 parameters of the randomly generated instances. To adapt the instances from the literature to the studied problem, the missing data, such as the quantities of dishes, due dates of jobs, machine capacities, and time windows of availability of machines, were randomly generated according to uniform distributions and by taking into account the data on the processing times of operations and the setup times of machines given in these instances. The results of the developed resolution methods for these different categories of instances are presented below.

Optimization of the Metaheuristics' Parameters
To optimize the parameter values of the developed metaheuristics, the Taguchi method was used. The choice of these parameters has a significant effect on the efficiency of the metaheuristic algorithms. The parameter values that are needed for optimization act like controllable factors in the design of experiments. The aim is to find an optimal combination of the parameters such that the total flow time is minimized. To employ the Taguchi Table 4.

Discussion of the Experimental Results
The optimization criteria of the developed metaheuristics are based on the quality of the solutions and rapidity. The quality and efficiency of the metaheuristics were proven by comparing the solutions obtained with these algorithms and the optimal solutions of the mathematical model. Regarding the rapidity, the computation times of the algorithms were compared with those of the mathematical model. From the results presented above (Tables 5-9), we remark that the two genetic algorithms are efficient in terms of quality and rapidity. The performance of the developed resolution methods depends on the types of instances and their sizes, and it also depends on the choice of heuristics for the generation of initial solutions. The first genetic algorithm is more efficient in terms of quality with the MMWA assignment heuristic and the SPT sequence heuristic, while the second genetic algorithm is more efficient with the MMWA and MNOR heuristics. For the iterated local search algorithms, the first algorithm gives better solutions with the SPT assignment heuristic and the MNOR sequence heuristic, while the second algorithm finds good solutions with the MMWA and MNOR heuristics. Regarding the rapidity, the four metaheuristics are more faster with the RA assignment heuristic and the RS sequence heuristic.
The results of the genetic algorithms for different types of instances (Tables 5-9) show that the developed metaheuristics are efficient relative to the quality of solutions. Table 5 represents the results of the different methods developed on a real instance with 82 jobs, 92 sub-lots, 370 operations, and 29 machines. From these instances, several sub-instances were built by increasing the number of jobs, sub-lots, and operations each time to see from what number of jobs, sub-lots, and operations the model is not able to find solutions. From Table 5, we observe that for the real instances of the HCT, the mathematical model quickly found solutions for the small instances with less than five dishes, five sub-lots, 24 operations, and 29 machines. It took a little longer for the instances with more than six dishes, six sub-lots, 29 operations, and 29 machines. However, for the instances with more than nine jobs, 44 operations, and 29 machines, after more than 3 h of execution, the mathematical model did not find solutions. For these instances, the two genetic algorithms succeeded in finding feasible solutions in very short computation times. For example, for the large instance with 82 jobs, 92 sub-lots, 370 operations, and 29 machines, the first genetic algorithm found a feasible solution that respected all the constraints after 5 min of execution.  Tables 6-8 present the performances of the resolution methods in terms of quality and rapidity for randomly generated instances and a comparison between the solutions obtained by these different methods. From the results presented in these tables, we remark that the genetic algorithms found feasible solutions for the large-size instances in reasonable resolution times.
In Table 9, we observe that for the instances adapted from the literature, the genetic algorithms make it possible to improve the solutions of the instances adapted from the literature. For example, for the instance from Lee et al. [35], the genetic algorithms brought about an improvement of 3.92% over the solutions obtained with the methods proposed by Lee et al. [35].   Comparing the two genetic algorithms in terms of rapidity, the first algorithm is faster than the second algorithm, while comparing them in terms of stability both algorithms are stable for the real instances of HCT and randomly generated instances, while for the randomly generated instances of the HCT type, the second algorithm is more stable than the first algorithm. Comparing the two algorithms in terms of quality of solutions, the performance of the algorithms depends on the types of instances. For some instances, the first algorithm is better than the second algorithm, while for other instances, the second algorithm is more efficient than the first algorithm.
By comparing the results obtained with the genetic algorithms and the iterated local search methods for all the tested instances, we find that the ILSs are worse than the GAs in terms of the quality of solutions obtained. However, in terms of rapidity, the ILS methods are faster compared to the GAs.

