Length : around 30 minutes
The modelEco_dynamique.gms model written in lesson 28 covers a period of 20 years.
Observe the lst. file. What rotations are carried out by the farmer ? What impact does the initial cropping pattern have ? What can you say about the “EPS” that appear in the marginal values of variables ? How can the dual value of the ROT constraint be interpreted ?
« An arable crop farmer that grows special crops (INOSYS Système GC 131 data) in the Centre-Val de Loire region has 110 ha of land. Irrigation and the economic environment of his farm offer him a large range of productions options : soft wheat, durum wheat, spring barley, potato for human consumption, sugar beet and rapeseed. Five of these crop types are irrigated in order to ensure high quality regular production. The farmer has 60 000 m3 of water.
Irrigation needs and economic data are shown in the table below :
| Irrigation water needs | ||||
| Crops | Vol in m3/ha | |||
| Soft wheat | 175 | |||
| Durum wheat | 350 | |||
| Spring barley | 700 | |||
| Potato for human consumption | 1800 | |||
| Sugar beet | 1750 | |||
| Other technico-economic data | ||||
| Crops | Yields (qx/ha) | Prices/qx (€) | Total costs (€/ha) | |
| Soft wheat | 85 | 16 | 460 | |
| Durum wheat | 71 | 28 | 565 | |
| Spring barley | 70 | 17.5 | 470 | |
| Potato for human consumption | 495 | 14 | 4210 | |
| Sugar beet | 950 | 2.6 | 1082 | |
| Rapeseed | 40 | 38 | 490 | |
Source : from the Système GC 131 of the INOSYS network of agricultural chambers in the Centre Val de Loire region. 2016
Crop yields depend on previous crops (a zero means that it is not possible to cultivate a given crop with that previous crop) :
| Crops | Previous crops | |||||
| Soft wheat | Durum wheat | Sugar beet | Rapeseed | Potato for human consumption | Barley | |
| Soft wheat | 0 | 80 | 85 | 85 | 85 | 80 |
| Durum wheat | 65 | 0 | 70 | 70 | 70 | 65 |
| Sugar beet | 950 | 950 | 0 | 0 | 0 | 950 |
| Rapeseed | 40 | 40 | 0 | 0 | 0 | 40 |
| Potato for human consumption | 495 | 4954 | 0 | 0 | 0 | 495 |
| Barley | 70 | 60 | 70 | 70 | 70 | 0 |
The initial cropping pattern is as follows : 10 ha of soft wheat, 20 ha of durum wheat, 30 ha of sugar beet, 0 ha of rapeseed, 40 ha of potato and 10 ha of barley.
The farmer maximizes his profit every year. »
Then check the solution : 
