TOPSIS-Based Methodology for Selecting Fused Filament Fabrication Machines

Abstract

Additive manufacturing (AM) has been gaining increased traction in the manufacturing industry due to its ability to fabricate prototypes and end use parts in low volumes at a much lower cost compared to conventional manufacturing processes. There has been research to select an AM process appropriate for fabricating particular parts. However, there is little extant research to select appropriate AM machines even though there is a growing number of AM machines with interesting topologies, structures, and systems. This paper proposes a methodology that aims to assist Technical Experts in selecting a machine for Fused Filament Fabrication (FFF). The methodology is built around a weighted Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), which uses the concept of relative closeness and attribute weights to rank the machines. The paper uses Monte Carlo simulations for sensitivity analysis to evaluate the impact of randomizing attribute scoring, perturbing weights assigned, and probability distributions used to model human decision variability. The methodology and the sensitivity analysis were applied to three case studies, with five FFF machines and seven attributes, and top machines ranked for a specific part were found to be largely robust.

1. Introduction

Additive manufacturing (AM) is a manufacturing process where a part is built layer by layer using one of the following processes: material extrusion, stereolithography, powder bed fusion, sheet lamination, material jetting, binder jetting, and directed energy deposition. There has been a lot of research and many algorithms developed to help the user select a suitable process for a part and its application [1]. In metals, the mechanical properties obtained usually influence both the selected process and the parameters that are selected for that process [2]. However, in polymer extrusion, some properties, such as material behavior and mechanical performance of the finished part, are dependent primarily on the extruder and features such as temperature, flow rate, nozzle diameter, etc. [3]. A similar methodology could be conducted to compare the different extruders, and both the extruder and the machine ranking must be taken into consideration when a final decision is made. Conceptually, in subtractive or conventional manufacturing, this is akin to selecting the machining center and the tooling for parts. Although the machining center constrains the compatible tool, it is the final combination that influences the overall performance. Incorrectly selecting machines can have detrimental effects on the desired part. This could occur in the form of early part failure and inconsistent tolerance compliance. A higher-level issue that can be caused is the inability to meet throughput requirements, which could be caused due to the longer loading times, larger support structure requirements, and longer post-processing times. Within material extrusion AM (Fused Filament Fabrication) alone, there exist several unique systems that build upon the advantages and disadvantages of the process by utilizing different nozzle/extruder mounting techniques.

Machine selection is a key gap in the literature space of FFF, as most of the selection-based literature seeks to help identify the type of AM process used, but not the specific machine type. S. Raja et al. [4] compared different AM methods by applying the Analytical Hierarchy Process (AHP). Y. Wang et al. [5] compare the different AM processes based on their suitability for Design for Additive Manufacturing (DfAM). Their approach is very suitable as a first step for additive manufacturing decision-making. However, once a suitable AM process has been determined, it becomes very challenging to identify a suitable machine within that AM process. For example, within FFF alone, there are several different machine types.

M. Palanisamy et.al. [6] compare commercially available machines within the selective laser sintering scope of AM. The authors have effectively captured the different elements of a decision-making process and have applied the best–worst method of MCDM. This approach is very suitable for selective laser sintering applications due to the increased complexity of the process. However, for a process like FFF, this approach would not work, as the quality of the manufactured part is more heavily dependent on the machine used. Conventionally and most frequently available machines have an extruder nozzle mounted on a gantry. However, due to the limitation of a gantry system in terms of print volume and design complexity capabilities, a lot of new novel approaches have been in development, and some have already been developed. For example, to counter the print volume limitation of the conventional gantry system, companies have introduced a belt-based system that extends the print volume unidirectionally [7]. These novel machines also have some limitations, usually cost or, in some cases, accessibility.

Kaill et al. [8] provides a comparative study between conventional gantry (3-axis) systems to robotic arm (5-axis) systems by comparing the performance of the manufactured samples. This is a good direction that takes advantage of the ability of researchers comparing their novel techniques to conventional ones. However, industry cannot apply these techniques, as it would require access to both the systems, making the comparison expensive and non-feasible. For a selection purpose, the problem is comparing the available techniques on an overall basis based on the requirements of the industry/company.