Application to an Industrial Case
This work was carried out in collaboration with the hospital center of Troyes (HCT). To effectively meet the needs of patients and to improve working conditions and employees' well-being, the hospital center of Troyes implements important measures to improve its daily efficiency. It is in this context that this study of hospital catering activity optimization takes place.
The HCT is carrying out a project to revise its supply chain, which must, in particular, consider the management of food flows. The contribution of the present work is to determine the best plan for meeting customers' demands in terms of food flows and to propose ways to improve the well-being and working conditions of employees of the catering service of the hospital center of Troyes. The aim is to provide methods and tools for scheduling meal-making processes throughout the day.
The hospital center of Troyes is the main member of the South Champagne Hospitals group. Its logistic network ( Figure 10) is composed of a set of customers whose meal needs are met from a warehouse, which is the central kitchen and a set of suppliers. These customers are hospitals, nursing homes, and psychiatric clinics. The central food production kitchen of the HCT produces, on average, 4800 meals per day. Its maximum daily production capacity is 5000 meals per day. The HCT catering service includes a production unit divided into several sectors, from the reception of raw materials to the dispatch of finished products and a coordination unit for menu management. In this study, we are particularly interested in the sectors from the pre-treatment of raw materials to the stock of finished products ( Figure 11). This figure represents the production areas of the studied system and the different machines available for carrying out the operations of the meal-production process.   Table 10 represents the results of the genetic algorithm for some examples of real production days with a comparison between the real solutions, as these production days were organized and the solutions were proposed by the genetic algorithm. In this table, for each instance, the number of dishes, the number of sub-lots of dishes, the total number of operations, the number of machines available, and the average number of meals produced per day are given. The performance indicators between solutions are based on the total flow time and the gaps between them. From these results, we remark that the gaps between the real solutions and those of the genetic algorithm are very important and significant. The performance of the genetic algorithm for these instances depends on their types and sizes. For example, for the instance with 62 dishes, 68 sub-lots, 218 operations, and 29 machines, we brought about a considerable improvement of 18.72% over the real solution, which shows the quality and performance of the developed algorithms.

Conclusions
The present article deals with the study of a new industrial problem. Different resolution methods for the scheduling of production processes in hospital catering were developed. A mathematical model integrating all the constraints of the studied problem was proposed. This model is an improvement of the standard flexible job shop scheduling problem with sequence-dependent setup times by integrating specific industrial constraints. An extensive study confirming the effectiveness of the developed model is presented. The computational results of the mathematical model for different types of instances show the limits of an exact resolution for the problem of scheduling production processes. To solve the large instances of the addressed problem, different metaheuristics were developed and tested on several types of instances. The computational results of these metaheuristics have proven their effectiveness and reliability for the scheduling of operations of the food production process and allowed significant improvements in the real current organization and system performance. As regards future research, this work is limited by the number of human resources available and does not take into account the possible hazards, such as the absence of staff, machinery breakdowns, and the unavailability of raw materials. Further research can be extended by considering these constraints. The present work also opens the way to other perspectives, such as the study of the production planning problem over several days, and our future work will focus on the development of resolution methods for this problem.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to confidentiality of the company.**Extraordinary 2-story home with a big backyard in a great location** From the beautifully landscaped front yard, to the open and spacious floorpan, to the oversized backyard, this one is sure to impress! The more than 1,700 square feet of living space is masterfully utilized, allowing for large open spaces, tall ceiling, 3 large bedrooms, (HUGE primary!) 2.5 bathrooms, a small loft and a walk-in closet so big, it could be considered a bedroom. (lol) But that's not all! All of the appliances are included! That includes the gas stove, the built-in