Facility location selection and layout planning through AHP, PROMETHEE, and CORELAP methods in the furniture industry

Abstract

Facility location selection and internal layout planning are critical strategic decisions for long-term sustainability. This study identified the most feasible location and optimal layout for a commercial bedroom furniture manufacturing facility through a seven-phase evaluation of Istanbul, Ankara, Izmir, and Bursa. The Analytical Hierarchy Process (AHP) and PROMETHEE were used for city and district selection, with AHP calculating criteria weights and PROMETHEE ranking alternatives. The Borda Count Method aggregated MCDM results, selecting Istanbul as the optimal city and Dudullu Organized Industrial Zone (O.I.Z.) as the most favorable district. The CORELAP method developed an optimal single-story layout for a 2688 m² production and assembly facility, enhancing production flow, reducing material handling costs, and improving efficiency. These findings underscore the importance of strategic facility location and layout planning in improving the furniture industry’s competitiveness and sustainability. The practical implications of this research are significant, as the findings can be directly applied to improve the competitiveness of the furniture industry. The study offers a comprehensive framework for strategic decision-making, providing valuable insights and a systematic approach applicable to similar problems in various sectors.

Full Article

Facility Location Selection and Layout Planning through AHP, PROMETHEE, and CORELAP Methods in the Furniture Industry

Melike Nur İnce,^a and Çağatay Taşdemir ^a,b,*

Facility location selection and internal layout planning are critical strategic decisions for long-term sustainability. This study identified the most feasible location and optimal layout for a commercial bedroom furniture manufacturing facility through a seven-phase evaluation of Istanbul, Ankara, Izmir, and Bursa. The Analytical Hierarchy Process (AHP) and PROMETHEE were used for city and district selection, with AHP calculating criteria weights and PROMETHEE ranking alternatives. The Borda Count Method aggregated MCDM results, selecting Istanbul as the optimal city and Dudullu Organized Industrial Zone (O.I.Z.) as the most favorable district. The CORELAP method developed an optimal single-story layout for a 2688 m² production and assembly facility, enhancing production flow, reducing material handling costs, and improving efficiency. These findings underscore the importance of strategic facility location and layout planning in improving the furniture industry’s competitiveness and sustainability. The practical implications of this research are significant, as the findings can be directly applied to improve the competitiveness of the furniture industry. The study offers a comprehensive framework for strategic decision-making, providing valuable insights and a systematic approach applicable to similar problems in various sectors.

DOI: 10.15376/biores.19.3.6478-6509

Keywords: Format; Multi-criteria decision making; Facility location selection; Facility planning; Analytical hierarchy process; Commercial furniture

Contact information: a: Department of Industrial Engineering (Grad. School), Bursa Technical University, Bursa 16130, Türkiye; b: Department of Forest Industry Engineering, Bursa Technical University, Bursa 16130, Türkiye; *Corresponding author: cagatay.tasdemir@btu.edu.tr

INTRODUCTION

Organizations carry out continuous improvement activities at many stages of their life cycle. During the establishment phase, executives face two major decision-making problems. These can be summarized with the questions of (1) where the facility will be established and (2) how the interior layout will look. Answers to such questions require multi-criteria decisions, which bear complex relationships.

With such selection decisions, these enterprises aim to increase productivity and efficiency. “Choosing the Place of Establishment” is of great importance but is also associated with a potential competitive advantage in the market, where firms face fierce challenges for the same market share (Alp and Gündoğdu 2012). For this reason, business managers want to start their attempts to reduce costs from the establishment stage of the organization.

Decision-making is a process that exists not only in the business world but also in all areas of life. Decision-making occurs in the lives of people and organizations in three different ways. The first of these is called uncomplicated decisions that are routinely made daily. These decisions do not require much thought because they require a low level of consideration regarding the risk they involve. As another form of decision, there are sudden decisions. While making these decisions, decision-makers act based on previous experiences and current judgments. Finally, it is possible to talk about decisions that can neither be made routinely nor instantaneously. To be able to make such decisions, the factors affecting the decision should be thoroughly examined and scrutinized. These decisions are made through a process called Multi-Criteria Decision Making (MCDM) (Emhan 2007). In such a decision, a goal is defined, and alternatives are determined according to this purpose. Then, a set of criteria is established to evaluate the identified alternatives, and a comparison is made.

