Dümmen Orange – Optimal Cutting Strategies for Flowers #SWI2016
Dümmen Orange is a leading company in the breeding and development of cut flowers, potted plants, bedding plants, and perennials with over a century of experience in the horticultural industry. In addition to a large marketing and sales network, Dümmen Orange has a strong network of production locations. In these production centra, so-called mother plants are planted and grown for a large number of varieties. When these mother plants are ready, cuttings are harvested during a period of approximately 16 weeks, after which the mother plants are removed. These cuttings are sold to growers, who either place orders beforehand or place orders during the harvesting. For each variety, the majority of sales takes place in the ‘peak weeks’, which is a period of approximately 10 weeks; the company has reasonably accurate demand forecasts per week available. Dümmen Orange experienced the following problem. For each variety, the number of mother plants to be planted is decided on the basis of sales forecasts to which a buffer of 10% is added. When orders come in, contracts are concluded with the
growers guaranteeing that the required number of cuttings will be delivered at the desired time. When the harvesting starts, at some point in time the availability of the buffer of 10% is reported to the sales agents, who then try to acquire orders for selling these additional cuttings. Unfortunately, when they are very successful, too many cuttings are required, and the mother plants cannot keep up this pace for too
many weeks in a row, which results in a shortage in later periods. This led Dümmen Orange to the question of when to report the availability of the buffer, and possibly to change its size.
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 for 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.