The aim of this paper is to present Technical Experts, decision-makers, and key stakeholders with a proposed solution to this problem. Using FFF as an example, the paper provides a step-by-step methodology that will help compare the different types of machines within an AM process scope. The proposed methodology is based on the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, which has been modified to account for different attribute weights. Three parts of different complexities are used for evaluating the proposed methodology. However, as TOPSIS relies on subjective decisions, a sensitivity analysis is performed to evaluate the robustness of the results obtained from the case studies.

2. Methodology

This methodology is designed to support Technical Experts (TEs) and decision-makers in identifying and ranking suitable Fused Filament Fabrication (FFF) systems for part production. Considering that decision-makers may not possess deep analytical or technical expertise, the input requirements have been deliberately simplified, and the objectives are linearly structured. This design choice aligns with findings in decision science, which indicate that individuals perform better when presented with simplified comparisons, especially in pairwise formats [9].

To develop the decision framework, three multi-criteria decision-making (MCDM) methods were evaluated and compared: the Analytic Hierarchy Process (AHP) [10], VIšekriterijumsko KOmpromisno Rangiranje (VIKOR) [11], and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). The AHP was excluded due to its complexity and susceptibility to inconsistency and bias in group decision-making scenarios. VIKOR offered robust trade-off modeling but was ultimately not selected. TOPSIS was chosen as the preferred method for its capability to effectively manage both benefit and cost-type criteria, scalability to large decision spaces, and interpretability by non-expert stakeholders.

The proposed methodology employs a weighted TOPSIS approach and proceeds through seven sequential steps, summarized below. The first four steps require expert input, while the final three involve computational procedures.

2.1. Compilation of Machine-Attribute Matrix

TEs compile a list of candidate FFF machines and associated performance attributes. Attributes may include capital cost, build volume, precision, and other relevant technical specifications. Let:

• M_j represent the jth machine, where j = 1, 2, 3, …, J;
• A_k represent the kth attribute, where k = 1, 2, 3, …, K.

The resulting matrix R of dimension J × K is structured as:

$$R=\left[\begin{array}{ccc}{A}_{11}& \dots & A_{1J}\\ ⋮& \ddots & ⋮\\ A_{K1}& \dots & A_{KJ}\end{array}\right]$$

Here, A_kj denotes the value of attribute k for machine j. All entries in a given column are expressed in consistent units.

2.2. Definition of Ideal and Non-Ideal Attribute Values

TEs define the ideal (most desirable) and non-ideal (least desirable) scores for each attribute. These form the basis for evaluating relative performance:

• I = Ideal score vectors
• NI = Non-ideal score vectors

2.3. Scoring and Normalizing

Each machine is evaluated against the defined attributes based on specification data and expert judgment. A normalized score matrix S is constructed:

$$S=\left[\begin{array}{ccc}{S}_{11}& \dots & S_{1J}\\ ⋮& \ddots & ⋮\\ S_{K1}& \dots & S_{KJ}\end{array}\right]$$

Normalization ensures that all attributes are scaled appropriately to allow valid comparison across different units and magnitudes.

2.4. Assignment of Attribute Weights

TEs assign relative importance weights W = [W₁, W₂, …, W_K] to each attribute. These weights may be derived from literature, stakeholder priorities, or requirements specific to the intended part applications. In cases involving multiple experts, differences in assigned weights can be reconciled using methods such as the rating or Borda count techniques.

2.5. Calculation of Distances from Ideal and Non-Ideal Solutions

Euclidean distances are computed between each machine’s performance and the ideal/non-ideal vectors:

$$\begin{gathered} D^{+}=I-S \\ {D}^{-}=S-NI \end{gathered}$$

These distances quantify how close each alternative is to the ideal and how far it is from the non-ideal solution.

2.6. Computation of Relative Closeness

The relative closeness of each machine to the ideal solution is then calculated:

$$C={\displaystyle \frac{D^{-}}{(D^{+}+D^{-})}}$$

Higher values of C_kj indicate greater desirability.

2.7. Aggregation and Ranking

The final score T_j for each machine is obtained by weighing the closeness values:

$$T_i=\sum _{n=1}^k(W_n \mathrm{\ast } C_{kj})\forall j$$

Machines are then ranked in descending order of T_j, with the highest score indicating the most suitable machine.

2.8. Sensitivity Analysis

To assess the robustness of the rankings and account for potential bias in the weights or scores, a sensitivity analysis is recommended. Monte Carlo simulation can be used to perturb the attribute weights within a predefined range and observe variations in the resulting rankings. This provides insight into the stability and confidence of the selection outcome.

