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Farmers autonomously make their decisions solving a Mixed Integer Programming (MIP) problem similar to those shown in Figure 1.
This happens any time farmers bid for renting a land plot in order to calculate its shadow price, or plan for new investments, or finally produce using the given assets.
Symbol 
in Figure 2 denotes a step in the model when one or more MIP problems have to be computed at the farm level.
From FADN data we can establish the initial farm's endowment: financial assets, availability of land, machinery, animals and so on. From a linear programming point of view, these data represent the right terms of the constrain equations (A in the cited figure). Any farmer choose from a list of activity options. They can be divided in two categories: activities that can be run entirely within one year (B) and activities that generate results over multiple years (investments, C). Investments are bounded to be integer and the same investment type is available in different size-options, allowing scale-effects to emerge in the model. Section 2.2.2 details the farmers finance modelling, including how investments enter the MIP together with yearly activities.
Individual activities to include in the model are left to the RegMAS users. Currently we implemented models where, very synthetically, all aspects of running a farm are considered, including financial and labour ones. To solve this problem the farmers chose the quantities (D) of the various activities that maximise the objective function (E). In our case, this is the maximisation of household income, and the gross margins of the various activities are the parameters of the objective functions(F).
Before entering the MIP, individual activies are ''filtered`` by the farmers. Currently, this is implemented in order to change the gross margins to include transport costs from the farmstead to the plot and to take into account the plot's altitude (under the hypothesis that mountain plots are less productive than plain ones). Finally, The matrix of the constraint coefficients (G) links the available activities (B+C) with their technical requirements (H).
RegMAS can take into account changes of resource endowment and activity gross margins, generated either endogenously to the MIP core, in case these changes occur as a consequence of the solving procedure (e.g., an investment improves the number of available activities) or exogenously to it, in case these changes occur in other parts of the model (e.g., renting/releasing land, or as a consequence of market prices changes).
Paris (1991); Arfini (2000) present respectively an in-deep analytical description and a literature review of linear programming techniques applied to farm problems.