The MCDM techniques have been used to solve complex problems in many sectors, such as finance (Steuer and Na 2003), renewable energy (Shang et al. 2021), marketing (Hung et al. 2012), transportation (Görçün 2021), food (Wang et al. 2023), health-care (Hsu et al. 2023), aviation (Chung and Tan 2022), agriculture (Wang 2022), and ecology (Sarkar et al. 2022). MCDM has helped address a wide range of industrial problems, including but not limited to logistics cost minimization (Yan et al. 2021), identifying tourism competitiveness of countries (Liu et al. 2021), measurement of entrepreneurship characteristics of business entities (Drejeris et al. 2021), green supplier selection (Li et al. 2021), leasing company selection (Chien et al. 2021), and storage management (Lin and Ma 2021). Another area in which MCDM is used is facility location selection. Site selection includes studies related to the determination of the region where the business will be established and the settlement within the region in a way that will minimize unit costs and allow for expansion and development (Özden 2016). Facility location selection is critical to preventing future problems because its location has a decisive role in the firm’s access to raw materials, proximity to the market, and access to a qualified workforce.

In contrast, the workplace arrangement constitutes a critical stage in the design of the production system. The workplace arrangement starts with determining the establishment location. It continues with the following stages: arranging the layout of existing departments, arranging the machinery/equipment, defining the movement areas of the workers and machinery in these sections, and arranging the individual workstations. While the individual workstations are arranged within the departments, ergonomics, work, time, and movement studies are carried out, and then an arrangement plan is prepared according to the results of these studies (Heragu 2008; Tompkins et al. 2010). In summary, when the in-plant arrangement is appropriately made, many invisible costs within the company could be minimized proactively, and an uninterrupted production flow that ensures the supply/demand balance could be achieved. For this reason, companies get help from scientific methods and experts in the field when deciding on in-plant arrangements after establishing the facility.

In recent years, several academic studies have focused on using MCDM methods in facility location selection and layout planning. A detailed examination of these studies revealed that MCDM has been used in many sectors for facility location selection and in-plant planning purposes. The following study sections reviewed and summarized previous literature on MCDM, facility location selection, and facility layout planning in this context.

Yang and Lee (1997) used the Analytical Hierarchy Process (AHP) method to determine the best location for a consulting firm (Yang and Lee 1997). Ertugrul and Karakasoglu (2008) employed Fuzzy TOPSIS and Fuzzy AHP methods to select a textile company’s facility location.

Similarly, Eleren (2010) used the AHP method to select the optimal location for a leather sector business, determining Istanbul as the preferred choice. Alp and Gundogdu (2012) utilized AHP and Fuzzy AHP methods to select a clothing production facility location in the textile sector, identifying Istanbul as the most suitable alternative. Akyuz and Soba (2013) employed the ELECTRE method to choose a location for a textile business in Usak, determining the Usak Organized Industrial Zone as the preferred alternative.

Ucuncu et al. (2017) used the Technique for Order of Preference by Similarity to the Ideal Solution (TOPSIS) method to evaluate alternative locations for a modular furniture factory, finding Kastamonu, Düzce, and Bolu to be the most favorable options. Gulsun and Sahin (2017) employed MCDM methods to select the best facility location for a whey powder production enterprise, determining Tekirdag as the most favorable alternative. Shanshan et al. (2018) compared AHP-based TOPSIS and ANP-based TOPSIS methods for facility layout planning.

Yesilkaya (2018) utilized AHP, TOPSIS, and Preference ranking organization method for enrichment evaluation (PROMETHEE) methods to determine a suitable location for a paper mill, selecting Mersin as the optimum facility. Yulu and Doldur (2019) investigated facility location selection factors in the automotive industry in Tu, considering criteria such as market, transportation, capital, labor, and raw materials. Yıldız and Demir (2019) used the Fuzzy TOPSIS method to select the optimum facility location for a domestic automobile factory, identifying Gemlik, Bursa as the most suitable option.

