Multi-Objective Optimization of Manufacturing Process Using Artificial Neural Networks

Abstract

This paper focuses on the optimization of a critical operation in the furniture manufacturing process, identifying it as a key priority for improvement by applying Systems Theory. The primary objective of this study is to develop a mathematical model for optimizing the detected key process by employing artificial neural networks (ANNs) which mirror adaptive management principles. Three input and three output parameters significantly impacting the effectiveness of this key process have been systematically identified and experimentally measured. It was necessary to perform multi-objective optimization (MOO), which consisted in achieving the minimum values of cost and process time and the maximum value of the quality index through the optimal setting of the input parameters (cutting speed, feed rate, and volume of removed material). The application of ANNs in MOO in this research study is a novelty in this field. The results obtained through application of the ANN method reveal the optimal values of the examined parameters, which represent the best combination of input technical variables leading to the best results in output economic parameters. This multi-objective optimizing solution facilitates enhanced process efficiency. By integrating Systems Theory, Complexity Theory, and adaptive management, this research advances sustainable process improvements by minimizing resource use, reducing waste, and enhancing overall system efficiency.

1. Introduction

Globalization’s impact continues to surge, intensifying competition in the market [1]. Many managers view process optimization as a solution to this challenging business landscape, offering the potential to enhance market positioning. Employing quality management practices, like Total Quality Management (TQM) and Six Sigma, control of cost consumption, control of quality and quantity of production, plan vs. reality, product pricing, use of benchmarking principles, comprehensive budgeting (revenue, cost, profit, cash flow, reserve), strategic tools (BSC, SWOT, GAP), and others, can empower businesses to boost their economy, improve operational efficiency, enhance production quality, and elevate customer satisfaction [2].

Only well-functioning management ensures a successful business operation in strong competition. An important role is played by decision-making based on situation analysis and an appropriate utilization of operational management and quality improvement tools and methods. On the other hand, integrated manufacturing management models have been developed. Paranitharan et al. [3] investigated the integration of various quality and production management concepts and proposed an integrated manufacturing business excellence system, consisting of ten constructs as performance-inducing factors and controlling factors.

According to Systems Theory, organizations and processes are considered interconnected systems where all components influence each other [4]. It emphasizes understanding the relationships and feedback loops within the entire system to enhance decision-making and problem-solving [5].

This research leverages Systems Theory to view manufacturing as an interconnected, dynamic system where components like cutting speed, feed rate, and tool lifespan interact, impacting the overall process. By applying Systems Theory, this study acknowledges manufacturing as a network of interrelated processes rather than isolated tasks. In a complex system, adjustments to any part of the process can lead to cascading effects across the system.

Our study uses artificial neural networks (ANNs) to dynamically model and optimize these relationships, adjusting the input parameters to find an ideal balance. This approach mirrors adaptive management principles, where decision-making is continuously informed by feedback and system responses. For example, the ANN can help predict how changes in CNC machine settings (such as spindle speed or feed rate) will affect both production costs and quality. By optimizing these settings based on the model’s predictions, manufacturers can make informed decisions that adapt to real-time conditions, reducing waste and improving efficiency. We adopt a systemic optimization approach, focusing on optimizing the entire manufacturing system rather than isolated components. By integrating Systems Theory [6], Complexity Theory [7], and adaptive management [8], this research advances sustainable process improvements by minimizing resource use (e.g., cost reduction through feed rate adjustments), reducing waste, and enhancing overall system efficiency (e.g., quality improvement through spindle speed optimization).

However, optimizing the overall production process is a multifaceted endeavor with far-reaching implications. It necessitates a systematic approach that begins with the thorough description of all processes, enabling the identification of key processes. Key processes hold exceptional significance for optimization efforts, as they wield the most substantial influence on overall performance [9]. The optimization task of key production processes often requires a multi-objective solution. The problem of multi-objective optimization (MOO) can be found in every area of manufacturing, and various methods have been applied, from simple Pareto and scalarization methods [10] to weighted sum approach [11] and finite element simulation [12].

A manufacturing process with its procedures, devices, or named units carries out the transfer, the transformation, or the storage and transportation of materials and energy. The output of a former activity is the input of the next activity; therefore, they link up and buffer-match each other [13]. Improvement in these processes is necessary to increase the overall business performance. Measuring, assessment, control, and, furthermore, the optimization of the enterprise processes are the assumed necessary activities for effective management and performance improvement. To evaluate the efficiency and performance of production processes, the key performance indicators should be implemented, which allow for the analysis of the overall performance of processes, and not only of the financial output [14].

In recent years, the integration of advanced technologies has revolutionized manufacturing processes, with a particular emphasis on optimizing efficiency, cost-effectiveness, and product quality. It is necessary to take into consideration the research results of scientific papers where researchers have employed various artificial intelligence methods for process optimization. Svobodová and Janků [15] utilized a method combining simulated annealing and genetic algorithms for the automatic placement of furniture within specific functional zones, achieving optimization in furniture arrangement. Another study by Tarigan et al. [16] employed the ant colony algorithm to design the scheduling of door leaf production. The main result of this work indicates that the ant colony method can slightly decrease the total lead time of the product by 3.06%. Furthermore, a scientific study by Wang [17] proposed a strength optimization design method for composite furniture structures based on the Particle Swarm Optimization Algorithm. This method facilitated finding optimal solutions for structural strength and design schemes.

Artificial neural networks (ANNs) are widely used across various fields [18], including in the optimization of manufacturing processes [19]. Quintana, Ciurana, and Brecher [20] created a model for predicting surface roughness parameter R_a using the ANN methodology, with steel as the experimental material. Madić et al. [21] used the ANN methodology to predict and determine optimal values for the surface roughness parameter of unreinforced polyamide material, depending on the depth of cut, the radius of the tool tip, cutting, and feed speed.

However, the application of ANNs in furniture manufacturing is comparatively less explored. Notable studies in this area include “Drilling Process Optimization in Particleboard Manufacture” [22], “Green Manufacturing Quality of Children’s Furniture” [23], “Forecast Sales for Furniture Manufacturing” [24], “Lean Production Control System for a Furniture Company” [25], and “Furniture Manufacturing Process Optimization by Application of Six Sigma Concepts” [26]. However, in today’s business landscape, entrepreneurs contend with an abundance of data, underscoring the importance of employing artificial intelligence tools to streamline process optimization.

While numerous studies have explored the application of artificial neural networks (ANNs) in various manufacturing sectors, a notable gap in research persists in the specific domain of furniture manufacturing. Despite the pivotal role that Computer Numerical Control (CNC) machines play in this industry, there is a limited body of literature that systematically investigates the application of ANNs for the optimal setting of CNC machines. In addition, multi-objective optimization tasks have not been optimized using ANNs in any research work. This paper aims to bridge these gaps by presenting a comprehensive research study focused on utilizing ANNs for the precise tuning of CNC machine parameters, with a keen emphasis on identifying the output indicators that secure the best possible process effectiveness.

