# Evaluating 3D Printers Using Data Envelopment Analysis
## 3 Data Collection and Implementation
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Tensile Strength** & **Young’s** & \multirow{2}{*}{**Stiffness**} & **Impact** & **Price** \\  & **(MPa)** & **Modulus (GPa)** & & **Resistance** & **(USD/kg)** \\ \hline ABS & 22–38 & 0.8–2.3 & High & Medium & 10–40 \\ ASA & 33–55 & 2.0–2.2 & High & Medium & 30–50 \\ PA & 39–85 & 1.0–2.4 & Middle & High & 25–65 \\ PC & 60–72 & 1.8–2.3 & High & Medium & 40–75 \\ PET & 50–53 & 2.1–3.6 & High & Medium & 20–60 \\ PLA & 39–65 & 1.3–3.3 & High & Low & 10–40 \\ TPE & 26–43 & 0.4–0.6 & Low & High & 30–70 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic properties and price range for common FDM materials [53–57]. extrusion/bed temperatures, infill pattern and percentage, deposition speeds, etc.) and the generation of support structures. They include, also, modules for simulating/previewing the generated G-code file. Advanced features such as multi-material support, mesh modifiers, break-away support structures, variable layer height definition and special infill patterns (e.g., gyroid, Hilbert, or adaptive cubic) are, also, available. For the identified printers, technical data concerning specific parameters were collected from relevant web sources, mostly from the manufacturers' official web sites but also from various 3D printing forums and sites. The technical characteristics, which were employed as parameters in the proposed DEA evaluation, were: build volume (effective machine volume), number of extruder heads, layer thickness (Z resolution), nozzle diameter, the existence or not of a heated plate, resolution of movement in the X-Y (layer) plane, variety of materials that can be processed by the printer, nominal power, printing speed, whether the printer is open source or not, weight, and, finally, the printer's market price. The 3D printer has been considered as a system whose inputs are associated with cost features, whereas its outputs are associated with its technical characteristics and capabilities. Therefore all the above parameters, but the last one, were evaluated as outputs, whilst market price was considered the sole input parameter. Taking the above statement into consideration, the primary objective of the evaluation is to evaluate whether DMUs can proportionally reduce their excess resources (cost) while keeping their characteristics constant. Thus input oriented DEA has been employed in the current analysis. It is evident that regarding certain parameters, enhanced 3D printer performance is associated with higher corresponding values. It is preferable, e.g., for a printer to have a higher printing speed or a larger printing volume. Nevertheless, there are also parameters related to the printer's performance that we prefer to be as small as possible, e.g., the minimum layer thickness or X-Y resolution possible. To overcome the different, ascending or descending, nature of the parameters, which cannot be handled by DEA, a simple transformation of values for descending-nature parameters was performed. In this case, the 'transformed' values of parameter were computed by subtracting the actual parameter value from the highest corresponding value that was observed at the selected group of printers. This way, the 'transformed' parameter obtains its lowest value, i.e., zero, when the actual parameter attains its worst, i.e., its maximum, value. Ascending parameters are retained unchanged. Binary parameters, such as whether a printer is open source or is equipped with a heated platform, were given a value of one, when the answer was negative, and two otherwise. Being open-source was considered advantageous because it allows easier and lower-cost equipment maintenance and modifications. Finally, the parameter associated with material variety obtained values from 1 to 4 according the number of different materials that the printer could reportedly process.