Figure 1 illustrates the full methodology workflow. Solid lines denote mandatory steps, while dashed lines indicate optional procedures, such as group-based weight reconciliation.

When an organization evaluates FFF adoption, it typically has specific part candidates in mind, with known dimensions, tolerances, production volumes, and cost constraints. The proposed methodology enables ranking of machines for each part. If a single machine consistently ranks highest across all parts, it becomes the clear choice. Otherwise, further analysis may be required to resolve conflicting rankings and optimize machine selection.

3. Evaluation and Discussion of Proposed Methodology

The proposed methodology is evaluated by performing three case studies using a set of 5 machines, 7 attributes, and 3 parts that have different weights. The machines and attributes selected are provided in

Table 1. List of machines selected for evaluation of the methodology.

Machines:
M1	Retrofit
M2	Gantry
M3	Assembled robot
M4	Belt Gantry
M5	Fixed nozzle

and

Table 2. List of attributes selected for evaluation of the methodology.

Attributes:
A1	Build volume
A2	Design freedom
A3	Support independence
A4	Max print speeds
A5	Ease of use
A6	Cost effectiveness
A7	G-code generation effort

, respectively.

Machine 1 is a retrofit FFF system [12], which is a custom-built 6-degree-of-freedom robotic arm with an extruder attached to the end. This machine is most suitable for single-use purposes, as it can be repurposed later. Machine 2 is a conventional gantry system. The extruder can be moved using either the Cartesian or the polar coordinate systems. This is the most commonly occurring FFF system, as most desktop systems are of this kind. Machine 3 is an assembled robot [13] and involves buying a whole pre-built robotic arm setup. The benefit of this is cost versus convenience. It is more suitable for large companies that want to use the system for mass production. Machine 4 is a belt gantry system [7]. It is a customization on the conventional gantry system, where instead of a traditional build plate, a moving belt is used to create an infinite axis. This is most suitable for bulk production or for unidirectionally large parts. This system is more expensive due to the customization of the conventional gantry system. Finally, machine 5 is a fixed nozzle system [14]. This is a novel take on the retrofit system where, instead of the extruder being attached to the robotic arm, the build plate is attached to the robotic arm. The extruder instead is fixed. This machine is most suitable for cases where multiple manufacturing processes are to be conducted on the same part.

The weights and scores are from Technical Experts (TEs); these are subjective and can vary from one expert to another even though they may be largely in agreement [15]. Specifically, these subjective values may vary based on the experiences of each expert as well as their frame of mind when evaluating the case. To test the sensitivity of the rankings obtained to changes in these subjective values, a Monte Carlo simulation [16] of 10,000 iterations was performed on the model. This was performed by modeling the scores as a triangular distribution with the assigned score as the mode and the lower and upper limits as 1 and 10, respectively. The rationale for the model is that the score assigned by the TEs may differ, but the probability of these differences decreases with increasing difference. This ensures each iteration of the simulation has randomized scores, with the assigned score being the most frequently appearing score.

To further evaluate the robustness of the model, the weights for Case 1 (Nema-23 adapter plate) were perturbed. The perturbation was performed by reducing the highest weighed attribute and proportionally distributing the reduced amount to the remaining weights (−10%, −20%). The perturbation was also performed by increasing the highest weighed attribute and proportionally removing the increased amount from the remaining weights (+10%, +20%). Figure 2 is the proposed evaluation methodology that has been used. The methodology for the Monte Carlo sensitivity analysis is outlined below:

• The first step of the sensitivity analysis is to repeat the initial steps of the TOPSIS methodology, which include compiling the R matrix, defining the I and NI values, assigning scores to the S matrix, and giving each attribute a weight (W matrix).
• Once the preparatory steps are completed, the next step of the sensitivity analysis is to use the values in the score matrix S as the mode to generate a matrix with a triangular distribution for each corresponding element. This triangular distribution will be used in a loop (based on the number of iterations) to generate a random number for the element score in each iteration.
• The third step of the sensitivity analysis is to perform the TOPSIS methodology at every iteration and store the ranks obtained. Once the ranks are determined and stored, the frequency of each rank appearing is observed and plotted.
• The next step is to perturb the weights and restart the TOPSIS methodology. The weight of the highest weighed parameter is perturbed, and the score is either distributed to or taken from the other weights. This also ensures that the weights remain normalized.