This paper’s objective is to construct a mathematical model for optimizing a subprocess of wood furniture manufacturing through the utilization of the artificial neural network (ANN) methodology. Our research outlines a procedure detailing how ANNs can be employed to optimize subprocesses within a specific furniture manufacturing company. Employing the ANN method to tackle optimization tasks has revealed optimal values for both input and output parameters in the key process. This research contributes not only to the broader field of manufacturing optimization, but also addresses the unique challenges faced by the furniture manufacturing sector. In addition, the simultaneous consideration of multiple input and output variables in the optimization process using ANNs is a new approach in this field. As for practical implications, this study’s findings can serve as a foundational framework for manufacturing companies, not only in furniture production.

2. Theoretical Background

2.1. Furniture Manufacturing Processes

The primary intention of a manufacturing process lies in increasing the value of raw materials and transforming them into products that satisfy customer needs [9]. Within the furniture manufacturing realm, the specific steps vary according to the final product categories, such as chairs, tables, beds, wardrobes, and more. The furniture production process can be categorized into two distinct types: processing operations and assembly operations. Processing operations are dedicated to transforming materials from one state of completion to a more advanced one, enhancing their geometry, properties, or appearance and, consequently, adding value. This category can be further subdivided into wood treatment and seasoning, cutting and sizing, planning, joineries, assembly, fixing, finishing, and dismantling and packing. Preceding these processing operations, procurement processes and material storage activities play a pivotal role. The overall process reaches its conclusion when the final product is meticulously packed, labeled, and stored in the expedition warehouse. The products of furniture production consist of individual pieces of furniture or furniture assemblies [27].

According to Ratnasingam [28], the process of transforming the sawn wood into a three-dimensional furniture product based on design specifications involves a series of machining, jointing, abrasive sanding, and finishing operations. Figure 1 is a graphical representation of a simplified process flow in one furniture manufacturing company.

In the production process, the physical and chemical properties of the raw materials are changed to create a product with specific properties or a product for a specific use [29]. The main characteristic of the enterprise production in the woodworking industry is that the raw material has a natural essence [13], so it is heterogeneous (different at the macro-, micro-, and sub-micro level of the wood structure), anisotropic (properties vary depending on direction), pourable (heterogeneous pored systems created by the diverse shaping anatomical elements of the wood), and hydrophilic (having a strong affinity for water) [30]. These facts affect the method of raw material processing, especially when lumber is an input. When wood-based materials are input, the heterogeneity is lowered. On the other hand, the natural properties of wood, as well as its color, smell, and pattern, are lost. These facts are mainly noticeable in the first stage, when the supplier of the raw material is selected. Most of the business units have an exclusive supplier because the quality level of the raw material is guaranteed [31].

By adopting Systems Theory, Complexity Theory, and adaptive management, furniture manufacturers can take a holistic approach to optimizing processes [6,8]. Recognizing the interdependencies between the cutting, assembly, and finishing stages ensures efficient system operation. Complexity Theory helps manage the unpredictable interactions between variables [7], such as material quality and machine speed, while adaptive management enables continuous monitoring and real-time adjustments in the furniture manufacturing process.

2.2. Systematic Manufacturing Process Optimization

Solving optimization problems means searching for the maximum or minimum values of target parameters. Problems involving more than one objective are referred to as multi-objective optimization [10]. In the context of manufacturing, optimization is closely linked to process engineering, which encompasses activities such as the description, simulation, projection, control, and management of manufacturing processes. The primary goal of process engineering is to improve the efficiency of operations, optimize production flow, enhance product quality, upgrade information systems, and reduce environmental pollution [13]. Adaptive management plays a pivotal role in this context, especially in furniture manufacturing, by facilitating continuous monitoring and real-time adjustments. For instance, when feedback highlights deviations in surface quality, adjustments to machine settings or the replacement of cutting tools can be made or carried out immediately, ensuring consistent product quality.

Process engineering relies on various types of technological processes, which include material and energy inputs and outputs, along with flows of information. These flows represent the movement of resources (such as materials and energy) and events within a production system. Systems Theory supports the conceptualization of the manufacturing process as a network of interrelated “nodes” (e.g., factory procedures and devices) and “connectors” (e.g., transport routes and equipment) [32]. This interconnected network facilitates the movement and interaction of resources and energy across departments, ensuring efficient production.

Complexity Theory comes into play when managing the interactions between multiple variables and subprocesses in a manufacturing system. In such a system, small changes in one area—such as material flow—can have significant, unpredictable effects elsewhere in the process [33]. Recognizing these interdependencies is critical for identifying opportunities to enhance efficiency, reduce resource consumption, and minimize waste.

The optimization process also involves evaluating how key subprocesses influence the overall quality of a product. These subprocesses can be prone to errors, especially in the initial phases of production, where mistakes have a more profound impact. Identifying these critical subprocesses presents an opportunity to improve the final product’s quality and the company’s profitability. The production of the company’s best-selling product significantly impacts on its overall profitability [34]. Making decisions based on both qualitative and quantitative data is crucial, as these insights inform the selection of appropriate tools for process optimization [35].

Finding an optimal solution requires balancing competing objectives, such as reducing material and energy consumption, minimizing product development costs, and cutting down production time. Optimization problems can be solved by identifying the best arrangement of design variables in a multidimensional parameter space [36,37].

Focusing on critical subprocesses—those tied to the most valuable products—allows for more targeted optimization efforts, especially in addressing errors and inefficiencies in early-stage production [38]. The introduction of variation in key variables during the creation of an optimization model leads to reductions in material inputs and production costs. Solving these complex optimization challenges requires the use of suitable models that capture essential system attributes [39]. Artificial neural networks (ANNs) can dynamically model CNC machining processes and optimize settings based on real-time feedback, aligning with adaptive management principles to enhance efficiency, reduce waste, and improve product quality. The ANN models demonstrate high accuracy in parameter prediction, benefiting industries that need to balance quality and energy efficiency [40,41].

2.3. Optimization Methods and Techniques

There exist two fundamental methods for addressing modeling optimization problems: analytical and numerical solutions. Numerical solutions, as indicated by Fusek and Halama [42] and Shein and Zemtsova [43], are inherently approximations. They transform the quest for continuous functions into the challenge of identifying a finite number of unknown parameters, effectively approximating these functions. This transformation represents a discretization of the initial continuous problem, which is then addressed through algebraic techniques characterized by a finite number of steps. Numerical solutions can, in principle, be applied to any problem that possesses a mathematical description. Nonlinear challenges are tackled through iterative methods, where the approach entails estimating the solution for unknown values and iteratively refining it until the solution error reaches a specified minimum [37].

Lahiri et al. [44] presents a visual depiction of various optimization techniques. Mukherjee and Ray [45] introduce modeling techniques designed to discern parameter relationships at the empirical input and output stages of a process and during in-process stages. This categorization of techniques has been enhanced by information from various scientific papers [13,46,47,48,49,50,51,52,53,54,55,56]. The mind map in Figure 2 provides a pictorial representation of these techniques.

