## 7 Conclusions  
In this paper, a novel approach to compute the necessary workforce in manual assembly systems was developed and then it was applied to a multi-model assembly line following the principles of LM. Multi-model lines have not been researched much and there is not a general procedure for multi-model lines as those developed for the SMALBP. Our method is based on the fact that verifying the balance between workload and resource capacity is necessary to assure that a production process is feasible in the considered time lapse. For this reason, we define the concepts of unit workload and capacity in order to avoid using time magnitudes (such as cycle time) since we assume that they are unknown. In Section 3, we derived the necessary equations to compute the required workforce without resorting to temporal magnitudes and used them to solve a small example. The same framework can be applied to other manufacturing strategies and thus, in Section 4, the method was applied to a multi-model assembly line. While many approaches in the assembly line balancing literature consider either a cycle time for each model [50] or a common cycle time as given, we state that there are practical cases in which a company will only have a daily schedule based on market demand. Therefore, computing an average cycle time may lead to inapplicable solutions. In our method, the need for operators is modeled in terms of workload and capacity, not on assembly times. The practical consequence is that it is not necessary to know any cycle time to solve the problem. Thus, this study furnishes practitioners with a better understanding of the relations between several variables to design, implement and control processes. In addition, it can be easily implemented (e.g., Tables 4-8 on an electronic spreadsheet) and quickly modified when the production mix changes. Then, the line can be balanced for each model using either well-known heuristics for single-model lines to find a feasible solution or linear programming as we did in this paper to be sure that we found the optimal solution. In all cases, the unknown cycle time is not necessary. Finally, our procedure was completed by means of a computer program coded in Python with the help of the OR-Tools library (which results in few lines of code, mainly devoted to manage data input and output). This allowed us to study all assembly lines together, based on linear constraints, in order to find an optimal solution--not just a feasible one--which minimized the number of workstations while aiming at a common number of workstations and even with a constant assignation of tasks to workstations, according to our interest. Besides not needing a previously defined cycle time, the result can be directly applied because real tasks are used instead of \"combined\" tasks. Using our algorithms will allow operations managers to quickly staff and balance (or re-balance) their multi-model assembly in order to guarantee a smooth operation (with few changes, if any, in the number of operators or in the tasks assigned to each operator during the workday). This will also ensure the production, in small batches, of the scheduled quantities and models to satisfy market demand. Results show that our approach is a suitable option for balancing multi-model lines, without great needs of assets (where light objects such as cell phones are assembled), and with labor (the number of workstations) being the only resource considered, and for considering the setup cost as a fixed cost because lot sizes are based on demand, not on cost minimization. These premises also constitute the limitations of our work and could be the basis of further research. Since we have been able to use our transformed data (\(Wu_{\vec{k}}\)) in methods originally intended for assembly times and cycle times (such as solving the SMALBP with linear programming), it would be interesting to study whether our approach can be used in combination with other extant techniques.