## 3 Theory: Problem Statement and Mathematical Formulation  
In the considered problem, we concentrated on grouping cross-trained workers and assigning parts to workers in each manufacturing cell simultaneously. Figure 1 illustrates the overview of the problem. We considered the TFWAP under the CCM system in a single-period operation. Our main focuses are: (1) to form a high TWQ team of skilled workers in each cell to satisfy the part production demands and (2) to assign parts to workers considering minimisation of inventory level and variation of workers' idle time in each cell. We represented the fairness issue by the minimisation of workers' idle time variation. The manufacturing cell consists of part families determined by the predefined cell formation, that is, types of tasks and parts are fixed in each cell. Workers are heterogeneous in terms of skill level and sociometric value. Operations in the cell are manual operations requiring workers' skills to perform the task. Some workers may be skilled in performing different tasks. A skilled worker with task skill coefficient \"1\" can execute the part at the standard part processing time, whereas an unskilled worker with task skill coefficient less than \"1\" requires more time than the standard part processing time. Thus, the part processing times of each worker differ depending on their task proficiency. The sociometric values indicate the workers' interpersonal relationships, rated from \"1\" to \"5\" as very bad, bad, neutral, good, and very good, respectively. The assumptions of the model were as follows:  
1. The part production demand is known and deterministic.
2. The available working time of all workers is equal and deterministic.
3. The amount of time that each assigned worker spends on each part is equal to one hour.
4. Worker walking time between different workstations is neglected due to a compact cell layout.
5. The setup time when workers change task is neglected.
6. The standard part processing time for all parts is known and deterministic.
7. Sociometric matrices of workers are assumed to be known in advance.
8. The skill levels of workers are static, with learning and forgetting effects being neglected.
9. Workers' processing time for each cycle is static, with fatigue effects being neglected.
10. The tools and equipment for all tasks are duplicated; thus, workers can operate parts together in the same task.
11. The number of workers in a cell is less than or equal to the number of tasks in the cell.
12. Working overtime and cell transfer are prohibited.
13. Minimum cell-cohesion levels are required in each cell.
14. All part production demands have to be satisfied.  
This paper presents two mathematical models--namely, Model A and Model B. Model A is a single-stage model that considers only the worker-part assignment problem. Model B is a two-stage model consisting of the two models B1 and B2. Model B1 is the team formation problem that intends to form a skilled workforce with a good relationship among team members in each cell. Model B2 is the worker assignment problem of each cell. The idea behind Model B1 is to assure Model B2 with skilled workers in satisfying part production demands. We developed Model B with the intention to clarify that the TFWAP is more suitable for the two-stage model. Owing to the model assumptions, both models are nonlinear using penalty functions.