Gunantara [10] presented simple methods by performing multi-objective optimization (MOO). The Pareto optimal front method was used, where the dominated and non-dominated solutions are obtained using a continuously evolutionary algorithm. The result is a compromise solution of performance indicators. The scalarization method uses weights by creating multi-objective functions. The weighted sum approach was applied in a study by Marler and Arora [11], who conclude that “using unrestricted weights is well suited for providing a single solution that reflects preferences and using a convex combination of functions is desirable when generating the Pareto set”.

Amouzgar et al. [12] deal with the multi-objective optimization of turning operation within the metal cutting process through metamodeling methods—finite element simulations and evolutionary algorithms. Two objectives as output parameters and two input variables were considered. The application of metamodels revealed the increase in process efficiency due to time reductions, as well as in effectiveness, by discovering new and better optimizing solutions.

Table 1. Classification of artificial intelligence methods for process optimization.

I. Expert Systems and Knowledge-based Systems
Ontologies and Knowledge	Domain, Upper and Task Ontologies Knowledge Representation Techniques (Semantic Networks, Frames, Description Logistic) Knowledge Modeling Approaches (Conceptual and Rule-based Modeling)
Expert Systems	Diagnostic Prescriptive Predictive
Rule-Based Systems	Rule Refinement Rule-based Machine Learning
II. Machine Learning
a. Supervised Learning
Regression Analysis	Linear Polynomial Ridge Lasso Support Vector Bayesian
Classification	Decision Trees Random Forest Support Vector Machines k-Nearest Neighbors Naïve Bayes Logistic Regression Discriminant Analysis
b. Unsupervised Learning
Clustering	K-Means Hierarchical Clustering Density-Based Spatial Clustering of Applications with Noise Gaussian Mixture Models
Dimensionality Reduction	Principal Component Analysis Singular Value Decomposition t-Distributed Stochastic Neighbor Embedding
Association Rule Learning	Apriori algorithm Eclat algorithm FP-Growth algorithm
Anomaly Detection	Isolation Forest One-Class SVM Local Outlier Factor
c. Ensemble Methods
Averaging Methods	Bagging (Bootstrap Aggregating) Random Forest
Boosting Methods	Adaptive Boosting Gradient Boosting Machines eXtreme Gradient Boosting Light Gradient Boosting CatBoost
d. Neural Networks
Artificial Neural Networks	Multi-layer Perceptrons Deep Neural Networks Recurrent Neural Networks Convolutional Neural Networks Long Short-Term Memory Autoencoders Feedforward Networks
Deep Reinforcement Learning	Reinforcement Learning with Neural Networks Q-Learning with Deep Q-Networks Proximal Policy Optimization Actor-Critic Methods

presents the subcategories of process optimization methods within artificial intelligence. The two main categories are Expert and Knowledge-Based Systems, and Machine Learning, which includes artificial neural networks. This method was chosen for optimizing the furniture manufacturing process in our research study, presented in this paper.

Quintana, Ciurana, and Brecher [20] created a model for predicting surface roughness parameter R_a using the ANN methodology, with Steel C45 (AISI 1043), 50-55HRS, as the experimental material. This research employed the ANN technique to develop a model for predicting the surface roughness average parameter (R_a) in vertical milling operations. Madić, Marinković, and Radovanović [21] used the ANN methodology to predict and determine optimal values for surface roughness parameters, depending on the depth of cut, the radius of the tool tip, cutting, and feed speed. In the experiment, unreinforced polyamide material was used, processed at three different levels of depth of cut, cutting speed, and feed rate, and two levels of tool tip radius. They conclude that the increase in feed rate results in a nonlinear increase in R_a.

Systems thinking, as a conceptual framework that emphasizes understanding the interconnections and interactions within complex systems, has been widely applied across various disciplines [57,58,59,60,61] to address complex problems by considering the whole system rather than individual parts in isolation. According to Monat, Amissah, and Gannon [59], systems thinking offers a valuable framework for addressing complex, interrelated processes in business. Understanding the application of systems thinking in organizational management will greatly assist organizations in prioritizing their strategies, especially when systems thinking plays a vital role in driving innovation and promoting sustainability [62].

Nowadays, the Fourth Industrial Revolution brings to the 21st century new concepts as well as Robotics and artificial intelligence [63]. It referred to as Industry 4.0, which is understood as a new atmosphere supported by era of innovation in technology, particularly AI-driven technology [64,65,66]. In the context of the COVID-19 pandemic and its consequences on organizational decision-making, it has become crucial for businesses to implement systems thinking to make effective and informed decisions [67]. Complexity Theory provides evidence that small changes can lead to large, unexpected effects [68]. Therefore, adopting Systems and Complexity Theory in organizational systems enhances their ability to adapt to change and evolve over time.

3. Materials and Methods

The optimization task was solved in the Slovak furniture manufacturing company with a long tradition. Input data were collected directly in the company. The main method used in the research was an experiment based on the measurement, the calculation of determined parameters, and the creation of an appropriate artificial neural network (ANN). Complex manufacturing systems must balance economic viability with environmental sustainability. Through multi-objective optimization, this study targets efficiency (time and cost) and sustainable practices (resource conservation, waste reduction). For example, reducing production time saves energy, and minimizing costs improves material efficiency. This systemic approach enables businesses to meet sustainability goals by identifying configurations that address multiple objectives, promoting responsible resource management. The data that support the findings of this study are available from the corresponding author upon reasonable request (xmarcinekovak@tuzvo.sk).

The initial phase in resolving the optimization problem involved identifying the flagship product (produced the most) and the critical manufacturing subprocess, encompassing the specific parameters, procedures, and durations of individual steps. The furniture manufacturing enterprise, subject to our investigation, produces 50 different product types. The wash basin closet, with a lead time of 34 min and 9.98 s, was chosen as the reference item for this study, and it is manufactured using medium-density fiberboard (MDF). MDF is a composite wood product widely used in furniture manufacturing due to its machinability, dimensional stability, and smooth surface, making it an ideal material for precise machining processes like milling. Its uniform density and predictable properties make it a preferred material for furniture manufacturing companies, and also for testing machining parameters, especially when using Computer Numerical Control (CNC) equipment [69]. Additionally, MDF’s machinability ensures consistent results, minimizing variability in experimental outcomes. To streamline the production process, focus must be directed towards the activity with the highest defect rate, emphasizing the technological procedure [70,71]. In light of these considerations, the milling process was identified as the critical subprocess.

Consequently, the input parameters were set as cutting speed and feed rate, both subject to variation. The depth of cut remained constant (a = 1 mm), and the total volume of removed material was calculated. The output parameters included surface roughness (Ra), process duration (machining time—T_M), and process cost (influenced by CNC machine settings—C_IPCD).

After parameter identification, an abstract model of the manufacturing process was developed using artificial neural networks. Through our experimentation, the cutting speed and feed rate were systematically altered using the CNC wood machine (Homag, Průmyslová, Czech Republic). In each variation, one output parameter (surface roughness) was experimentally measured, while the remaining parameters were computed.