Aydemir Karadağ (2019) studied the optimal location for a solid waste landfill facility, selecting Gölbaşı district as the preferred choice using AHP and GP methods. Inag and Arikan (2020) conducted a site selection study for a solid waste collection center, determining Çukurambar District as the most suitable location. Seker and Aydin (2020) conducted a site selection study for a hydrogen production facility, favoring Sinop as the best location.

Kayadelen (2021) conducted a facility location selection study for a furniture factory, suggesting the Marmara Region as the most suitable option based on the main criteria and the Central Anatolia Region as the best alternative considering sub-criteria. Ekin and Okutkan (2021) used the PROMETHEE method to select an office supplies facility location, determining Ankara province as the best alternative.

Kara et al. (2022) conducted a branch selection study for a maritime sector company, using AHP, ARAS, and fuzzy TOPSIS methods to favor the city of Izmit as the most suitable location. Durak et al. (2022) employed AHP and TOPSIS methods to select a technology development zone, identifying the ITU Technopark as the best alternative.

A concise review of several case studies focusing on facility layout planning was presented, highlighting the methodologies employed and their corresponding outcomes: Rawabdeh and Tahboub (2006) developed a new package program called FLASP to optimize the facility layout of a mineral oil manufacturing and filling plant. They compared the three new layouts with the existing layout based on flow distance, travel cost, and free space. New Layout 3 achieved the best results, showing significant improvements in flow distance (68.6%), travel costs (62.6%), and free space (6.4%) (Rawabdeh and Tahboub 2006).

Ertay et al. (2006) developed an organization planning framework using DEA/AHP methodology to evaluate 18 plant layout alternatives in the plastic profile manufacturing sector. Nine relatively effective alternatives were identified, with the 16th option being the most efficient (Ertay et al. 2006). Deshpande et al. (2016) utilized the CRAFT and ALDEP methodologies in the alloy steel industry, resulting in a 0.10% improvement with CRAFT and a 23% improvement potential with ALDEP compared to the current layout (Deshpande et al. 2016).

Binoy and George (2018) addressed productivity issues in the steel forging industry by optimizing a layout using the CORELAP algorithm. The modified layout showed a 7.98% improvement in productivity (Binoy and George 2018). Mebrat et al. (2020) compared two alternative layouts for a mechanics workshop using the CORELAP algorithm, concluding that the layout plan designed based on weight placement value achieved higher efficiency (71.4%) (Mebrat et al. 2020).

Bagaskara et al. (2020) examined various algorithms for facility layout planning, such as SLP, GBT, Integer Linear Programming Model, CORELAP, and BLOCPLAN. The authors emphasized the need to select algorithms based on specific problem dynamics and requirements (Bagaskara et al. 2020). Kiran (2021) explored facility layout techniques, suggesting the integration of 3D modeling options alongside existing 2D modeling approaches. Evaluation techniques, such as Multi-Purpose Optimization, DEA, Simulation Non-Linear Programming, and Fuzzy Constraint, were highlighted as valuable tools for productivity analysis (Kiran 2021).

Tjusila et al. (2021) applied SLP, CRAFT, and CORELAP methods to develop facility layout alternatives for an industrial packaging company. The SLP method significantly reduced distance and material handling costs (Tjusila et al. 2021). Belachew (2021) optimized plant layout in the manufacturing industry using CORELAP and CRAFT Excel methods and achieved a 22.1% reduction in distance traveled compared to the current layout (Belachew 2021). Wahyudi et al. (2021) used the CORELAP algorithm and the CRAFT method to enhance facility layout organization in a mattress production company. The layout created with the CRAFT technique demonstrated a 26% efficiency improvement (Wahyudi et al. 2021).

