Note: More Gymnastics

The paper by P. M. Ellis and R. W Corn, “Using bivalent integer programming to select teams for intercollegiate women's gymnastics competition” [1984] has some fascinating aspects and can be used as an illustration for alternative formulations of integer programming problems.

The authors observed that it was easy to obtain ILP solutions and that usually the LP solution was also integer. With the formulation presented in this paper it can be shown that (with four all-rounders and four events) there is always an optimum LP solution which satisfies the integer constraints.