Application of the TOPSIS decision-making method for selecting a manufacturing technique for children’s furniture elements with therapeutic functions

The rapid development of the furniture industry in recent years has forced furniture manufacturers to become competitive and follow current trends as they create new pieces (Imad et al. 2022; Nasir and Cool 2018). For example, manufacturers are looking for new materials that can be produced for furniture or furniture elements (Ramage et al. 2017). The use of composite materials has attracted wide interest. Aguilera and Davim (2017) described the production and characteristics of this type of material. Increased competitiveness in the automation and robotization of production is desired, and the implementation of industry solutions is based on Industry 4.0 (Muhuri et al. 2019). Attention has been given to the cooperation between researchers and industrial manufacturers. Schajer (2016) wrote about this topic. New manufacturing techniques (e.g., additive methods) and combinations of these methods (e.g., hybrid manufacturing methods) have been explored (Davim 2011). The direction of production for a specific end user and the selected needs of individual customers are clearly visible (Koskinen et al. 2014). In modern production, various computational and simulation methods are used, such as the finite element method (FEM) and artificial neural networks (ANNs) (Davim 2017). Notably, in industrial applications, statistical methods are used to find correlations between variables and process results (Davim 2012). Examples of design of experiments (DoE) methods and their applications were presented by Davim (2016). Moreover, created collections of furniture (especially children's furniture) very rarely take into account the needs of people at different stages of development or with dysfunctions (e.g., children with intellectual disabilities, children at risk of developmental dyslexia, and children born prematurely). There is a lack of children's furniture that supports the psychomotor and cognitive development of children from their birth to the age at which they are ready for schooling (usually for children under 7 years of age). Research that underlines the main patterns of sensory integration function and dysfunction of human behavior was presented by Lane et al. (2019). Ayres was one of the first occupational therapists to conceptualize sensory integration (Kilroy et al. 2019). Sensory processing problems and related dysfunctions are among the most common conditions in children with autism spectrum disorder. For example, Kashefimehr et al. (2018) examined the effects of sensory integration therapy on different aspects of occupational performance in 3- to 8-year-old children. Schoen et al. (2019) presented a review of research on the evaluation of the effectiveness of sensory integration. Supporting various stimuli at the early stage of child development can reduce the risk of disorders such as dyslexia (Hahn et al. 2014).

An important aspect of human development is the sense of touch. Determining the impacts of measurable physical surface characteristics on a person's tactile response is important for the manufacturing of furniture and household goods. Currently, there is a trend to consider tactile experiences in product design, development, and quality control. The quality of wood surfaces or furniture components after manufacturing and the optimization of surface parameters has often been analyzed from a technological point of view, as reported in studies such as Gaitonde et al. (2008b, a), Malkoçoğlu (2007), and Guo et al. (2023). For example, in the field of milling medium-density fiberboard (MDF), Davim et al. (2009) showed that the surface roughness decreases with increasing cutting speed. Another approach to surface characterization involves combining psychophysical research with both materials science and materials processing technology. Tactile preferences related to the roughness, friction, and thermal properties of surfaces were investigated by Skedung et al. (2020). Hollins et al. (2000) described the subjective perception of different surfaces and concluded that characteristics such as roughness/smoothness and softness/hardness are very relevant for individual surface perception. In turn, Chen et al. (2023) examined the visual and tactile perception of milled surfaces for humans by taking into account surface roughness. The results showed that a rough surface can be accurately identified regardless of the sensory conditions of the study participants. Similarly, Hartcher-O’Brien et al. (2019) studied surface roughness perception for 3D-printed materials and reported that even minor changes in printing speed lead to detectable differences in surface roughness. Participants can reliably discern differences between various samples, even when the values of the Ra and Rq parameters are comparable. Wongsriruksa et al. (2012) presented results on the relationship between the measured surface roughness, elastic modulus, thermal effusivity, and perceptual properties of roughness, hardness, and coldness for woods, polymers, and metals. The scholars reported a strong correlation between the physical and psychophysical properties of the material that influence tactile perception.

Creating a collection of children's furniture that directly impacts the comprehensive mental and physical development of a child is very difficult. From the designer's point of view, the basic objective is to determine the specific properties and functionalities of children's furniture that can have a direct positive impact on development. Moreover, furniture designed in this manner must be able to perform operational functions. Therefore, this type of final product has dual functions. Furthermore, despite the existence of some general developmental regularities, each child develops somewhat differently. The solution may be a collection of modular furniture that allows for the selection of compatible furniture elements with educational and therapeutic benefits, permitting the adaptation of the properties of furniture to the changing needs of children at different stages of their development. From the point of view of the exploitation and production of furniture, it is difficult to choose the material and production technique of furniture and furniture elements. This difficulty lies in choosing the optimal quantitative and qualitative characteristics of the solution.

