## 6 Conclusions and Perspectives  
In this paper, a real world scheduling problem from a plastic injection company has been studied and solved. This problem considers sequence dependent setup time, parallel machines and compatibility constraints between machines and resources (molds). The considered objective is to minimize the jobs' tardiness (i.e., the difference between the completion time of the jobs and their due date). First, a mathematical formulation of the problem has been provided. Then, an optimization method aiming to solve the big-sized instances has been developed. The proposed tool consists of a hybridization of a list-algorithm and a metaheuristic and can be seen as a master/slave approach. The obtained results show that the method provides high quality results for the proposed problem, outperforming a two-stage heuristic previously developed for the same problem [30] and currently used by the case-study injection plant. This hybridization has been proposed instead of a classical metaheuristic because it is easier to develop. Indeed, using a classical metaheuristic needs to define a neighborhood system to browse the solution space. This neighborhood system can be complex: the neighbor solution needs to respects all constraints of the specific problem. In our approach, the neighbor is a swap between two jobs in the list of jobs and then the application of the list algorithm ensure the constraints respect. This has two interests. Our tool aims to solve industrial applications, so an easy, friendly tool may have more chance to be \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Current Approach**} & \multicolumn{6}{c}{**Proposed Approach**} \\ \cline{3-8}  & & & \multicolumn{3}{c}{**Stochastic Descent**} & \multicolumn{3}{c}{**Simulated Annealing**} & **Time** \\ \hline
**Instance** & **Jobs** & **Tardiness** & **Setup** & **Tardiness** & **Setup** & **Tardiness** & **Setup** & **Time** \\ \hline
4 & 47 & 8.32 & 16 & 0 & 33 & 0 & 31 & 4 min \\
5 & 53 & 37.76 & 26 & 24.37 & 40 & 17.98 & 42 & 37 min \\
6 & 57 & 159.6 & 23 & 136.29 & 33 & 66.16 & 27 & 3 min \\
7 & 79 & 395 & 37 & 241.26 & 49 & 148.63 & 44 & 6 min \\
8 & 80 & 77.8 & 33 & 0.98 & 49 & 0 & 41 & 1 h \\
9 & 81 & 165.9 & 28 & 52.56 & 39 & 46.17 & 43 & 1 h \\
10 & 177 & 1020.4 & 82 & 963.95 & 114 & 343.82 & 101 & 5 h \\
11 & 191 & 580.2 & 83 & 786.18 & 122 & 579.5 & 124 & 4 h \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of results between the benchmark method and the proposed approach. used by a company. Plus, we intend to solve others industrial applications, using the same tool, only adapting the list algorithm and the objective function (see [1] for other implementation of this tool). Ultimately, a generic tool that could be used to solve several different operational management problems could be developed. A strong point of the proposed method is that the metaheuristic can be used without any change for a large portfolio of problems. The intended tool would thus have a generic part composed of this metaheuristic and a library of list algorithms, which will allow rapid implementation by different companies, facing different planning, scheduling and assignment issues. Several ways of improvement are considered to go deeper in the development of our tool. Within the hybridization, new metaheuristics could be used for the proposed method, including other single solution-based methods as iterated local search or population-based metaheuristics, such as particle swarm optimization using parallel computation with GPU. This will make it possible to assess the effectiveness of the proposed tool under different metaheuristic approaches. New list algorithms are currently proposed for different industrial problems. We are currently collecting data in companies with lot-sizing, scheduling and assignment problems. These problems take into account new constraints, as precedencies between jobs.