What are the rotations carried out by the farmer ?
In the first year, the model determines the optimum cropping pattern by taking into account the initial cropping pattern.
From year 2 onwards, results recur every other year, the model reproduces a “routine cycle” that takes place over two years, which we will call year A and year B. Cropping patterns are as follows :
1 cycle
| Cropping pattern | Year A(ha) | Year B (ha) | Year A (ha) | Year B (ha) | |
| Durum wheat with previous rapeseed crop | 20.278 | 44.444 | 20.278 | 44.444 | |
| Durum wheat with previous potato crop | 19.722 | 25.556 | 19.722 | 25.556 | Etc … |
| Rapeseed with previous wheat crop | 44.444 | 20.278 | 44.444 | 20.278 | |
| Potato with previous wheat crop | 25.556 | 19.722 | 25.556 | 19.722 |
Two different rotations can therefore be observed : durum wheat/rapeseed/durum wheat/rapeseed and potato/durum wheat/potato/durum wheat
It is as if the farmer had 4 plots dedicated to the following rotations : durum wheat/rapeseed on 20,278 ha ; durum wheat /potato on 19,722 ha ; rapeseed/durum wheat on 44,444 ha ; potato/durum wheat on 25,556 ha. In year A he thus grows 40 ha of durum wheat, 44.5 ha of rapeseed, 25.5 of potatoes ; while in year B, he grows 70 ha of durum wheat, 20.3 ha of rapeseed and 19.7 ha of potatoes.
His income varies each year according to the chosen cropping pattern. In year A it is 171090 € and in year B 172180 €.
The land and water equations are binding. The farmer would be willing to rent 1 ha of land at the price of 1030 € /Ha per year and to buy 1 m3 of water at the price of 0.939 €/m3.
What impact does the initial cropping pattern have ?
The distribution of the obtained cropping pattern over the different years depends on the initial cropping pattern. Let us consider the following initial cropping pattern : 20 ha of soft wheat, 30 ha of durum wheat, 0 ha of sugar beet, 10 ha of rapeseed, 30 ha of potato and 10 ha of barley. Results are as follows :
| Cropping pattern | Year A (ha) |
Year B (ha) |
| Durum wheat with previous rapeseed crop | 36.389 | 28.333 |
| Durum wheat with previous potato crop | 23.611 | 21.667 |
| Rapeseed with previous durum wheat crop | 28.333 | 36.389 |
| Potato with previous durum wheat crop | 21.667 | 23.611 |
What can you say about the “EPS” that appear in the marginal values of variables ?
In the results table of the variables (SolVar), it can be observed that certain marginal values of variables whose level is 0 are equal to zero or epsilon (EPS – i.e. a value very close to zero). This comes from the fact that the gross margins of these variables are the same as those of solution variables as seen in the following gross margin table. But these variables are not selected due to the rotation constraint.
| Gross margin in € according to the crop and its previous crop | ||||||
| Soft wheat | Durum wheat | Sugar beet | Rapeseed | Potato | Barley | |
| Soft wheat | -460 | 820 | 900 | 900 | 900 | 820 |
| Durum wheat | 1255 | -565 | 1395 | 1395 | 1395 | 1255 |
| Sugar beet | 1388 | 1388 | -1082 | -1082 | -1082 | 1388 |
| Rapeseed | 1030 | 1030 | -490 | -490 | -490 | 1030 |
| Potato | 2720 | 2720 | -4210 | -4210 | -4210 | 2720 |
| Barley | 755 | 580 | 755 | 755 | 755 | -470 |
How can the dual value of the ROT constraint be interpreted ?
The rotation constraint says that for each previous crop, the sum of the areas with the same previous crop must be lower than the area dedicated to the previous crop in the previous year (X_init(P)). In the solution (SolEQU), the results of the constraint are written for each crop considered as a previous crop (and not as a crop of the current year). The durum wheat crop therefore shows that its maximum level is 40 ha, which means that in the previous year 40 ha of durum wheat were cultivated. And that in the current year, 40 ha of land are dedicated to a crop with a previous wheat crop, the equation is therefore binding. It is the same thing for rapeseed and potato. Furthermore, their marginal value is 36.389, which means that if the farmer could grow an additional ha of a crop with a previous rapeseed (or potato) crop, he would earn an additional 36.389 €. For the sugar beet, the farmer apparently did not grow any the previous year, he therefore does not currently grow a crop with a previous sugar beet crop, but if he had been able to cultivate a ha, he would have earned 36.389.