In general, in the field of multicriteria optimization, two types of selection criteria are distinguished, namely, quantitative and qualitative (Triantaphyllou 2000). The assessment values of these criteria are expressed in different units or are dimensionless and have different definitions; therefore, the values must be assigned appropriate weights resulting from the requirements or preferences of the decision-maker. For example, in the area of decision-making, based on multicriteria methods, one can distinguish the weighted sum model or weighted product model, the analytic hierarchy process, the method of elimination by comparison in pairs for each criterion and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The methods have been described in detail by many authors, e.g., Triantaphyllou (2000), Velasquez and Hester (2013) and Behzadian et al. (2012). In the furniture industry, optimization techniques that are directly related to the manufacturing of wooden materials are used. For example, Gaitonde et al. (2008b, a) presented the Taguchi optimization method for the simultaneous minimization of the delamination factor at the entrance and exit of holes in the drilling of a SUPERPAN DÉCOR (melamine coating layer) MDF panel. In turn, Rao and Davim (2008) presented a logical procedure for material selection for a given engineering design. The procedure is based on a combined TOPSIS and analytic hierarchy process method. The proposed material selection index can be used to evaluate and rank materials for a given engineering design. One of the most effective methods for assessing and selecting the best solution variant is the APEKS method, which is a type of TOPSIS method. The description and application of this method were presented by Szybka (2021). The basic principle of choosing a solution is to compare existing evaluated solutions to APEKS variants, which are the optimal simulated values. This method allows for the selection of the best option using quantitative and qualitative assessment criteria. The APEKS variant is created by assigning the best rating values of an actual variant to it for each assessment criterion.

According to the literature analysis, there are no guidelines for selecting methods for manufacturing furniture elements for special applications. A new approach in this regard is the use of the fast and flexible APEKS method from the TOPSIS group. In this article, a comparative analysis of two methods—the defective milling method and the additive 3D printing method—for producing furniture elements with a structure similar to that of the natural bark of a tree was conducted. The APEKS method was used to select the best solution, taking into account quantitative criteria (values of quality parameters for the surface) and qualitative criteria to characterize aesthetic and functional values.

The main aim of the APEKS method was to compare the analyzed solution variants with the best variant (APEKS variant). This method allows one to choose the best option by using it to assess quantitative and qualitative criteria. The APEKS variant is simulated and is created by assigning the best rating values of the actual variants to it for each assessment criterion. The procedure for the APEKS method is shown in Fig. 1.

According to the procedure presented in Fig. 1, in the first two steps, the solutions to be compared should be compiled. From these solutions, the best option should be selected, and the criteria by which they will be evaluated should be specified. Three variants were adopted for the analysis: natural materials, such as wood bark, milled wood, and additive manufacturing-based printed materials. The following parameters were analyzed: selected dimensions, hill heights, selected area depths, and 3D surface parameters. A list of mixed, i.e., quantitative and qualitative, evaluation criteria K₁–K₈ was determined. 3D surface parameter values (K₁-K₆)—Sa, Sz, Ssk, Sku, Sp, and Sv—were chosen (Stout and Blunt 2000). The quality criteria included parameters that determined the usability and aesthetic values. The evaluation values for the quality criteria were determined by a group of experts by adopting values on a ten-point scale (K₇ – usability, K₈ — aesthetics).

Then, the weights for the assessment criteria adopted were determined using the “forced decisions method. For each pair of criteria, specific values were assigned: “1” for the more important criterion and “0” for the less important criterion. The value of the final weight w_j was calculated by Eq. (1):where:

d_j – the sum of the values obtained by the j-th criterion in all comparisons,

Subsequently, on the basis of the value of the a_ij marks for each of the variants and the assessment criteria adopted, the best rating values for the APEKS variant were assigned. The value of the APEKS variant was “idealized” and had all the best features (ratings) among the criteria considered. In the next step, on the basis of relationship (2), the relative percentages of the C_ij estimates for the criteria considered and the options analyzed were determined.where:

a_ij – the evaluation value for the i-th variant of the j-th assessment criterion,

a_Aj – the evaluation value for the APEKS variant according to the j-th evaluation criterion.

The exponent of the quantitative criteria was + 1 when a higher rating value was better and -1 when a lower rating value was better. In the case of quality criteria, + 1 indicated that a value on a scoring scale was adopted, and a better rating was awarded more points. In the last step, the relative percentage of the critical values K_cri was determined using Formula (3), and the best of the options compared was selected.

A comparative analysis of the material properties and methods for mapping the surface structures of natural materials, i.e., ash bark, was carried out. The mapping of the natural surface of the wood bark was performed using two methods of shaping materials: subtractive and additive methods. Samples of materials were made using the method of surface milling on a CNC milling machine and additive, i.e., 3D printing in fused filament fabrication (FFF) technology. In this study, three types of samples with dimensions of 70 mm × 50 mm × 20 mm were subjected to a comparative analysis of the following materials (Table 1).