3.1. Nema-23 Motor Adapter Plate [17]

This part, displayed in Figure 3, has a relatively small build volume and simple geometry without overhangs, so it does not require significant support material. Therefore, attributes that are important for this part are print speed, cost of the printer, setup simplicity, and G-code generation simplicity. Accordingly, weights are assigned and presented in

Table 3. Assigned weights for the case of the Nema-23 motor adapter plate.

Criteria/Parameter	Weights
Build volume	0.05
Design freedom	0.05
Support independence	0.05
Max print speeds	0.3
Ease of use	0.25
Cost effectiveness	0.2
G-code generation effort	0.1

, and

Table 4. Weighted score calculation for the case of the Nema-23 motor adapter plate.

Criteria/Parameter	Weighted Scores (Weight × Score)
	Retrofit	Gantry	Assembled Robot	Belt Gantry	Fixed Nozzle
Build volume	0.02	0.03	0.02	0.04	0.03
Design freedom	0.04	0.02	0.04	0.03	0.04
Support independence	0.04	0.01	0.04	0.02	0.04
Max print speeds	0.13	0.27	0.13	0.27	0.13
Ease of use	0.08	0.22	0.14	0.17	0.08
Cost effectiveness	0.16	0.13	0.04	0.09	0.16
G-code generation effort	0.02	0.10	0.08	0.10	0.02
Net	0.49	0.78	0.49	0.71	0.51

presents the weighted scores for each of the machines under consideration. Based on this, the best machine would be the gantry (score of 0.78), followed by the belt gantry (score 0.71). The ranked order is M2 gantry, M4 belt gantry, M5 fixed nozzle, M1 retrofit, and M3 assembled robot.

3.2. Five-Blade Impeller [18]

This part, displayed in Figure 4, has a relatively small build volume but has a complex geometry with significant overhanging features, so support independence becomes important. Because of these part requirements, the cost, G-code generation, and maximum print speeds are given higher weights. Accordingly, weights were assigned and are presented in

Table 5. Assigned weights for the case of the five-blade impeller.

Criteria/Parameter	Weights
Build volume	0.05
Design freedom	0.3
Support independence	0.3
Max print speeds	0.1
Ease of use	0.05
Cost effectiveness	0.1
G-code generation effort	0.1

, and

Table 6. Weighted score calculation for the case of the five-blade impeller.

Criteria/Parameter	Weighted Scores (Weight × Score)
	Retrofit	Gantry	Assembled Robot	Belt Gantry	Fixed Nozzle
Build volume	0.02	0.03	0.02	0.04	0.03
Design freedom	0.23	0.13	0.23	0.17	0.23
Support independence	0.23	0.03	0.23	0.10	0.27
Max print speeds	0.04	0.09	0.04	0.09	0.04
Ease of use	0.02	0.04	0.03	0.03	0.02
Cost effectiveness	0.08	0.07	0.02	0.04	0.08
G-code generation effort	0.02	0.10	0.08	0.10	0.02
Net	0.65	0.49	0.66	0.58	0.69

presents the weighted scores for each of the machines under consideration. Based on this, the best machine would be the fixed nozzle (score of 0.69), followed closely by the assembled robot (score 0.66) and retrofit (score 0.65).

3.3. Vertical-Axis Wind Turbine [19]

This part, displayed in Figure 5, has a relatively large build volume with a complex geometry, so support independence becomes important. Because of this part’s requirements, the build volume, design freedom, and support independence are given higher weights. Accordingly, weights are assigned and presented in

Table 7. Assigned weights for the case of the vertical-axis wind turbine.

Criteria/Parameter	Weights
Build volume	0.3
Design freedom	0.15
Support independence	0.15
Max print speeds	0.1
Ease of use	0.1
Cost effectiveness	0.1
G-code generation effort	0.1

, and

Table 8. Weighted score calculation for the case of the vertical-axis wind turbine.

Criteria/Parameter	Weighted Scores (Weight × Score)
	Retrofit	Gantry	Assembled Robot	Belt Gantry	Fixed Nozzle
Build volume	0.13	0.17	0.13	0.27	0.17
Design freedom	0.12	0.07	0.12	0.08	0.12
Support independence	0.12	0.02	0.12	0.05	0.13
Max print speeds	0.04	0.09	0.04	0.09	0.04
Ease of use	0.03	0.09	0.06	0.07	0.03
Cost effectiveness	0.08	0.07	0.02	0.04	0.08
G-code generation effort	0.02	0.10	0.08	0.10	0.02
Net	0.54	0.59	0.57	0.70	0.59

presents the weighted scores for each of the machines under consideration. Based on this, the best machine would be the belt gantry (score of 0.7), and other machines are clustered together but have significantly lower weighted scores.

