====== The space dimension in the decision LP matrix ======


{{model:agentsbehaviour:dtm_30m_valleesina.png|DTM Colli Esini}}

A great difference with AgriPoliS is that the MIP is spatially explicit. So it will be composed of the following activities:
  * <m>n</m> spacial explicit activities * <m>m</m> plot numbers
  * <m>i</m> spacial explicit investments * <m>j_i</m> suitable plots
  * <m>z</m> other spacial implicit activities
  * <m>q</m> other spacial implicit investments



The spacial explicitness has the disadvantage of a much larger matrix, especially in case of farmers with many plots, but it has the following advantages:
  * transport costs are associated directly with the individual pixels and already included in the Gross Margin;
  * pixel heterogeneity (e.g. different slopes) can be included straightforward, just changing the gross margins;
  * an explicit map of the region can be draw to show the different productions
  * binds on individual pixels can be easily inserted on the map (e.g. if the plot_4 is already employed for perennial crops, the matrix will not have the activity option "maize on plot_4" till the perennial crop investment will dead).

An example of matrix following such approach is given:


^ Resources            ^  ^Prod. activity 1\\ on plot1 ^Prod. activity 1\\ on plot2 ^Prod. activity 1\\ on plot3 ^Prod. activity 2\\ on plot1 ^Prod. activity 2\\ on plot2 ^Prod. activity 2\\ on plot3 ^Inv. activity 3\\ on plot3 ^   ^Used recourses ^Available resources ^  
| Gross margin         |  |300                         |295                         |305                         |60                          |58                          |62                          |140                        |   |               |                    |
| ...                  |  |                            |                            |                            |                            |                            |                            |                           |   |               |                    |
| Plot1                |  |1                           |                            |                            |1                           |                            |                            |                           |   |0              |1                   |
| Plot2                |  |                            |1                           |                            |                            |1                           |                            |                           |   |0              |1                   |
| Plot3                |  |                            |                            |1                           |                            |                            |1                           |1                          |   |0              |1                   |
| ...                  |  |                            |                            |                            |                            |                            |                            |                           |   |               |                    |
| Other resources      |  |...                         |...                         |...                         |...                         |...                         |...                         |...                        |   |...            |...                 |
| ...                  |  |                            |                            |                            |                            |                            |                            |                           |   |               |                    |
| Quantities           |  |0                           |0                           |0                           |0                           |0                           |0                           |0                          |   |               |                    |

Gross margin already take into account that plot1 is closer than plot2 and that plot3 is even more close to the farm.\\
If the farmer decide to invest activity3 //(a perennial crop)// on plot3, the following years, "Prod. activity 1 on plot3" and "Prod. activity 2 on plot3" will obviously not be available.

This appoach let us fully differentiate between plots, e.g. on their elevation or even on their slope or exposure.