adequate order of sets when an order of items is available. In addition, it is shown how to reduce both bilevel models to single level models. Two illustrative computational studies are presented, the first with collected on 25 tennis players and ATP statistics and the second with Biomedical data. Both examples illustrate the good behavior of the models and the interest of their application in a real case scenario