Choosing a winning team for mixed medley events

The swimming medley event consists of teams of four swimmers (all men or all women) competing to complete a medley of four strokes in the quickest time. A new idea has emerged where swimming teams of two women and two men may now compete against each other in the same medley event. This new problem may be formulated as a classical assignment problem with an additional side constraint. We propose a simple back-of-the-envelope algorithm for selecting the fastest mixed team. The mixed-medley model is also generalised to other possible sports events (e.g., in gymnastics and track and field). Reformulating the problem by standard Lagrangian relaxation allows us to solve it in an iterative fashion with the well-known Hungarian method. Thus, the problem is suitable in a classroom environment for students and practitioners of OR.