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

Abstract

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 per week. This sounds like an easy problem, but working with living material (plants) introduces complications that are rarely encountered in optimization problems: there is no list with possible cutting patterns, describing the average number of cuttings taken from a mother plant per week. More importantly, there is no easy way to find out whether a cutting pattern is feasible, that is, whether the mother plants can keep up delivering the number of cuttings required by the cutting pattern each week: the only alternative to asking for an 'expert's opinion' is to apply a field-test, which takes a lot of time (and there are very many options to check).We have tackled this problem by a combination of data mining and linear programming. We apply data mining to infer constraints that a feasible cutting pattern should obey, and we use these constraints in a linear programming formulation to determine the minimum number of mother plants that are needed to supply the demand. Due to the linearity of the constraints obtained by data mining, this formulation can be reformulated such that it becomes trivially solvable. Next, we look at the problem of finding the optimal number of mother plants for the case that we can sell a given number of the remaining cuttings on the market for a given price; we show that this problem can be solved efficiently through linear programming