## 5 Case Study and Discussion
### Multi-Objective Solution  
The case study was initially solved using the weighted-sum objective model, as presented in Table 5. The computation time was also solved in seconds since the problem size of the case study was relatively small. Each obtained objective function was then used as an ideal solution of the non-preemptive method (i.e., \(Z_{1}^{I}\), \(Z_{2}^{I}\), \(Z_{3}^{I}\), and \(Z_{4}^{I}\) were 6158, 5.92, 139, and 10, respectively). By converting the maximization to minimization and vice versa, the non-ideal solutions were obtained (i.e., \(Z_{1}^{AI}\), \(Z_{2}^{AI}\), \(Z_{3}^{AI}\), and \(Z_{4}^{AI}\) were 16,596, 0, 663, and 46, respectively). Solving each objective function alone yielded different printer schedules. The parts assigned to each printer during the production process and distributed to each location during the distribution process differed depending on the planning objectives. For example, solving \(Z_{1}\) with the minimum cost policy resulted in the least usage of the smallest-sized printers (i.e., the small ME, SLA, and SLS printers) and a small number of parts assigned to meet the minimum requirements or a daily operation with the minimum possible cost. Conversely, solving \(Z_{2}\) (i.e., maximizing the load balance of all printers, regardless of AM type) and \(Z_{3}\) (i.e., minimizing lateness) required all existing printers to be used. Solving \(Z_{4}\) (i.e., minimizing the total number of unassigned parts) required that all existing printers be used, except the small SLA printer. The solution set of each single-objective model highlighted trade-offs among the criteria. For example, solving \(Z_{1}\) yielded the lowest total operating and distribution cost (i.e., $6,158); however, the outputs related to the load balance and total lateness did not outperform solving other objective functions, and a high number of parts were left unassigned when the holding costs were considered. Meanwhile, solving \(Z_{3}\) provided the least total lateness (138 days), the total operating cost was higher \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Details** \\ \hline
**Part and Printer-Related Parameters** & \\ \hline Projection length/width/height (mm.) & ME: Uniform (80, 220); SLA: Uniform (90, 230); \\  & SLS: Uniform (100, 250) \\ \hline Shrink-wrap and bounding box volume (mm.) & Magics \\ \hline  & ME (Small 235 \(\times\) 200 \(\times\) 200, Large 300 \(\times\) 305 \(\times\) 457); \\ Printer capacity (mm.) & SLA (Small 128 \(\times\) 128 \(\times\) 200, Large 450 \(\times\) 450 \(\times\) 300); \\  & SLS (Small 385 \(\times\) 330 \(\times\) 460, Large 700 \(\times\) 380 \(\times\) 580) \\ \hline Fraction determining the minimum area/volume of a & 3\% \({}^{a}\) \\ printer & \\ \hline Fraction determining the minimum number of parts & 20\% \({}^{a}\) \\ required to operate a printer & \\ \hline \multicolumn{2}{c}{**Logistics-Related Parameters**} \\ \hline Transportation distance (km.) & Uniform (50, 100) \\ \hline Demand and order (pieces) & Uniform (5, 30) \\ \hline Shipping capacity (m\({}^{3}\)) & Uniform (5, 8) \\ \hline \multicolumn{2}{c}{**Time-Related Parameters**} \\ \hline Print time for an individual part (hours) & Magics \\ \hline  & ME: Uniform (5, 30); SLA: Uniform (10, 35); \\  & SLS: Uniform (3, 20) \\ \hline Labor working hours & 8 h/day \\ \hline Lateness computed from the customers’ due dates & U (–5, 5) \\  (days) & \\ \hline Wait time for the next period for parts that are not & 7 days \\ assigned (days) & \\ \hline \hline \end{tabular} \({}^{a}\): The parameter value was adjusted according to the number of parts and printers.  
\end{table} 
Table 4: _Cont._than that of \(Z_{1}\) (i.e., $15,827 vs. $6,158), the load balance was less than that of \(Z_{2}\) (i.e., 4.76% vs. 5.92%), and there were a greater number of unassigned parts than that of \(Z_{4}\) (i.e., 8 vs. 5). Then, a multi-objective solution was obtained by applying a non-preemptive method.