Peat and pots: An application of robust multiobjective optimization to a mixing problem in agriculture

In horticultural settings, mixing problems arise when choosing a suitable growth substrate for potted plants. The aim of practitioners is to choose a pot and a growth substrate mixture such that environmental emissions and costs are simultaneously minimized. The impact of the plant's quality on the selling price should also be considered. The decision problem outlined here is affected by two types of uncertainty. First, the problem parameters are uncertain due to the nature of the input data. For example variations in the agronomic characteristics of the growth media and in the weather conditions lead to imprecision. Second, the composition of the growth media is generally not implemented exactly due to variability in the mixing process itself. If these uncertainties are ignored, the problem can be addressed using deterministic multiobjective optimization. If these uncertainties are to be considered, the problem can be addressed by means of robust multiobjective optimization. In this paper, we apply both a deterministic and a robust approach to the problem, with and without uncertainty. We present a case study of an Italian plant nursery and we compare deterministic and robust solutions. Our results show that the robust solutions are preferable to the deterministic ones, and that the robust approach is indeed worth considering for horticultural mixing problems and might also be used effectively in other settings where similar mixing decisions arise.