# Multi-Objective Production Scheduling of Perishable Products in Agri-Food Industry
## 5 Implementation and Experimental Results
### Interpretation  
The schedule's Gantt chart representation correspond to the best obtained solution found by the ACO and GA algorithms. The schedules in Figures 3 and 4 are obtained after applying the proposed GA and ACO algorithms, respectively.  
When considering deterministic scheduling with an objective to minimize makespan, there are no preferences in selecting one as both have the same makespan, which is 63 time units. However, when considering the number of perishable products, the schedule found by GA algorithm is better than the solution found by ACO. In fact, the GA algorithm gives a solution with a perishable product when solving the instance with six jobs and three machines.  
For instance, with eight jobs and three machines, the ACO algorithm provides a better result in terms of the number of perishable products (only one) compared with the result found by the AG algorithm (two perishable products).  
However, the makespan value of the best solution found by AG is better than that found by ACO, equals to 76 (see Figures 7 and 8) For the instance with nine jobs and three machines, the GA algorithm provides a better result compared with that of ACO. The schedule in Figure 9 is more efficient than the schedule in Figure 10 since it has a lower makespan value and lower number of perishable products. The makespan value equals 88, which is better than the 90 found by ACO. Additionally, there are only two perishable products in the schedule in Figure 9, but with ACO, there are four perishable products.  
The computational results indicate that the schedules generated using the proposed genetic algorithm GA have statically superior performances in terms of makespan and the number of perishable products compared with the ACO algorithm.  
To complete our study and to assess the performance of our algorithms more, the B&B algorithm is used to obtain a lower bound. The computational results mentioned in the  
\begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline
**Tested Instance** & \multicolumn{2}{c}{**B \& B**} & \multicolumn{4}{c}{**GA**} & \multicolumn{4}{c}{**ACO**} \\ \hline  & **Best Solution** & \(\mathbf{C_{max}}\) & \(\mathbf{Pp_{min}}\) & **Best Solution** & \(\mathbf{C_{max}}\) & \(\mathbf{Pp_{min}}\) & **Best Solution** & \(\mathbf{C_{max}}\) & \(\mathbf{Pp_{min}}\) \\ \hline
6\_Jobs & 124356 & 63 & 0 & 124356 & 63 & 0 & 312456 & 63 & 1 \\
7\_Jobs & 1234567 & 66 & 1 & 1523467 & 66 & 1 & 1532467 & 66 & 1 \\
8\_Jobs & 21345678 & 74 & 1 & 45231678 & 76 & 2 & 54231687 & 77 & 1 \\
9\_Jobs & 321456789 & 77 & 2 & 532416897 & 88 & 2 & 514326798 & 90 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Experimental results of the B&B, GA, and ACO algorithms.  
Figure 13: Comparison of the perishable products.  
table below indicate that the performance of predictive schedules generated by the GA are similar to or near those found by the B&B algorithm. In fact, the GA provides similar schedule performances for the instances with six jobs and seven jobs to that of the B&B. When considering bigger instances with eight and nine jobs, the GA provides solutions with similar values of makespan (76 compared with 74 by the B & B) and similar values of the number of perishable products (\(Pp_{min}=2\) compared with \(Pp_{min}=1\) by B&B ).