Hanum (2021) employed CORELAP 1.0 software to design a facility layout for a heavy equipment manufacturing facility, achieving a 39.5% reduction in the total distance (Hanum 2021). Lufika et al. (2021) proposed alternative facility layouts for a bread-producing firm using the CORELAP and BLOCPLAN algorithms. The layout developed through the BLOCPLAN algorithm was selected due to its superior efficiency (Lufika et al. 2021).

The reviewed facility layout planning studies utilized methodologies such as DEA/AHP, CRAFT, ALDEP, CORELAP, SLP, GBT, Integer Linear Programming Model, and BLOCPLAN. Evaluation techniques were used to compare and assess alternative facility layouts, including Multi-Purpose Optimization, DEA, Simulation Non-Linear Programming, and Fuzzy Constraint. The reviewed case studies and methodologies in facility layout planning emphasize the significance of selecting appropriate techniques and evaluating productivity gains. These findings contribute to informed decision-making and improving efficiency in various industries. Based on these studies, it was evident that different methodologies and algorithms could effectively address facility layout planning problems across many industries. The selection of the most suitable approach depends on the specific sector, problem requirements, and available data.

The literature review also revealed that a wide range of MCDM methods, such as AHP, VIKOR, ELECTRE, PROMETHEE, and TOPSIS, have been extensively and effectively employed in numerous studies addressing facility selection challenges in diverse sectors, including furniture, automotive, aviation, and solid waste storage. These methods have proven effective in facilitating informed decision-making for optimal facility placement. Based on the literature review, within the furniture industry and related sectors, the TOPSIS (Üçüncü et al. 2017) and Fuzzy TOPSIS (Kayadelen 2021) methods were preferred for facility location selection while CORELAP and CRAFT methods were applied by Wahyudi et al. (2021) for the facility layout planning.

Furthermore, the literature on MCDM, facility location selection, and facility layout planning demonstrates the development and utilization of various criteria to address industrial facility location selection and planning problems. In past studies, site selection criteria are typically identified through literature review, expert consultation, and empirical analysis. Studies often start by reviewing existing research to identify criteria and best practices commonly used in similar contexts. For example, Yıldız and Demir (2019) employed a literature review and expert opinion to determine the criteria for site selection in the automotive sector. Similarly, İnağ and Arıkan (2020) employed a literature review and expert opinion to ascertain the criteria for site selection in the context of the paper industry. Similarly, Kayadelen (2021) used a combination of a literature review and expert input to enhance and validate the site selection criteria as they pertain to the furniture industry. This approach ensures the criteria are comprehensive and relevant to the specific industry context.

While previous studies have explored facility location and layout planning using various MCDM methods, there is a lack of comprehensive models that simultaneously address both problems within the context of the furniture industry. Most existing research tends to focus on either facility location selection or internal layout optimization, but not both in a unified framework. Furthermore, the specific needs and operational characteristics of the commercial bedroom furniture sector, such as the importance of proximity to raw material suppliers and market access, have not been adequately addressed in the literature. Therefore, the objectives of this study were as follows: (1) to identify the optimal city alternative for the commercial bedroom furniture manufacturing facility, (2) to decide on the optimal district alternative within the selected city, and (3) to determine the most suitable in-plant layout planning through a systematic approach using MCDM methods.

This study was designed to contribute to the intersection of multi-criteria decision-making (MCDM), facility location selection, and in-plant optimization by integrating these processes into a cohesive framework specifically for the commercial bedroom furniture manufacturing sector. It employed AHP and PROMETHEE for city and district selection and used the CORELAP method for internal facility layout planning. This comprehensive approach ensured strategic decision-making that enhanced long-term sustainability and operational efficiency.

The expected outcomes of the study included (1) the identification of the most feasible city for establishing the commercial bedroom furniture manufacturing facility, (2) the selection of the optimal district within the chosen city, and (3) the development of an optimal facility layout plan that would potentially help to minimize material handling costs and maximizing production efficiency.