A sample size of 23 measurements was evaluated using statistical tests, including variance analysis and correlation metrics, which confirmed the dataset’s representativeness. Variance and standard deviation for input parameters were low, indicating consistency across measurements. Correlation coefficients for key variables exceeded 0.7, demonstrating strong relationships within the dataset. Moreover, training and testing splits revealed consistent ANN performance, with an R² value of 0.95 for the training set and 0.92 for the testing set, supporting the adequacy of the dataset for predictive modeling. Various combinations of input variables were utilized in the experiment, as detailed in

Table 2. Input parameters for neural network model (milling process in furniture manufacturing).

Parameter:	Spindle Speed	Cutting Speed	Feed Rate
No.	[rev.min−1]	[m.min−1]	[m.min−1]
1.	10,000	2419.03	4.00
2.	12,000	2902.83	4.00
3.	14,000	3386.64	4.00
4.	16,000	3870.44	4.00
5.	18,000	4354.25	4.00
6.	10,000	2419.03	8.00
7.	12,000	2902.83	8.00
8.	14,000	3386.64	8.00
9.	16,000	3870.44	8.00
10.	18,000	4354.25	8.00
11.	10,000	2419.03	10.00
12.	12,000	2902.83	10.00
13.	14,000	3386.64	10.00
14.	16,000	3870.44	10.00
15.	18,000	4354.25	10.00
16.	18,000	4354.25	12.00
17.	18,000	4354.25	14.00
18.	12,000	2902.83	12.00
19.	12,000	2902.83	14.00
20.	14,000	3386.64	12.00
21.	14,000	3386.64	14.00
22.	16,000	3870.44	12.00
23.	16,000	3870.44	14.00

.

To quantify the total amount of material removed, we used the SketchAndCalc™ application (Domains by Proxy, Scottsdale, AZ, USA). This tool was employed to calculate the surface area of the material removed based on the cross-sectional details of the workpiece, as outlined in the blueprints. The cross-section was divided into geometric components, including a triangle, a rectangle, and an irregular polygon, which were measured and summed to determine the total area. The calculated cross-sectional area was then multiplied by the length of the workpiece to obtain the overall volume of material removed during processing.

The calculation of the removed material volume (V) followed the formulation in Equation (1), wherein S_m represents the size of the removed area, l stands for the length of the processing workpiece, and N_W denotes the cumulative count of processing workpieces.

$$V=S_m\times l\times N_W$$

(1)

We used medium-density fiberboard (MDF) with a density of 750 kg·m⁻³ to meet the requirements of the EN 622-1 and EN 622-5 standards [72]. In addition to its density, MDF’s moisture content (6–8%) and moderate hardness (Brinell Hardness: 2.2–2.5 N/mm²) were critical factors influencing machining outcomes. These properties contribute to its suitability for precise milling, ensuring the smooth surface finishes while maintaining dimensional accuracy. The material was milled under predetermined conditions, with thickness being the milling parameter. After the operation was completed, a sample with dimensions of length 1000 mm, width 22 mm, and thickness 29 mm was cut out. This sample was used to create a test specimen, where the surface roughness was measured using two methods along a track of 11 mm. The samples were processed using the HOMAG BOF 41/30/R CNC wood machine (Homag, Průmyslová, Czech Republic) (maximum revolutions per minute: 18,000). In the experiment, a polycrystalline diamond (PCD) end mill with a diameter of 77 mm was employed.

The roughness parameter R_a was experimentally measure using two methods, and the results are presented in

Table 3. Comparative measurements of surface roughness: laser profilometer vs. contact roughness tester data.

	LPM 4	MITUTOYO SJ-210					Median
		1	2	3	4	5
1.	9.926	10.155	9.385	9.04	9.58	9.245	9.483
2.	8.535	9.194	8.337	9.59	8.5214	8.679	8.607
3.	7.791	8.035	8.449	7.907	7.958	7.266	7.933
4.	8.094	9.061	7.755	8.364	7.996	8.542	8.229
5.	8.62	8.045	9.878	9.337	8.324	8.892	8.756
6.	8.883	11.254	10.786	11.208	9.856	10.987	10.887
7.	9.009	10.656	12.241	11.459	9.456	10.127	10.392
8.	10.486	11.155	10.865	10.567	10.257	10.366	10.527
9.	8.541	9.49	11.123	10.666	9.254	9.842	9.666
10.	9.095	10.068	8.833	8.197	8.951	9.012	8.982
11.	10.107	11.656	10.021	13.927	11.246	10.899	11.073
12.	9.225	9.181	10.575	10.357	9.587	9.46	9.524
13.	8.368	11.683	9.196	8.83	9.257	8.622	9.013
14.	8.478	11.036	10.462	10.765	8.752	10.254	10.358
15.	10.032	11.605	11.355	10.54	11.245	10.822	11.034
16.	7.76	9.014	9.84	9.1	8.002	7.892	8.508
17.	7.85	9.601	7.659	9.379	8.569	8.262	8.416
18.	11.25	12.621	9.335	9.74	11.367	12.606	11.309
19.	12.478	12.427	14.995	13.687	13.953	12.606	13.147
20.	9.533	8.215	9.864	11.271	9.659	10.337	9.762
21.	11.284	10.423	11.388	10.982	11.321	12.898	11.303
22.	9.262	9.232	8.619	8.539	9.163	11.889	9.198
23.	9.854	9.772	10.128	10.181	9.822	9.561	9.838

:

(1)

Initially, it was measured using the laser profilometer LPM 4, assembled at the Department of Woodworking of the Technical University in Zvolen in collaboration with the development company [73].

(2)

Subsequently, a contact roughness tester MITUTOYO SJ-210 (Japan Mitutoyo, Kawasaki City, Japan) with a sliding heel for production measurements was used [74]. Five measurements were conducted within the test sample, with the evaluated length set at 12.5 mm.

The output parameters, process duration T_M, and process costs C_IPCD were calculated using the formulas presented below. Equation (2), provided below, outlines process duration (T_M) as the sum of the milling time (T_m) and the idle time of the milling tool (T_IT). The setup and finishing time were excluded from the total process duration formula, as these activities were consistent across all machining scenarios and did not vary with changes in input parameters (cutting speed, feed rate, etc.). Including these constant values would not contribute to our understanding of the relationship between process parameters and machining efficiency. However, these times can be considered in future studies focusing on comprehensive cost and time analyses:

$$T_M=T_m+T_{IT}$$

(2)

The total process costs (C_IPCD), influenced by the CNC machine setting, were calculated as the sum of energy cost (C_E), labor cost (C_L), and cost of the PCD end mill (C_PCD), as you can see in Equation (3). The setup and maintenance costs were excluded from the current analysis as their contribution to the overall cost variation was deemed negligible compared to machining-specific factors such as cutting speed, feed rate, and tool wear. Since these costs are largely fixed and do not fluctuate significantly across different machining conditions, their inclusion would have had minimal impact on the comparative analysis of parameter optimization:

$$C_{IPCD}=C_E+C_L+C_{PCD}$$

(3)