3.4. Sensitivity Analysis

Given that the scores and weights are subjective inputs, it becomes important to assess how sensitive the rankings provided by the methodology are, particularly when the top ranked ones are close to each other. For example, an input from a decision-maker may not precisely represent their opinion and may be somewhat approximate. The challenge therefore is to assess how the rankings for the machines change if the scores and weights are changed. Therefore, sensitivity analysis was performed using Monte Carlo simulations for all three cases.

Figure 6 shows the number of times a specific ranking of the five machines occurred for Case 1 in 10,000 runs of Monte Carlo simulation. It can be observed from the figure that the ranking [4,6,8,20,21] occurred 445 times, i.e., M2 was the top, followed by M4, M5, M1, and M3 at the bottom. This is consistent with the baseline ranked order of M2 gantry, M4 belt gantry, M5 fixed nozzle, M1 retrofit, and M3 assembled robot. Furthermore, in Figure 6, it is observed that there was a significant drop in rank frequency when there was a change in the top two machines. If we compare the data in Figure 6 with those in Table 4, it is observed that the scores of the gantry and the belt gantry system were significantly higher than the other machines, which is further confirmed by the data in Figure 6. Therefore, in this case, the rank order can be considered robust to small variations in human input.

Similarly, Figure 7 and Figure 8 show Cases 2 and 3, respectively, with the number of times a particular rank order is obtained after 10,000 runs of Monte Carlo simulation. It is observed that the top two machines that have been recommended based on baseline human input match the ones from the simulation about 40% of the time. In Figure 7, there are three machines that are rotating in the top two recommended machines. This can be attributed to scores that are relatively close to each other in Table 6, further confirming that the baseline human decision is robust in this case.

In Table 8, the belt gantry system has the best score by a significant margin from the other machines, whose scores are all close to each other. From Figure 8, it is observed that the belt gantry system is top ranked most often. Since the other systems have scores close to each other, there is no significant difference between them, and the baseline human decision can be considered robust in this case also.

From the Monte Carlo simulation of the scores, the recommended printer matched the ones from the case studies. From this, it is evident that the TEs’ assigned scores display some level of flexibility and the overall methodology can be considered robust. The third case study is the only one that shows a deviation in the ranking of printers, albeit the rankings of the worst were interchanged. This is acceptable, as their scores are relatively close to each other.

From the Monte Carlo simulations of the varied weights, we can observe that the ranking of the printers did not change with perturbations. In particular, the machine that was top ranked remained the same regardless of the amount of perturbation or direction of perturbation, as shown in

Table 9. Frequency of each machine ranking first in the Monte Carlo simulation after perturbing weights.

Machine	Perturbation%
	−20%	−10%	0%	10%	20%
Retrofit	7.10%	6.74%	6.58%	6.50%	6.40%			High
Gantry	48.07%	48.21%	47.88%	47.72%	47.44%
Assembled robot	7.05%	6.58%	6.52%	6.36%	6.38%
Belt gantry	29.85%	31.35%	32.14%	32.70%	33.24%
Fixed nozzle	7.93%	7.12%	6.88%	6.72%	6.54%			Low

. This is because the methodology depends on the overall ratio of all parameters rather than on the weight of a particular parameter, which makes it robust.

Another aspect of robustness is the choice of probability distribution used to characterize variation in human input and the number of simulation runs: e.g., whether the top ranked machine remains the same for 1000 simulations, 5000 simulations, and 10,000 simulations. All the above Monte Carlo simulations model human input variation as a triangular distribution. Alternatively, instead of triangular distribution, normal or beta distributions can be considered.

Figure 9 illustrates a histogram of 10,000 computed samples for triangular distribution for machine 1, attribute 1, with a specified mode of 5, an upper limit of 10, and a lower limit of 1. Similarly, Figure 10 and Figure 11 illustrate histograms for normal and beta distributions. The specified (and computed) parameters of the triangular distribution are mean 5 (5.34), mode 5 (5.13), and standard deviation 1.5 (1.82). The specified (and computed) parameters of the normal distribution are mean 5 (4.99), mode 5 (4.93), and standard deviation 1.5 (1.53). The specified (and computed) parameters of the beta distribution are mean 5 (5.0), mode 5 (4.95), and standard deviation 1.5 (1.34). Given the close agreement between specified and computed values of the parameters, the Monte Carlo simulation program can be considered an accurate computational model.