MATERIALS AND METHODS

Regardless of the industry, one of the most critical decisions in the facility establishment is the facility location selection and facility layout planning. These decisions are of great importance for the success and future sustainability of the company, as they are part of strategic planning, are not made frequently, are not easy to change, and have high costs. This study focuses on determining the most feasible location and facility layout planning for a commercial bedroom furniture production facility. The study was initiated upon request of a conglomerate company whose headquarters was in Türkiye and who wanted to make a new venture with the aim of market expansion. The company’s name was not shared throughout the study due to the confidentiality agreement signed with the company. To select the establishment location and decide on the facility’s departmental arrangement most accurately, the systematic steps, consisting of seven phases shown in Table 1, were followed.

The researchers and the investor company decided on the methods preferred and criteria used based on a deliberate literature review and discussions to ensure practical outcomes were in the firm’s favor while providing the scientific merit and validity of the systematic research approach.

For establishing a facility, the city alternatives where the facility could be established must be determined first. After determining the city, an answer is sought as to which region it would be based in the selected city. For this reason, four alternative cities were chosen as the potential hosts of the facility (Phase 1). The city alternatives were identified as Istanbul, Izmir, Ankara, and Bursa based on the strategic plan and preferences of the investor company, as shown in Fig. 1. The investor company was willing to establish the new facility in one of the most industrialized cities in the nation. The ISO 500 ranking reports the first 500 firms contributing the most to the nation’s economy. The alternatives mentioned above were the largest four cities in the nation with the highest contribution to the country’s economy, with approximate sales revenues from manufacturing activities of $2,146 billion, $1,697 billion, $1,626 billion, and $1,298 billion, respectively (ISO 500 2022). The company executives were persistent in establishing the new facility in a highly industrialized city. Therefore, the industrialization levels of cities played a decisive role in specifying the geographical scope of this study. The specific constraints also included the total land cost and the size of the available land. The firm needed a construction-ready land area of at least 6500 m². The budget limit of the company for the total land cost was around ₺35.2 million ($1.1 million). These constraints were influential in the district selection phase. Following an extensive literature review, a pool of criteria was created for use in the site selection phase. The criteria were selected through three rounds of the Delphi survey involving three furniture industry professionals and two academic subject matter experts. The furniture industry professionals and academics were selected based on their past experiences and proven merits. The consensus was reached when there was more than 70% agreement on the suitability of the selected criteria.

Table 1. Phases-Based Systematic Approach of the Study

Table 2. Decision Matrix Used in the City Selection Phase

Table 3. Decision Matrix Used in the District Selection Phase

From a pool of criteria, a total of 8 criteria, including five main criteria and three sub-criteria, were agreed upon by the experts with consensus. After a series of deliberate back-and-forth communications, the availability of raw material suppliers, the total value generated by ISO 500 companies in the city (as an indicator of industrialization strength), availability of by-product/accessories suppliers, total employment in the sector, and proximity to potential customers were included in the study as the main criteria. The proximity to potential customers criterion had three sub-criteria: the number of dormitories, hotels, and hospitals (Phase 2). The decision matrix containing the corresponding values of each criterion per each alternative is presented in Table 2. Regarding the district selection phase, as the results of the Delphi method indicated and were supported by the literature findings, the following five criteria were included in the study: total land cost, competitors, major suppliers nearby, available land size, and proximity to highways (Phase 4). The decision matrix with corresponding values for each criterion used for the district selection analysis within the scope of AHP be PROMETHEE methods is given in Table 5.

All the data presented in Tables 2 and 3, excluding the Total Value Generated by ISO 500 Companies, were obtained from an independent service provider’s market research report prepared for the organization.

Fig. 1. Geographical illustration of city and district alternatives

AHP and PROMETHEE methods were applied to select the most feasible city (Phase 3) and district (Phase 5), and a final decision was reached by comparing the analysis results through the Borda Count method. The selection of these two methods for facility location decision-making was based on a review of existing literature, which revealed their frequent utilization in site selection issues. The Analytic Hierarchy Process (AHP) was chosen for its simplicity and effectiveness in deriving criteria weights through pairwise comparisons. PROMETHEE was selected for its ability to handle higher-level rankings and provide clear preference structures. The Borda Count method was used to aggregate individual rankings from AHP and PROMETHEE to obtain a final decision, ensuring a balanced and comprehensive evaluation. CORELAP was chosen for its effectiveness in optimizing facility layout by minimizing material handling costs and improving workflow efficiency. The AHP method was used to determine the criteria weights and to evaluate district alternatives comparatively. The criterion weights determined by AHP were also used as input in the PROMETHEE method.