The individual components of the equations were calculated using the following formulas (Equation (4)), where P represents the performance of the CNC machine in N_W, η is the energy conversion efficiency, and P_E is the energy price:

$$C_E=\left[\left({\displaystyle \frac{P}{\eta }}\times 1000\right)÷60\right]\times \left[P_E÷60\right]\times T_M$$

(4)

It is widely acknowledged that PCD tools have a longer lifespan when compared with carbide tools [55,56]. Milling tool vendors and manufacturers report 50–100 times longer lives for tools made from PCD [75]. Based on the research results of Bai, Yao, and Chen [76], a qualified estimate was made, and the lifespan of the diamond milling cutter was calculated to be 30 times that of the T03SMG milling cutter. The lengths of processed material were estimated based on tool wear data provided in [76]. According to the graph, the polycrystalline diamond (PCD) tool processed a total length of 2668 m (2573 m plus an additional 95 m). In comparison, the tungsten carbide tool was able to process only 95 m before reaching the same wear threshold. These data underscore the significantly longer lifespan and processing efficiency of PCD tools.

Equations (5) (cost of labor) and (6) (cost of PCD end mill tool) are presented above. Here, W_SG represents the super-gross wage of the machine worker, T_L(PCD) is the tool life of polycrystalline diamond, calculated as 30 times the tool life of milling blades made of hard alloy (T_LT03SMG), and P_PCD is the price of the PCD end mill:

$$C_L=\left[\left(W_{SG}÷160\right)÷60\right]\times T_M$$

(5)

$$C_{PCD}=T_m÷T_{L_{\left(PCD\right)}}\times 100\%\times P_{PCD}$$

(6)

The percentage of the remaining lifespan of the diamond tool knife was calculated based on the operation’s duration, and this percentage was multiplied by the price of the PCD end mill (€735). The resulting calculated price constitutes a significant portion of the variable costs for the operation (ranging from 59.44% to 90.32%).

To model these relationships, an artificial neural network (ANN) was developed. The high variability of the R_a parameter was a key consideration in selecting the most suitable ANN. A network with high correlation coefficients in estimating costs and machine time was favored, as these coefficients were used to evaluate the predictive accuracy of the ANN. A minimum threshold of 0.9 for both the training and testing datasets was established to ensure reliability, aligning with standard practices in neural network modeling.

In addition to correlation coefficients, the distribution of values in space was assessed using 3D graphs to validate the ANN’s performance visually. Another critical aspect in selecting the ANN architecture was minimizing the number of hidden neural layers, which was kept within the range of input and output variables to maintain model efficiency and prevent overfitting.

4. Results

Input and output parameters, identified as factors influencing the effectiveness of the milling, were measured and calculated during the experiment. The machine time (T_M), total material removal (V), energy consumption amount (E) for specific operations, tool life (T_LPCD), calculated value and costs (C_S) affected by CNC settings (C_IPCD), unaffected by CNC settings (C_NI), and medians of measured R_a values are shown in

Table 4. Calculated and measured values of output parameters.

	V	E	TM	TL(PCD)	CI(PCD)	CNI	CS	Ra
No.	[m3]	[W]	[min]	[min]	[€]	[€]	[%]	[mm]
1.	102.48	210.27	0.517	240.66	0.76	0.41	74.65	9.483
2.	204.96	210.27	0.517	163.64	1.12	0.05	79.83	8.607
3.	307.44	210.27	0.517	118.10	1.56	0.05	84.58	7.933
4.	409.92	210.27	0.517	89.04	2.06	0.04	87.91	8.229
5.	512.40	210.27	0.517	69.40	2.65	0.04	90.32	8.756
6.	614.88	159.40	0.392	240.66	0.38	0.12	63.34	10.887
7.	717.36	159.40	0.392	163.64	0.56	0.04	71.76	10.392
8.	819.84	159.40	0.392	118.10	0.78	0.04	77.88	10.527
9.	922.32	159.40	0.392	89.04	1.03	0.04	82.36	9.666
10.	1024.80	159.40	0.392	69.40	1.32	0.05	85.70	8.982
11.	1127.28	149.22	0.367	240.66	0.31	0.12	59.44	11.073
12.	1229.76	149.22	0.367	163.64	0.45	0.05	68.30	9.524
13.	1332.24	149.22	0.367	118.10	0.62	0.04	74.91	9.013
14.	1434.72	149.22	0.367	89.04	0.83	0.04	79.84	10.358
15.	1537.20	149.22	0.367	69.40	1.06	0.04	83.56	11.034
16.	1639.68	142.44	0.350	69.40	0.88	0.12	81.52	8.508
17.	1742.16	137.60	0.338	69.40	0.76	0.04	79.58	8.416
18.	1844.64	142.44	0.350	163.64	0.37	0.04	65.17	11.309
19.	1947.12	137.60	0.338	163.64	0.32	0.04	62.31	13.147
20.	2049.60	142.44	0.350	118.10	0.52	0.05	72.16	9.762
21.	2152.08	137.60	0.338	118.10	0.44	0.13	69.61	11.303
22.	2254.56	142.44	0.350	89.04	0.69	0.04	77.47	9.198
23.	2357.04	137.60	0.338	89.04	0.59	0.17	75.23	9.838

.

In our research project, we utilized the Statistica 12 program to develop an artificial neural network (ANN). This network incorporates three input variables (cutting speed, feed rate, and total material removal) and three output variables (operation cost, machined surface quality, and milling time).

We chose a specific neural network based on its correlation coefficients, which exhibited high values in estimating costs and machine times. The number of hidden layers in the ANN was minimized to maintain model simplicity, reduce computational complexity, and avoid overfitting. In line with standard practices in neural network modeling for manufacturing tasks, the number of hidden layers was kept within the range of input and output variables, as is recommended [49]. Cross-validation tests indicated that additional layers did not significantly improve model accuracy, confirming this choice as optimal for the specific problem. The resulting network features three hidden neural layers, a logistic hidden activation, and an exponential output function, and employs the BFGS (Quasi-Newton) training algorithm. All conditions for the suitability of the ANN were met.

Table 5. Comparison of measured value of R_a with ANN predictions and calculated deviations.

No.	Ra	Ra net	Deviation Ra
1.	9.483	8.775	7.46%
2.	8.607	8.415	2.23%
3.	7.933	8.258	−4.10%
4.	8.229	8.179	0.60%
5.	8.756	8.134	7.10%
6.	10.887	10.743	1.32%
7.	10.392	10.827	−4.19%
8.	10.527	10.147	3.61%
9.	9.666	9.582	0.87%
10.	8.982	9.251	−3.00%
11.	11.073	10.940	1.20%
12.	9.524	9.534	−0.11%
13.	9.013	9.330	−3.52%
14.	10.358	10.200	1.52%
15.	11.034	10.987	0.42%
16.	8.508	8.705	−2.31%
17.	8.416	8.974	−6.63%
18.	11.309	11.258	0.45%
19.	13.147	13.336	−1.44%
20.	9.762	9.939	−1.82%
21.	11.303	10.884	3.70%
22.	9.198	9.462	−2.88%
23.	9.838	9.902	−0.65%
	2.66%

,

Table 6. Comparison of calculated value of C_O with ANN predictions and calculated deviations.

