Flower power: Finding optimal plant cutting strategies through a combination of optimization and data mining

We study a problem that plays an important role in the flower industry: we must determine how many mother plants are required to be able to produce a given demand of cuttings. This sounds like an easy problem, but working with living material (plants) introduces complications that are rarely encountered in optimization problems: the constraints for cutting such that the mother plant
remains in shape are not explicitly known.
We have tackled this problem by a combination of data mining and linear programming. We apply data mining to infer constraints that a cutting pattern, stating how many cuttings to harvest in each period, should obey, and we use these constraints in a linear programming formulation that determines the minimum number of mother plants necessary. We then consider the problem of
maximizing the total profit given the number of mother plants and show how to solve it through linear programming.