On the problem of compensatory mating in animal breeding

Animal breeding relies on two processes to achieve its objectives: the selection and the mating systems. Mating systems devise a particular plan to perform one or more breeding goals, which often encompass improving the herd's health and maximising financial gains in animal production systems. Compensatory mating is a strategy to produce animals with more homogeneous selection trait characteristics, discarding the production of exceptional animals in favour of a more balanced herd. This paper defines and investigates the complexity class of the optimal compensatory mating problem, proving that a polynomial-time algorithm can solve it.