No.	CO	CO net	Deviation CO
1.	1.2	0.91	11.42%
2.	1.41	1.34	4.78%
3.	1.84	1.86	−1.36%
4.	2.35	2.36	−0.49%
5.	2.93	2.76	5.85%
6.	0.60	0.62	−2.20%
7.	0.78	0.78	0.67%
8.	1.00	1.3	−2.82%
9.	1.25	1.31	−4.25%
10.	1.54	1.55	−0.51%
11.	0.51	0.57	−10.50%
12.	0.66	0.67	−1.27%
13.	0.83	0.83	−0.24%
14.	1.3	1.3	0.63%
15.	1.27	1.20	4.95%
16.	1.8	1.8	0.45%
17.	0.95	0.96	−0.86%
18.	0.57	0.61	−5.74%
19.	0.51	0.57	−10.65%
20.	0.72	0.73	−0.96%
21.	0.64	0.66	−3.16%
22.	0.89	0.87	1.66%
23.	0.78	0.79	−0.83%
	3.31%

and

Table 7. Comparison of calculated value of T_M with ANN predictions and calculated deviations.

No.	TM	TM net	Deviation TM
1.	0.517	0.527	−2.05%
2.	0.517	0.517	−0.09%
3.	0.517	0.515	0.31%
4.	0.517	0.519	−0.36%
5.	0.517	0.526	−1.77%
6.	0.392	0.391	0.28%
7.	0.392	0.393	−0.37%
8.	0.392	0.392	−0.21%
9.	0.392	0.392	−0.06%
10.	0.392	0.392	−0.19%
11.	0.367	0.362	1.30%
12.	0.367	0.359	2.04%
13.	0.367	0.359	2.06%
14.	0.367	0.362	1.17%
15.	0.367	0.365	0.43%
16.	0.35	0.353	−0.72%
17.	0.338	0.35	−3.51%
18.	0.35	0.352	−0.44%
19.	0.338	0.351	−3.73%
20.	0.35	0.35	0.13%
21.	0.338	0.349	−3.12%
22.	0.35	0.348	0.44%
23.	0.338	0.347	−2.75%
	1.20%

display the measured values of the specified parameters in comparison with the outputs of the ANN (MLP 3-3-3). Individual deviations (D) are calculated as their proportions, representing the differences between the measured values and the network outputs. R_{a net} represents the predicted surface roughness output generated by the specific ANN. It is based on the input parameters of cutting speed, feed rate, and material removal volume. The ANN was trained using experimental roughness measurements and calibrated to account for variations due to factors such as tool wear and material properties, ensuring alignment between the predicted and actual machining outcomes.

The correlation coefficients are presented in

Table 8. Correlation coefficients.

Parameter	Training Power	Test Power
Ra	0.983539	0.731064
CO	0.997696	0.998569
TM	0.996817	0.996756
Total	0.992684	0.908797

. The correlation coefficient for total training power is 0.992684, and for test power, it is 0.908797. For the R_a parameter, the correlation coefficients are 0.983539 for the training data and 0.731064 for the test data. Regarding the N_O parameter, the correlation coefficients are at the level of 0.997696 for training data and 0.998569 for test data. The correlation coefficients of 0.996817 for training data and 0.996756 for test data correspond to the T_M parameter. The correlation coefficients for total training and testing power were close to 1. The correlation coefficients for the training data were nearly 1 for every output parameter, indicating that the input parameters were correctly determined, and they accurately describe the essence of the analyzed process. However, the test power for the R_a parameter was lower because accurately measuring surface quality is difficult, and deviations in the measurements can cause a decrease in the correlation coefficients.

Three-dimensional graph illustrating the influence of cutting speed and feed rate on surface roughness are presented in Figure 3. It shows the output from the ANN. This graph was constructed using the least squares method.

The network predicts values almost identical to the experimentally obtained ones, with the highest deviation being −0.558 µm (−6.63%). The 3D graphs comparing experimental and ANN-predicted values revealed two distinct local minima for surface roughness (R_a). The first one is in the range of the highest cutting speed (above 3787.34 m.min⁻¹) and low feed rate (3.00 to 3.63 m.min⁻¹). The second one is in the range of high cutting speed (over 3900.72 m.min⁻¹) and high feed rate (13.11 to 15 m.min⁻¹). These visualizations confirmed the ANN’s ability to capture nonlinear relationships between input and output parameters. Additionally, data clustering around these minima indicated the network’s robustness in predicting optimal machining conditions.

On the other hand, the highest roughness of the workpieces is observed when processing with CNC equipment set to a high feed rate (14.37 to 15.0 m.min⁻¹) and simultaneously with the spindle speed set to the lowest level (9095 to 11,907 rpm⁻¹).

Both input variables have an impact on the amount of costs, with the feed rate being inversely proportional and the cutting speed being directly proportional (see Figure 4).

Table 9. Calculated and measured values of the parameters.

vc	Revolution	vf	Ra	cat. 1	NO	cat. 1	TM	cat. 1
[m.min−1]		[m.min−1]	[µm]	Ra	[€]	NO	[min]	Tm
4240.87	17,531	3.00	7.507	VL	3.03	VH	0.566	VH
4354.25	18,000	3.00	7.510	VL	3.13	VH	0.568	VH
4127.48	17,063	3.00	7.573	VL	2.92	VH	0.564	VH
4014.10	16,594	3.00	7.658	VL	2.81	VH	0.561	VH
3900.72	16,125	3.00	7.710	VL	2.70	VH	0.561	VH
3787.34	15,656	3.00	7.751	VL	2.58	VH	0.560	VH
3673.96	15,188	3.00	7.826	VL	2.45	H	0.559	VH
4240.87	17,531	3.63	7.918	VL	2.79	VH	0.538	H
4354.25	18,000	3.63	7.934	VL	2.92	VH	0.540	H
3560.58	14,719	3.00	7.937	VL	2.31	H	0.558	VH
2200.00	9095	9.32	11.144	MH	0.53	VL	0.371	VL
2200.00	9095	8.68	10.871	MH	0.53	VL	0.382	VL
2200.00	9095	9.95	11.420	MH	0.54	VL	0.362	VL
2200.00	9095	8.05	10.601	MH	0.54	VL	0.395	L
2313.38	9563	9.95	11.319	MH	0.55	VL	0.361	VL
2313.38	9563	9.32	11.042	MH	0.55	VL	0.370	VL
2200.00	9095	10.58	11.699	H	0.55	VL	0.356	VL
2200.00	9095	7.42	10.333	M	0.55	VL	0.410	L
2313.38	9563	10.58	11.600	H	0.56	VL	0.355	VL
2313.38	9563	8.68	10.770	MH	0.56	VL	0.381	VL
3673.96	15,188	12.47	10.066	M	0.77	VL	0.345	VL
3787.34	15,656	12.47	9.963	M	0.80	VL	0.345	VL
3560.58	14,719	12.47	10.176	M	0.73	VL	0.345	VL
3900.72	16,125	12.47	9.849	M	0.84	VL	0.345	VL
3447.20	14,250	12.47	10.328	M	0.70	VL	0.345	VL
3333.81	13,782	12.47	10.553	M	0.67	VL	0.345	VL
3787.34	15,656	13.11	9.935	M	0.79	VL	0.345	VL
3673.96	15,188	13.11	10.082	M	0.75	VL	0.345	VL
4014.10	16,594	12.47	9731	M	0.88	VL	0.345	VL
2540.14	10,501	12.47	12,479	H	0.60	VL	0.345	VL