The impact of triangular, normal, and beta distributions were evaluated by running 10,000 simulations for the case of Nema 23 plate. Specifically, for the triangular distribution, the mode was set to the score assigned by the TEs along with lower and upper bounds of 1 and 10, respectively. For the normal distribution, the mean is the TE-assigned score and the standard deviation is 1.5. For the beta distribution, to have a mean of 5, mode of 5, and standard deviation of 1.5, the shape parameters specified are α = 4.44, β = 5.56, with a concentration of 10. Minor adjustments are made in the Monte Carlo simulation program to ensure that scores computed are bounded between 1 and 10 by rounding up/down to the nearest bound. As shown in

Table 10. Results of the Monte Carlo simulations with different distributions.

Type of Distribution	Triangular	Normal	Beta
Recommended machines	2, 4	2, 4	2, 4
Frequency	4141	5469	7184
Frequency percentage	41.41%	54.69%	71.84%

, the top two machines were consistent regardless of the distribution used. Therefore, in this case, the methodology can be considered robust to the probability distribution used to model the variation in human input.

The triangular distribution had the lowest frequency of occurrence of the top two recommended machines. From the frequency plots, all three distributions followed the same trend. The difference in the frequencies between different recommendations was more severe in the normal and beta distributions. There was very little difference between the orders within the top two machines, which was observed in the triangular distribution. Figure 12 provides the frequency of the top eight recommended systems for each distribution.

To evaluate the sensitivity of the ranked order to the number of simulation runs, Monte Carlo simulations were run for 1000, 5000, and 10,000 runs. As shown in

Table 11. Results of the Monte Carlo simulations with different runs for the case of the Nema-23 motor adapter plate.

Number of Iterations	1000	5000	10,000
Recommended machines	2, 4	2, 4	2, 4
Frequency	430	2078	4117
Frequency percentage	43.00%	41.56%	41.17%

, the top two machines were consistently M2 and M4 for all runs. Therefore, in this case, the methodology can be robust to the number of simulation runs beyond 1000.

4. Conclusions

This paper proposed a TOPSIS-based methodology for selecting FFF machines and applied the methodology to rank machines for fabricating three different parts. The parts considered were a NEMA 23 adapter plate, an impeller blade, and a vertical turbine, which varied in complexity and the need for support structures. Five FFF machines with different architectures were considered. This methodology has several advantages:

• Computationally simple. No complex algorithm that requires high computational power is used.
• Easily expandable/modifiable. As the scores do not mutually influence each other, additional machines can be added in the future without having to repeat the human input elicitation for earlier machines.
• Part specific performance: This methodology ranks machines based on the requirements for the specific part under consideration.

One limitation of the methodology is that it relies on human inputs for scoring machines for various criteria and weights for these criteria, all of which are subjective and can vary based on the individual’s expertise and experience. Monte Carlo simulation was used to perform several sensitivity analyses to evaluate the impact of changes in human input to the ranked order of machines for the three parts. It was found that the top two machines consistently remained on top even when scores were changed randomly in the simulation. Moreover, +/− 10% or +/− 20% perturbations in the most important weight did not change the top ranked machine for any of the three parts. Furthermore, the proposed methodology was also found to be robust to the probability distribution used to characterize variability in human input across triangular, normal, and beta distributions. Lastly, top-ranked machines did not change for 1000, or 5000, or 10,000 Monte Carlo simulations. Therefore, it can be reasonably concluded that the proposed methodology is robust in terms of variability in human inputs of scores, weights, and the probability distribution used to model human variability.

5. Future Work

The focus of this paper was selecting machines for FFF for a given part. Future work should include ranking extruders for various materials and mechanical properties. Much of the proposed methodology can be reused for other additive manufacturing machines and processes. Another worthy topic would be to include assistance in the selection of suitable weights for each criterion. The use of explainable MCDMs such as VIKOR could also be implemented alongside the methodology to provide additional details on the tradeoffs that help the decision-makers understand the reasoning behind the TOPSIS ranking.