The space dimension in the optimisation problem

As result of the spatial explicitness the farmer maximisation problem is composed of the following activities:

• $i$ spacial explicit activities * $p_i$ suitable plots;
• $j$ spacial explicit investments * $p_j$ suitable plots;
• $q$ other spacial implicit activities;
• $z$ other spacial implicit investments.

Is the researcher task to select which characteristics need to have a plot to be considered for each spatial explicit activity. Within the input data, he/she can select which land types and even which spatial objects need to be already present for each activity. To make an example, growing wine requires land type 221 (vineyards) and the presence of a wineGrapePlant object. All activity_x_plot combination that miss this requirements are automatically discarded even before entering the MIP, reducing the MIP dimension and therefore the required computational power ⁶.

Even with this trick, the spacial explicitness has the disadvantage of a much larger matrix, especially in case of farmers with many plots, but it has also many advantages:

• transport costs are associated directly with individual pixels and already included in the Gross Margin;
• pixel heterogeneity (e.g. different slopes) can be included straightforward, just changing the gross margins (e.g. through the ''filter`` function cited in the previous section);
• an explicit map of the region can be draw to show the different productions;
• binds on individual plots can be easily inserted on the MIP problem.