# A Multi-Criteria Assessment of Manufacturing Cell Performance Using the AHP Method
## 4 A Practical Example
### Assessment of Manufacturing Cell Designs Using AHP Method  
Firstly, the hierarchical structure of the AHP method is created. The overall focus is aimed at the selection of the optimal manufacturing cell design(s) from the five cell design alternatives. For this purpose, these five alternatives are compared using the criteria shown in Figure 6.  
Once the hierarchy is constructed, the alternatives are pairwise compared for each of the criteria based on the preferences using the scale of relative importance (see Table 3). The performance of each cell design (CD) with regard to each criterion is indicated by the following pairwise comparison matrices, and at the same time, it is assumed that all criteria are equal to each other (see Figure 7). Subsequently, the priority vectors are calculated according to the additive normalization method for all the criteria shown in Table 4. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Cell Designs** & **Makespan** & **OPF Makespan** & **PCI** & **BCI** & **PLB** \\  & **(min)** & **(min)** & **(bits)** & **(bits)** & **(\%)** \\ \hline
1 & 5926 & 3610 & 47.8 & 2.1 & 92.4 * \\
2 & 5014 & 3108 & 50.7 & 2.24 & 78.7 \\
3 & 5049 & 3079 & 53.9 & 2.45 & 78.2 \\
4 & 5438 & 3194 & 44.8 * & 1.62 * & 85.6 \\
5 & 4650 * & 2927 * & 47.1 & 2.14 & 50.7 \\ \hline \hline \end{tabular}
* Best obtained value.  
\end{table} 
Table 2: Enumerated results of all the criteria and sub-criteria. Figure 6: Hierarchical structure of the AHP method for selection of an optimal manufacturing cell. Moreover, from the obtained results of the computational experiments, it can be noted that:  
According to both complexity indicators, the three-cell solutions are less complex than the two-cell solutions. The lower complexity of the three-cell designs against the two-cell designs can be comprehended in a way that the scheduling of cell designs with a higher number of cells is less complicated than in the case with a smaller number of cells. This statement comes from the fact the probability that parts are produced on given machines is higher than in the case of the CM design with a smaller number of cells;  
Based on the makespan results, the three-cell solutions better satisfied the minimization of the total time needed to finish all the jobs than the two-cell solutions;  
From the viewpoint of the PLB indicator, the two-cell solutions offer better balancing of machines than the three-cell solutions. As mentioned, the case study was taken from the work of [PERSON] and [PERSON] [65], who compared two-cell solutions with three-cell solutions based on selected criteria such as the number of intra-cell flows and inter-cell flows, scheduling, etc., to point out the advantages and disadvantages of two-cell solutions and three-cell solutions. Our aim was to identify the optimal cell design solution(s) from the alternatives based on a multi-criteria decision-making approach, where five selected criteria were used. The main benefit of the used approach lies in the objective approach of the pairwise comparison of cell design alternatives in the decision-making process. Related future research could be oriented to employ other criteria to assess manufacturing cells design performance in order to bring new findings for practitioners and researchers. Conceptualization, V.M. ; methodology, V.M. and Z.S. ; validation, Z.S. ; formal analysis, V.M. and Z.S. ; writing--original draft preparation, V.M. and Z.S. ; writing--review and editing, V.M. ; visualization, Z.S. and J.N. ; supervision, V.M. ; project administration, V.M. All authors have read and agreed to the published version of the manuscript. This research was funded by the KEGA Project No. 025 TUKE-4/2020 granted by the Ministry of Education of the Slovak Republic. Not applicable. The authors declare no conflict of interest.