Land allocation and land market

An obvious problem when dealing with spatially explicit agent based models is the localisation of the agents and of their spatial objects. The problem is complicated by the fact that there is already an informative layer, consisting of the land use, and we have to keep this layer consistent with the model, applying the farm allocation over it.

Firstly, farms are assigned a random location picking up a plot compatible with their assets, starting from the less common. The idea is that rare land use types have the precedence over common land use types to minimize distances from them to the farmsteads. So if a farm has both fruit land and arable land, the farmstead will be placed within a fruit land type.

Subsequently, plots are assigned to the closest farm that has still an uncompleted capacity for that specific soil type, giving precedence to owner plots in comparison to rented ones.

This is not a optimization algorithm as plots are not assigned to farms in a way that minimize the total plots-farmsteads distance. But on the other hand also the real world situation is far from an optimal land (de)fragmentation, as physical bounds and hereditary rules often split the farmer land in various disconnected plots. Figure 3 shows the result of the initial land allocation, with the plots assigned to their owner farm (each colour represent a different farm).

Figure 3: Owned plots after initial land allocation.

During the simulation farmers can bid to rent new plots. Currently (as in AgriPoliS) RegMAS doesn't allow for land transfer nor for direct farmer-to-farmer renting contracts. Instead, farmers can only rent land owned by an anonymous agent that collect the land arising from farms leaving the model and from the initial pool of rented plots to make it available in a bid to the farmer offering the highest price.

Farmers asked to bid offer a share of their shadow price for such plot, to take into account of fixed and variable negotiation costs and overheads. The shadow price for the new plot is calculated simply performing two MIP problem optimisation, with and without the plot, and calculating the difference.

While AgriPoliS can use some optimisation techniques as land is homogeneous within the same soil type, the full heterogeneity of plots in RegMAS prevent using such tricks, making this process very computationally intensive. Therefore RegMAS offer the option to limit the bidding process to farmers within a certain range from the plot. The natural trade-off when increasing this option is on one side that it increases the likelyhood to get the highest bid, but on the other side that it dramatically increases the computational time.

Once the plot is assigned to a farm a rental contract is established for a random period (within user defined limits) and the plot enter the farmer's MIP problem as a new resource.