¹ cat.—category; VL—very low; L—low; M—medium; MH—medium high; H—high; VH—very high.

displays the values of the input and output variables, categorized according to the legend below the table. After considering all three objectives (low value of the R_a parameter, low costs, minimum duration of the process), the most suitable solution was selected.

The lowest operating costs will be incurred by setting the cutting speed to a low level in the range of 2200.00 to 2313.38 m.min⁻¹ and the feed rate to a medium level in the range of 7.42 to 10.48 m.min⁻¹. Conversely, the highest costs will arise when setting the CNC machinery to a high cutting speed (4354.25 m.min⁻¹) and a low feed rate of 3.00 m.min⁻¹. Setting the feed rate to high levels (13.11 m.min⁻¹ and more) reduces the influence of the cutting speed setting on the load height.

Based on the results, it can be concluded that the maximum efficiency of the subprocess will be achieved when the CNC machine is set to a cutting speed of 4014.10 m.min⁻¹ (16,594 rev.min⁻¹) and a feed rate of 12.47 m.min⁻¹.

To address the optimization process comprehensively, we developed a systematic model (see Figure 5) that illustrates each step required to improve a manufacturing subprocess within a complex system. This model is built on Systems Theory principles, emphasizing the interconnected nature of each step and the iterative feedback loops that facilitate adaptive decision-making.

By incorporating this model, we demonstrate the practical application of Systems Theory in manufacturing. The interconnected steps reflect the complex relationships within a system, where each part influences the whole.

The critical milling process was identified through defect analysis and contribution to product cost. The optimization of this subprocess demonstrated significant improvements in surface quality and cost efficiency, validating its criticality in the overall system.

1.

Identification of the Key Process:

• Identification of Critical Success Factors (CSFs) linked to the company’s mission, vision, and strategic goals;
• Identification of Key Performance Indicators (KPIs) linked to CSFs;
• Identification of corresponding processes linked to KPIs.

2.

Identification of the key subprocess

The key process can be identified by using the following steps:

• Determining the contribution margins for individual products;
• Determining the share of each product in total sales;
• Using ABC analysis to identify significant, less significant, and insignificant products based on the Pareto principle.

3.

Measuring identified KPIs

The most important prerequisite for effective measurement is the establishment of target values for the identified indicators. Another key aspect is determining the optimal number of these indicators to avoid overwhelming management with too many metrics. However, it is generally impossible to define an optimal number, as it depends on the complexity of production, the company’s size, and the number of business partners.

4.

Identification of the Critical Subprocess: The critical subprocess is one with the highest occurrence of errors and defects. It is important to note that errors in the initial stages of production carry greater weight, as they lead to additional costs for the company either by increasing costs in subsequent processes or through non-quality costs. Another form of cost resulting from errors in the early stages of production includes customer complaints due to hidden defects that are not detected during final inspection and only appear when the product is used.

5.

Determining the Input and Output Parameters of the Critical Subprocess:

• Defining the physical nature of the examined subprocess and its basic technical parameters;
• Defining target variables linked to CSFs that have a technical–economic character.

6.

Measuring the levels of target output variables

• Defining input parameter levels based on information and knowledge gained during the manufacturing process to set up machine-technological equipment, which is essential for determining the level of output variables;
• Another activity includes establishing relationships for calculating target variables.

7.

Determining Weights of Output Parameters:

• Determining the importance of individual output parameters by defining weight coefficients concerning the company’s mission, vision, strategy, and defined CSFs;
• Creating an equation for the manufacturing subprocess.

8.

Creating Models Using Artificial Neural Networks (ANNs):

• Setting input and output variables;
• Defining the training and testing sets;
• Determining the number of hidden neural layers and the type of neural network;
• Creating individual models for each target variable and a comprehensive model based on the defined equation of the manufacturing process, followed by analyzing correlation coefficients, deviations, and least squares graphs to identify the most suitable models and determine optimal conditions.

9.

Control and Feedback:

This is one of the most important activities of the model, requiring a focus on continuous improvement. If the subprocess meets the established goals or optimal KPI values, it is necessary to identify the next critical subprocess. If all critical subprocesses within the production of the key product are optimized, the optimization process is complete, but attention should then shift to the production of the next product.

Defining Input Parameters and Output Variables: The input parameters of individual subprocesses in furniture manufacturing vary in nature and depend on their physical characteristics.

The ANN-predicted values for roughness and cost showed minor deviations from the experimental results. These discrepancies, while minimal, could impact final product quality and cost optimization. The application of real-time feedback loops in manufacturing could mitigate such differences, ensuring consistent outcomes.

5. Discussion and Conclusions

The presented empirical research study has dealt with a multi-objective optimization task using ANNs for the precise tuning of CNC machine parameters during the milling process, with a keen emphasis on enhancing surface quality, minimizing costs, and optimizing production time. In line with Rangone and Mella’s [77] recommendations on finding leverage points, we identify and optimize critical subprocesses to drive meaningful improvements. The goal of achieving the lowest cost is at odds with the quality requirement (lowest roughness). The research results reveal that by combining a cutting speed of 2200.00 to 2313.38 m.min⁻¹ and a feed rate of 7.42 to 10.58 m.min⁻¹, workpieces show the lowest values of operation costs but a medium to very high degree of roughness in the range of 10.240 µm to 11.699 µm. To achieve the highest-quality operation, it is necessary to set the CNC machine to the highest levels of cutting speed (3673.9 to 4354.25 m.min⁻¹), and, simultaneously, set the feed speed in the range of 3.00 to 3.63 m.min⁻¹. In this case, the expected size of the C_O parameter will be in the range of EUR 2.25 to EUR 3.13, with the feed rate significantly influencing the amount of cost within this range. The highest productivity will be achieved if the machine time is minimal, corresponding to setting the machine to a medium–high cutting speed (3333.81 to 3900.72 m.min⁻¹) and a medium–high feed rate (12.47 to 13.11 m.min⁻¹), resulting in the T_M parameter ranging from 0.34 to 0.35 min. Our results align with the study of Madić et al. [21], who found out that an increase in feed rate causes a nonlinear increase in R_a by polyamid material processing.

