## 2 Literature Review
[PERSON] and [PERSON] [27] published a literature review on the methods used to solve the FJSP and the studied objective functions (Figure 1). In this bibliographic study, it was found that almost 59% of the papers used hybrid methods ([PERSON] and [PERSON] [28], [PERSON] and [PERSON] [29], [PERSON] and [PERSON] [30]) or evolutionary algorithms. The minimization of the makespan turned out to be the most widely studied criterion. In 88 research papers (44.67%), the makespan was used as the sole objective function, while in another 78 papers (39.59%), makespan was used in combination with another objective function. However, the minimization of the total flow time, which is the target criterion in this work, has been studied very little in the literature. Table 1 represents some research works on flexible job shop problems with minimization of flow time. These works are classified according to the fields of its application in research or an industrial case, the resolution methods used, some workshop details, and the studied objective functions. Finally, it is worth mentioning that, to the best of our knowledge, there are almost no studies addressing the problem of scheduling food production processes in hospital or collective catering. Most existing works in the literature on scheduling food production processes are from the food and dairy industries, where the production systems are parallel machine, flow shop, and single machine, in most cases. Moreover, in the majority of these works, the expiration date of products is unknown, while in this study, it is known. The works found in the literature cannot be adapted to the problem addressed in this study, since the production systems are different. In addition, several constraints specific to the considered problem have not been taken into account in the existing works, and they do not have the same objective of optimization. \begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Author** & **Year** & **Application** & **Algorithm and Workshop Details** & **Objective Function** \\ \hline The problem considered in this paper & 2021 & Research and industry & Mathematical model and metaheuristics for a flexible job shop problem with sequence-dependent setup time and job splitting & Minimum of total flow time \\ \hline [PERSON] et al. & 2018 & Research & Mathematical model and discrete Java algorithm & Minimum of makespan, total flow time, machine workload, and total machine workload \\ \hline [PERSON] et al. & 2017 & Research & Resolution approaches for uncertain resource assignment and job sequence in an automated flexible job shop & Minimum of makespan, number of late jobs, total flow time, and total weighted flow time \\ \hline [PERSON] et al. & 2013 & Research & Gene expression programming, dynamic flexible job shop problem with job release dates & Minimum of makespan, mean flow time, and mean tardiness \\ \hline [PERSON] et al. & 2013 & Research & Heuristic with priority rules & Minimum of makespan, total flow time, mean tardiness, number of tardy jobs, and max tardiness \\ \hline [PERSON] et al. & 2012 & Research & Heuristic & Minimum of makespan and mean flow time \\ \hline [PERSON] et al. & 2009 & Research & Multi-swarm particle swarm optimization & Minimum makespan of total flow time \\ \hline [PERSON] et al. & 2004 & Industry & Genetic algorithm and priority dispatching rules & Minimum ratio of tardy jobs, variance of the flow time, amount of mold changes, and maximum efficiency of machines \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Some research works on flexible job shop problems with flow time minimization.