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Han Hoogeveen: Flower power: Finding optimal flower cutting strategies through a combination of optimization and data mining

Abstract: We study a problem that plays an important role in the flower industry: harvesting cuttings from mother plants. Given the (non-constant) demand per week, we must determine beforehand how many mother plants we must plant, and we must decide for each mother plant how many cuttings we must harvest per week. Furthermore, if we cut off more than requested, then we have to decide in which week to cut and sell this. This does not sound very complicated, but working with living material introduces constraints that are rarely encountered in optimization problems. It is well known that if we cut off too many cuttings per week, then the plants cannot sustain this pace, and the production will drop sharply, but the exact relation is unknown. If we show a cutting pattern, which describes how many cuttings are cut per week, to an expert, then he can judge whether it is valid, but there are no properties known that a cutting pattern must satisfy to be valid. 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. Due to the linearity of the constraints obtained by data mining, this formulation can be reformulated such that it becomes easily solvable.