## 5 Evaluation
### Case Studies
#### 5.2.1 Scenario 1  
Table 7 gives the list of crops used in the first scenario, their botanical family and production time. However, the sowing period of each crop has been ignored since favorable conditions, mainly the water quantity to grow a particular crop can be provided using an irrigation system, as it is done in the Local Development Support Programme where tomatoes and onions are grown throughout the year thanks to the irrigation system (The Local Development Support Programme is implemented by Concern Universal with Irish Aid funding. [[https://www.irishaid.ie/stories-of-progress/casestudies/archive/2013/september/irrigation-extending-the-growing-season/](https://www.irishaid.ie/stories-of-progress/casestudies/archive/2013/september/irrigation-extending-the-growing-season/)]([https://www.irishaid.ie/stories-of-progress/casestudies/archive/2013/september/irrigation-extending-the-growing-season/](https://www.irishaid.ie/stories-of-progress/casestudies/archive/2013/september/irrigation-extending-the-growing-season/)), accessed on 10 July 2021). For the first example of our problem, both solvers have reached the same value of the objective function which is 259,500,000 XAF with two different planning. Figures 1 and 2 illustrate the representation of the solutions obtained using the two solvers. Cbc provided a solution after 10 s of running, while GLPK took 10 min. The adjacency constraint is satisfied in both Figures 1 and 2. In addition, cabbage (from the same family with broccoli) is not cultivated to satisfy biophysical constraints. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Interval 1** & **Interval 2** & **Interval 3** & **Interval 4** \\ \hline Plot 1 & 150 & 90 & 58 & 85 \\ Plot 2 & 90 & 100 & 80 & 90 \\ Plot 3 & 70 & 98 & 110 & 105 \\ Plot 4 & 130 & 95 & 115 & 75 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Nutrient amendments on plots in Kg/ha. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Case 1** & **Case 2** & **Case 3** \\ \hline Period & 12 & 15 & 24 \\ Plot & 4 & 4 & 4 \\ Crop & 4 & 6 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Details of the planning problem for each case. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Interval 1** & **Interval 2** & **Interval 3** & **Interval 4** \\ \hline Plot 1 & 150 & 90 & 58 & 85 \\ Plot 2 & 90 & 100 & 80 & 90 \\ Plot 3 & 70 & 98 & 110 & 105 \\ Plot 4 & 130 & 95 & 115 & 75 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Sample of the crops used in Scenario 1 with their botanical family and cultivation duration. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Case 1** & **Case 2** & **Case 3** \\ \hline Period & 12 & 15 & 24 \\ Plot & 4 & 4 & 4 \\ Crop & 4 & 6 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Adjacency matrix corresponding to the given farm, with blue cells indicating adjacent plots and black cells non-adjacent plots. Figure 3 presents the variation of the income according to the availability of resources in scenario 1. Only three types of resources are considered. The expression [2,1,0] means  
Figure 1: Representation of the solution obtained by GLPK for Case 1. On the first plot, tomato is cultivated twice and carrot once. On the second plot, Broccoli, tomato, and carrot are cultivated once. On the third plot, carrot is cultivated twice and tomato once. On the last plot, broccoli and carrot are cultivated once. Figure 2: Representation of the solution obtained by Cbc for Case 1. Tomato is cultivated once on each plot. Carrot is cultivated once on plots 1, 3 and 4, and twice on plot 2. Broccoli is cultivated once on plots 1 and 3.  
we have two resources of type 1, one resource of type 2, and no resource of type 3. An obvious observation is that the income is increasing with the availability of resources, as far as the quantity of required resources is greater than the available resources. This is justified by the fact that the limitation in terms of quantity of resources limits the set of crops that can be grown simultaneously.