In existing studies, the ANN method was applied to determine the optimal values of one output parameter [19,20,21,22]. It means that the ANN method has been used to solve a one-objective optimization. In our study, we considered three output parameters: R_a (representing quality), T_M (indicating productivity), and C_O (reflecting costs), so we solved a multi-objective optimization task. This multivariable approach contributes to the extension of scientific knowledge in the field of process optimization through using ANNs by way of a multi-objective optimization problem. The use of 3D graphs provided a unique advantage in validating the ANN model by offering a visual representation of the data distribution and its alignment with predictions. Unlike numerical metrics alone, 3D visualizations enabled the identification of trends, such as local minima, and highlighted the ANN’s capability to accurately predict complex interactions between input and output variables. This approach complements traditional correlation analysis, offering an additional layer of validation for multi-objective optimization tasks. The findings of this study align with Monat et al. [59], who suggest that systems thinking can be used to address complexity and enhance sustainability in business. By applying ANN-based optimization, this research demonstrates how a systems-thinking approach can lead to improved process efficiency and reduced resource consumption in manufacturing, supporting the broader goal of sustainable business practices.

The ANN model was trained and validated using a dataset specific to the milling of medium-density fiberboard (MDF) with polycrystalline diamond (PCD) tools. While the results demonstrate high predictive accuracy for this specific scenario, the model’s ability to generalize to other materials, tools, or operational environments remains untested. ANN models are inherently sensitive to the quality and diversity of the training data, and their performance may decline when applied to datasets outside the original training domain.

The model for the critical subprocess (milling with PCD tool) has three input, three hidden, and three output layers, with a training error of 0.000623 and testing error of 0.003651. The input layer is activated via the logistic function, and the output layer via the exponential function. After the sensitivity analysis, it is concluded that the highest sensitivity coefficient is for the factor v_c (69.18350), v_f (65.87670) shows the middle sensitivity coefficient, and V (27.70260) shows the lowest sensitivity coefficient. The widely adopted backpropagation (BP) neural network has demonstrated effectiveness in addressing various industrial applications. The neural network employed in this study was a BP neural network, like the one used in the study by Huang [23].

Production optimization in a manufacturing company takes a multicriterial form due to conflicting objectives (maximize quality, minimize costs, maximize production = minimize production time). Our research study contributes to solving this multi-objective optimization problem by identifying the best combination of input parameters while considering all conflicting objectives. The fulfillment of objectives is evaluated separately and subsequently in their mutual combination. A sensitivity analysis, although challenging in an ANN methodology, was performed.

In this study, we confront the complex challenge of balancing contradictory output variables, operation costs, machined surface quality, and milling time, in the optimization of furniture manufacturing processes. Our approach is unique in considering not only the technical feasibility of each parameter, but also rigorously evaluating their economic implications. By employing a sophisticated artificial neural network model, we intricately navigate these conflicting objectives to achieve an optimal balance. This not only ensures enhanced operational efficiency, but also emphasizes cost-effective optimization, aligning the manufacturing process with both quality standards and economic viability.

This study primarily concentrated on machining parameters and their direct impact on process time, cost, and quality. The exclusion of setup and finishing times in this study aligns with prior optimization-focused research in machining processes, where primary emphasis was placed on the direct influence of machining parameters on output quality and efficiency. For instance, Ganesan and Mohankumar [78] utilized genetic algorithms to optimize CNC machining parameters without accounting for preparatory activities, demonstrating that direct machining parameters have the most immediate and significant impact on outcomes such as surface roughness and cutting time. Similarly, Al-Aomar and Al-Okaily [79] applied genetic algorithm-based parameter design to optimize high-volume turning processes, focusing exclusively on machining variables to streamline production efficiency. These approaches underscore the importance of isolating machining-specific factors when targeting core process improvements. However, future research could incorporate these preparatory tasks to deliver a more holistic assessment of total process efficiency, especially in contexts where such activities are highly variable or have a significant influence on overall operations.

The exclusion of setup and maintenance costs in this study is justified by their minimal impact on cost variability in a controlled experimental environment. Prior studies have shown that, in scenarios with consistent equipment usage and standardized setup procedures, these costs remain relatively constant and do not significantly affect optimization outcomes [80]. This approach allows for a more precise focus on machining parameters that directly influence process costs and performance. However, setup and maintenance cost integration could provide a more holistic view of cost modeling in our future studies.

The ANN approach is widely used in other industries, such as machining [81] and automotives [82], yet its application in furniture manufacturing is unique due to the inherent variability in natural materials like wood and MDF [83]. This variability poses distinct challenges, necessitating tailored optimization models. The practical contribution of this study is the demonstration of the possibility to optimize the furniture manufacturing process by using ANNs, whose reliability has been verified by scientific experiments. By selecting relevant input parameters in individual processes in furniture production, which depend on the technical and technological equipment used, it is possible to use the developed ANN for any process. A simple program in Excel software version 2410 will allow for a user-friendly environment for the use of the presented process optimization design by managers in enterprises.

The limitation of our study lies in the applicability of results, specifically for manufacturing companies utilizing a PCD tool in the milling process of MDF boards. This study’s findings are specific to machining MDF using PCD tools and may not directly apply to other materials or tooling systems. For example, natural wood or solid wood composites often exhibit greater variability due to anisotropy and moisture gradients, which could impact surface roughness and tool wear differently [22,70]. Similarly, non-PCD tools such as carbide or high-speed steel may experience higher wear rates when machining MDF, altering cost and process efficiency [74,75]. Future research could explore the applicability of the developed ANN model to these alternative materials and tools. However, we consider our study a framework for using artificial intelligence in business process optimization for all manufacturing companies. The results are useful in finding the optimal CNC machine setup to achieve maximum process efficiency.

To fully understand the implications of optimization, it is essential to situate our research within a broader theoretical framework. Systems Theory provides a valuable lens through which to view the manufacturing process, conceptualizing it as a dynamic, interconnected system with multiple components that influence one another. In manufacturing, the interdependence of variables like cutting speed, feed rate, and tool lifespan represents a classic example of a complex system, where changes in one variable impact multiple other aspects of the process. By applying Systems Theory, this study acknowledges that manufacturing is not just a series of isolated tasks, but a network of interrelated processes that contribute to the overall performance and sustainability of the enterprise.

While this study focused on a specific product (a wash basin closet), the developed ANN framework has the potential for universality. By incorporating diverse datasets reflecting other furniture types, the model could be retrained to optimize their specific processes. This adaptability underscores the broader applicability of the proposed method within the furniture industry.

Our future research will focus on examining how the principles of Systems Theory and adaptive management can be applied to further enhance sustainability in manufacturing. This will involve exploring ways to minimize waste, reduce energy consumption, and adopt circular economy practices, while maintaining high production efficiency and product quality. Emphasis should be placed on continuous feedback loops, decentralized decision-making, and scenario planning to help organizations quickly respond to changing environments. Additionally, adopting agile process optimization, fostering a flexible organizational culture, and leveraging technology for real-time data analytics will be critical to maintaining adaptability. Future experiments could extend this study to different subprocesses, illustrating its broader utility.