# Minimum-Energy Scheduling of Flexible Job-Shop Through Optimization and Comprehensive Heuristic
## 6 Conclusions  
This study addressed the problem of minimizing the energy spent in a flexible production workshop with the operation of its machines and its internal logistics. The hypotheses retained led to the formulation of a particular scheduling problem that fits well with operational practice in this field. There, the operation of the flexible job shop is considered not as a mere juxtaposition of tasks but as a set of coordinated production flows that can be assigned to different machines. The field of application of this study goes well beyond the scheduling in industrial job shops and, among others, can also cover the operation of inter-modal transport terminals. This is particularly important in the case of airport operations when considering the ground handling activities for aircraft at arrival and departure. There, due time constraints have an essential role in guaranteeing the punctuality of departure flights, while the energy consumption and the emissions of the numerous ground handling vehicles must be minimized as much as possible [45]. The optimization problem considered in this study was formulated as a mono-criterion optimization problem, avoiding the introduction of relative weights or the exploration of a Pareto frontier involving energy and make-span. At the same time, the consideration of release and due times allows the integration of a flexible job shop into more global processes of Industry 4.0. Its two-level structure is the result of having adopted as decision variables, besides the scheduling variables of the operations, the assignment of machines to the different operations of the jobs. This two-level structure offers opportunities to use known optimization approaches to obtain exact solutions for real-size instances of this problem. However, considering its computational complexity and the requirements to generate efficient schedules in the dynamic environment of flexible job shops, an ad hoc heuristic was designed. With this heuristic, the machine assignments to operations are not generated a priori for each job but are constructed step by step according to the information available about the downstream operational state of the job shop. The solution generated by this heuristic derives from a permanent trade-off between energy and delays, where the subsets of candidate machines to perform an operation can be enlarged to include less energy-efficient machines that operate faster, satisfying the due time constraints for each job. This heuristic was applied with success to a small-size case study, where it outperformed two basic scheduling rules. Given the results obtained so far, it seems interesting to evaluate the performance of this heuristic when applied to higher-dimensional problems targeting other application domains. The present research can be completed following different directions:  
* Enlarging the scope of the problem by considering other sources of energy consumption (idle machines, for example). \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Energy Cost** & **Make-Span** \\ \hline HET & 725 & 65 \\ \hline TTE & 745 & 62 \\ \hline ETT & 725 & 70 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Performances of heuristic HET and priority rules TTE and ETT. Enhancing the efficiency of the heuristic--for example, by integrating priority rules, such as the critical ratio (between the time remaining until the due date and the work time remaining), to better cope with the due date constraints [46]. To further examine the quality of the solutions provided to the minimum-energy flexible job-shop scheduling problem, this study can be a basis for the development of metaheuristics, such as those described in [47; 48]. This will allow the use of artificial intelligence techniques to cope more globally with the search for an efficient solution. Conceptualization, O.A.O., F.L.P.K. and F.M.-C.; methodology, O.A.O., F.L.P.K. and F.M.-C.; validation, O.A.O., F.L.P.K. and F.M.-C.; investigation, O.A.O., F.L.P.K. and F.M.-C.; writing--original draft preparation, O.A.O.