Natural ash bark was adopted as a reference material for 3D scanning of the bark surface. The surface scan was made using the “EINSCAN-PRO HD RED” 3D scanner from “SHINING 3D” with the “EXScan Pro_v3.5.0.9” software. The nonuniformity of the scanned object was taken as a reference point to combine subsequent scans. To develop a solid model, the result obtained by scanning the surface of the ash bark was processed using the computer program Blender v. 2.83.4. Then, the solid model was used in the CAD/CAM software to develop milling with an engraving cutter of surfaces in oak wood. Figure 2 presents a scan of the bark surface (reference) and a solid model of a selected fragment of the scanned surface together with a photograph of a fragment of the ash bark surface.

Sample No. 2 was made of solid oak wood by multiaxis milling at the CNC machining center “Homag Venture 316 L”. The machining files were prepared in the “Aspire 10.5” program using a surface rowing strategy with a 0.2-mm path covering and a V-type carving tool 20° with a diameter of 1.5 to 9.0 mm. Figure 3 shows the tool paths generated in CAD/CAM, a photograph of the oak wood sample after engraving, and the machining tool used.

Sample No. 3 was obtained through 3D printing from a wood PLA filament from Spectrum with a laser beam diameter of 1.75 mm. This printing process was carried out at 190–220 °C. Machine files were created in IdeaMaker using a 3D model based on a scan of wood bark. Figure 4 shows the software window settings and photographs of the sample after 3D printing. The following print parameters were used: nozzle diameter, 0.6 mm; nozzle temperature, 205 °C; and layer height, 0.2 mm.

Microscopic examinations were performed with a Keyence 3D VHX 7000-type microscope with dedicated software. Microscopic comparative analyses of the surface and its profiles were carried out, and selected 3D surface roughness parameters were measured (Stout and Blunt 2000).

Figures 5, 6 and 7 show examples of the obtained microscopy images of the surfaces of the analyzed samples.

Microscopic analysis and measurements of the topography of the obtained surfaces were carried out. Particular attention was given to the elevations and depressions that could characterize the compared surfaces. The surface of the tree bark (Fig. 8) was characterized by deep valleys with steep slopes and sharp hills distributed nonuniformly in a random manner. Numerous cracks microcracks, burrs and irregularities were observed on the surface. In the case of the surface obtained by milling, good reflection of the shape was observed. Due to the constant diameter of the tool and the radius of the blade corner, the valley depths obtained were lower than those observed in the naturally shaped tree bark. In addition, the shape of the hills on the surface was characterized by large radii. On the surface, a visible reflection of the shape of the cutter was observed in the material, in addition to a few irregularities resulting from the extraction of wood fibers (different densities of wood grains). An example is shown in Fig. 9b. In the case of a surface obtained by the additive method, the observed layered structure of the surface resulted from the implementation of the 3D printing process (Fig. 10). The obtained surface was characterized by heterogeneity and porosity. In addition, melts of the material used in the process and a few powder particles of the material that did not completely melt on the surface were observed. Figure 11d shows an example of a layered bow with the thickness of the obtained layers measured during the production of the element.

Figure 11a shows the structures of the elements analyzed in a cross-sectional view. A comparison of the mean values used to measure the elevation of the hill and the angle between the hills is shown in Figs. 11b and d. Similar values of valley depth and elevation height were observed for samples obtained by subtractive and additive methods. In this case, the mean values differed by 0.3 mm. The average values of the elevation angles and the angles between the slopes of the climbs for the milled and 3D-printed samples differed by 0.5 degrees. Conversely, when comparing the measured values with a sample of tree bark, the differences were approximately 11 degrees.

In the next step, measurements of the 3D parameters characterizing the analyzed surfaces were carried out for the entire surface area of each sample.

A summary of the parameter values for the adopted variants is presented in Table 2. On the basis of the assessment values, the APEKS variant was determined. The value of this variant was taken as the best rating assigned for each of the criteria considered. The APEKS variant is also included in Table 2.

The values of the weight indicators of the evaluation criteria are presented in Table 3.

The values obtained for the relative percentages of estimates and the critical values for the variants analyzed are summarized in Table 4.

Based on the obtained critical value of K_cri = 79.36%, it was assumed that the best method for producing furniture elements in this case would involve the multiaxis milling of oak wood. The K_cri value for 3D printing was K_cri = 77.86%. In the case of wood bark, the K_cri value was essentially influenced by the result of estimating the suitability of wood bark as a material from which furniture elements could be constructed. In this case, the value of K_cri = 68.74%.

Based on the analysis of the test results obtained, the following conclusions could be drawn.

The APEKS method permitted the best option to be selected by accounting for quantitative and qualitative criteria in the assessment. Additionally, this method reduced the time and cost of manufacturing furniture components by allowing for the selection of the correct manufacturing method at the design stage of the production process. The results of the paper could be applied to many wood processes, particularly to subtractive and additive methods for manufacturing furniture products.