This system describes a farm and a restaurant belonging to a same project. Consequently, they function in full cooperation.
Description of the system : https://doi.org/10.1007/s10666-024-10014-w
The object computed is a viability kernel. The model is discrete in states, controls and time.
The computation takes a moment (4088s on my computer), be patient...
Model
States and controls
State variables
Notation | Description | Number of points | Maximal value | Minimal value |
| $x_1$ | Cumulative cash flow (€) | 41 | 100 000 | 0 |
| $x_2$ | Restaurant attractivity coefficient (no unit) | 31 | 1 | 0 |
| $x_3$ | General Index for Soil Quality | 51 | 1 | 0 |
upper limit of $x_1$ can be relaxed.
Control variables
Notation | Description | Number of points | Maximal value | Minimal value |
|---|---|---|---|---|
$u_1$ | Choice of $N$-crops rotation | 126 | 126 | 1 |
$u_2$ | Surface dedicated to market gardening (in ha) | 21 | 2 | 0.05 |
$u_3$ | Price of a meal (in €) | 21 | 15 | 2 |
Dynamics
Notation | Description |
| $R(x_3,u_1,u_2)$ | Agricultural production |
| $G(x_2,u_3,R(x_3,u_1,u_2))$ | Restaurant economic outcome |
| $\alpha(x_2,u_3,R(x_3,u_1,u_2))$ | Transition function for the restaurant attractivity |
| $\Phi(x_3,u_1,u_2)$ | Transition function for the GISQ |
| $E(u_1,u_2)$ | Cost of agricultural production |
cf article for further details
Some dynamics require to use grid parameters. Consequently, a function has been implemented into the source file to get these values.
Constraints
Implementation parameters
Time horizon
The time horizon (for trajectory computations) is 20 years.
Algorithm parameters
Default parameters are used.
System parameters
We used the parameters for a low-hypotheses computation.
"SYSTEM_PARAMETERS": {
"DYNAMICS_TYPE": 2,
"DYN_BOUND": 1,
"DYN_BOUND_COMPUTE_METHOD": 2,
"IS_TIMESTEP_GLOBAL": 0,
"LIPSCHITZ_CONSTANT": 1,
"LIPSCHITZ_CONSTANT_COMPUTE_METHOD": 2,
"TIME_DISCRETIZATION_SCHEME": 4
}