# Allocating Students to Industry Placements Using Integer Programming and Ant Colony Optimisation
## 7 Experiments and Results
### Integer Programming and Real Data  
The IP model was run on real datasets. The original allocations were built by hand taking several hours over a two week period of the scheduler's time. In a few cases in the manual allocation, private arrangement students were allocated to companies that had not interviewed them. This process was incorporated in the simulations by making a comparison with these students included and excluded from the student data set. In the former case, their ranking was given a value of 2.  
The results are presented in Table 3. The first column specifies the year and semester (_Year-Sem._). The second and third columns specify the number of students and the number of companies for the corresponding year/semester. For the original allocation, we report the average allocation (_Avg._), the number of first preferences assigned (#1_s_) and the number of last preferences assigned (#3_s_). (Note: the IP model does not allow these by implementing it as a hard constraint.) For the IP model, the average allocation (_Avg._), number of first preferences (#1_s_) and time taken in seconds (_Time_ (s)) to allocate are reported.  
\begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline  & & & & & **Original Allocation** & & **IP Model** \\ \hline
**Year-Sem.** & **Stu.** & **Comp./Depts.** & **Avg.** & **\#1**s** & **\#3**s** & **Avg.** & **\#1**s** & **Time (s)** \\ \hline
2012-1 & 43 & 21 & 1.35 & 28 & 0 & 1.21 & 32 & 0.073 \\
2012-1 \({}^{*}\) & 42 & 21 & 1.33 & 28 & 0 & 1.21 & 32 & 0.084 \\ \hline
2012-2 & 62 & 33 & 1.29 & 45 & 1 & 1.10 & 55 & 0.141 \\
2012-2 \({}^{*}\) & 61 & 33 & 1.28 & 45 & 1 & 1.10 & 55 & 0.135 \\ \hline
2013-1 & 46 & 31 & 1.39 & 29 & 2 & 1.24 & 35 & 0.140 \\ \hline
2013-2 & 53 & 31 & 1.38 & 39 & 6 & 1.04 & 46 & 0.123 \\ \hline
2014-1 & 38 & 31 & 1.37 & 25 & 1 & 1.44 & 34 & 0.090 \\ \hline
2014-2 & 60 & 41 & 1.24 & 46 & 2 & 1.05 & 57 & 0.162 \\ \hline
2015-1 & 51 & 47 & 1.39 & 31 & 0 & 1.21 & 40 & 0.148 \\
2015-1 \({}^{*}\) & 50 & 47 & 1.38 & 31 & 0 & 1.20 & 40 & 0.147 \\ \hline
2015-2 & 75 & 65 & 1.25 & 58 & 2 & 1.09 & 68 & 0.265 \\ \hline
2016-1 & 44 & 52 & 1.41 & 26 & 0 & 1.25 & 33 & 0.139 \\
2016-1 \({}^{*}\) & 42 & 52 & 1.38 & 26 & 0 & 1.21 & 33 & 0.138 \\ \hline
2016-2 & 82 & 55 & 1.13 & 71 & 0 & 1.02 & 80 & 0.257 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison between the IP model and actual (manually created) schedules. Adjusted runs (*) remove students who were not interviewed by any of the partners, as there are no preferences for these students. For 2012-1 and 2012-2, the IP model is unable to place 1 student, and for 2013-2, two students.  
In all but one instance, the IP model achieves better average allocation outcomes than the manual allocation. The only exception is 2014-1, where the IP model has a higher average allocation. The reason this happens is because the sector constraints were overridden by the manual allocation and as this is implemented as a hard constraint in the IP model, the IP is unable to find improvements. However, if this constraint is relaxed in the IP model, the average allocation improves to 1.15, which is significantly better than the manual allocation.