Geometric Clustering for the Consolidation of Farmland and Woodland

I nmany agricultural areas, farmers cultivate a large number of small lots that are scattered across an extended region. In a typical farming area in Bavaria, Germany, about 7 – 20 farmers cultivate between 300 and 1000 lots; Figure 1 provides a visual impression of a typical distribution. In such a situation, the farmers face serious disadvantages. Because the individual lots are scattered across a large region, there is considerable overhead driving, resulting in an excess of personal and transportation cost. Calculations of the Bavarian State Institute for Agriculture show that these additional costs often add up to more than 30% of the part of the farmers’ net income coming from their agricultural production. (EUand other subsidies that constitute a substantial additional part of the income are, of course, typically independent of such aspects of cost-efficient production.) Also, because the single separate lots are rather small, modern heavy machinery cannot be used profitably. Hence, the cost of cultivation is much higher than it would be for fewer, larger lots of the same total size. In its classical form, land consolidation consists of a complete restructuring of the agricultural area, discarding the current and creating a new lot structure. This process involves extended surveying and new legal assignments of property, and is hence costly, lengthy, and inflexible. After the decision is made, farmers are forced to participate in this process. A typical classical land consolidation process lasts more than a decade and costs about 2500 Euro per hectare. Of course, the land distribution is less rigid in agricultural areas where farmers other than the lot owners cultivate the majority of the lots, through lend–lease agreements. (This is partly causedby inheritance regulations and partly due to the tough economic situation of small farmers.) So, even districts that underwent a classical form of land consolidation in the recent pastmay look like rag rugs. This is a common situation in Northern Bavaria. On the other hand, a farmer who rents a lot for cultivation is generally less tied to the lot, and is hence more willing to ‘‘trade’’ it to improve the overall cost structure for his operations. This opens the possibility for conceptually simple lend–lease agreements based on the existing lot structure, i.e., without the nullification of the property structure. For an optimal redistribution there are some main aspects to be considered. Because large connected pieces of land are desirable for each farmer, while the lot structure, i.e., the dissection of the region into individual lots, is not changed, one aims to assign adjacent lots to the same farmer. Naturally, certain balancing constraints need to be satisfied. For instance, the total size of each farmer’s land should not change too much in the course of redistribution, neither should its quality of soil, the EU-subsidies attached to his lots, or other possibly relevant parameters. Also, ecological constraints play a role. The quality of soil, in particular, is typically different in different parts of the region. This means that, in practice, the assigned lots of each farmer will form certain connected patches, which, in turn, should be as close to each other as possible. The lend–lease agreements are completely voluntary. In particular, farmers are allowed to fix some of their lots