## 2 Production Process  
Figure 1 shows the eight main stages of the production process: (1) Preparation, (2) Mixing, (3) Division and Rounding, (4) Repose, (5) Press, (6) Bake, (7) Cooling, (8) Stacking and Packing. In this paper, we consider a hybrid flow shop with six stages (from 2 to 7), with different numbers of machines in the stages 2, 4, and 6. In the production of wheat flour tortillas, the raw ingredients prepared in Stage 1 are transferred to a large mixer (Stage 2), where they are combined to create the dough. Corn tortilla production starts with a process called nistamalization, in which the corn is soaked in an alkali solution of lime (calcium hydroxide) and hot water. The dough is divided into fragments with round shapes (Stage 3). These fragments repose in a controlled environment to obtain a certain consistency as to the temperature and humidity (Stage 4). Next, they are pressed to take the shape of a tortilla (Stage 5). Rows of tortillas are heated in stoves (Stage 6). The next steps are to cool (Stage 7), stack, and pack them (Stage 8). Figure 1: Tortilla production line. The process is distributed among flow lines with several machines per stage (Figure 2). It is operated in a semi-automated way controlled by operators. Tables 1 and 2 present the capacities of the machines in each stage. These are represented by the amount of work (tortillas in kilograms) that can be processed on each machine. Table 1 demonstrates that Stage 2 has six machines with processing capabilities of 80, 80, 100, 130, 160, and 200 kg per minute that can process jobs from 1 to 5. Machines 1 and 2 have the same capacities. Table 2 shows that Stages 3, 4, 6, and 7 have identical machines, and Stages 2 and 5 have unrelated machines. Table 3 shows the power of the machines in each stage in kW per minute. The consumption is independent of the type of job to be processed. Machines in Stage 4 do not consume energy. The equipment is cabinets, where dough balls remain for a given period. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Stage** & \multicolumn{5}{c}{**2**} \\ \hline
**Machines** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline Jobs 1–5 & 80 & 80 & 100 & 130 & 160 & 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The processing capacity of machines in Stage 2 (kg per minute). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Stage** & **3** & **4** & **5** & **6** & **7** \\ \hline
**Machines** & **1–6** & **1–6** & **1–3** & **4–6** & **1–6** & **1–6** \\ \hline
**Jobs** & 1 & 1.3 & 200 & 7.2 & 9.6 & 9.6 & 9.6 \\
**Jobs** & 2 & 1.3 & 200 & 6.4 & 8.8 & 8.8 & 8.8 \\
**Jobs** & 3 & 0.44 & 200 & 2.4 & 4 & 4 & 4 \\
**4** & 0.31 & 200 & 3.2 & 4.8 & 4.8 & 4.8 \\
**5** & 1.3 & 200 & 4 & 8.8 & 8.8 & 8.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The processing capacity of machines in Stages 3–7 (kg per minute). Figure 2: Six-stage hybrid flow shop. Table 4 shows characteristics of the jobs. We consider a workload with five jobs for production of the five types of tortillas most demanded by industry: Regular, Integral, Class 18 pcs, Taco 50, and MegaBurro. Each job is characterized by its type, group, and batches required for production. It has several assigned batches. This quantity must be within a certain range that is obtained from the standard deviations of the average monthly production in kilograms of tortillas for a year. The batch indicates the number of 10 kg tasks that have to be processed in the job. A job with one batch indicates processing 10 kg, and with five batches indicates processing 50 kg. The group indicates the compatibility of the job tasks. Job tasks belonging to the same group may be processed simultaneously. For instance, they can be processed on all unrelated machines of Stage 2, if their sizes are less than or equal to the capacity in kilograms of the machines (Table 1). The job tasks of the same type of dough can be combined, forming compatibility groups.