As for the validation of the results, the AHP method includes a consistency analysis within its methodology (see page 11, step 6). The Consistency Ratio (CR) is calculated using the eigenvector obtained from pairwise comparisons. If the computed Consistency Ratio is below 0.1, the accuracy of the results is confirmed. This methodology is also applied in the Super Decisions software. Since no significant differences were observed in the results between the AHP method and the PROMETHEE method, a sensitivity analysis was not conducted for the PROMETHEE results. However, the Borda Count Method ensured increased robustness of the analysis results.

The Super Decision software package was used to determine criteria weights and evaluate alternatives using the AHP method. All sensitivity analyses and consistency ratios were calculated using the same software program. The Visual PROMETHEE software package was utilized to apply the PROMETHEE method.

AHP Method

The AHP method enables us to identify the importance of the criteria in complex multi-criteria and multi-alternative problems and helps reduce multi-dimensional problems to one-dimensional ones. In the AHP method, pairwise comparison matrices were constructed based on expert inputs from the Delphi survey. Experts rated the importance of each criterion relative to others on a scale of 1 to 9, where 1 indicates equal importance, and 9 indicates extreme importance of one criterion over another, as given in Table 4. The individual pairwise comparison matrices from the experts were aggregated using the geometric mean method to form a consensus matrix, as shown in Eq. 1 (Saaty 2008),

(1)

where A_k is the pairwise comparison matrix from expert k, and m is the number of experts. This approach ensures that the final criteria weights reflect the collective judgment of the expert panel. The consistency ratio (CR) was calculated to ensure the reliability of the comparisons. The CR was obtained by calculating the eigenvector and eigenvalue of the pairwise comparison matrix, computing the consistency index (CI), and dividing the CI by the random index (RI) corresponding to the matrix size. A CR value of less than 0.1 was considered acceptable, indicating a consistent comparison matrix. The detailed steps and formulas used are outlined in the following parts of the methodology section.

Table 4. Table of Importance Levels Used in Pairwise Comparisons

Step 1: Setting the Goal

Within the scope of the AHP method, an objective was first determined. In this case, the objective was to select the facility location city and district-wise. A hierarchical structure was established to achieve such an objective (Saaty 1980). The general representation of the hierarchical structure created for this study is given in Fig. 2.

Fig. 2. The hierarchical structure of the AHP method

Step 2: Establishing the Pairwise Comparison Matrix (Matrix A) and Determining the Priorities

After establishing the hierarchical structure, a comparative evaluation of the criteria and alternatives was carried out. These evaluations were done with pairwise comparison matrices of n × n size (Saaty 1980). The structure of comparison matrices is shown in Eq. 2.

(2)

The factors were compared for all matches above the diagonal line of the comparison matrix, using the value scores in Table 2 according to their relative importance. The calculations were completed using Eq. 3 for the matches under the diagonal.

(3)

Step 3: Normalizing the Pairwise Comparison Matrix

Each element a_ij of the pairwise comparison matrix A is divided by the sum of its respective column to produce a normalized matrix à (Saaty 1980). The resulting matrix is given in Eq. 4.

(4)

Step 4: Calculating the Eigenvector

The mean of the elements in each row of the normalized matrix à is calculated from the eigenvector as shown in Eq. 5 (Forman and Selly 2001).

(5)

The resulting eigenvector W is:

(6)

Step 5: Computing the Principal Eigenvalue

After the criterion weights were determined, the consistency test stage was started. This calculation compares the number of factors with the Principal Eigenvalue (λ) coefficient. To calculate λ, first, the comparison matrix A and the eigenvector W are multiplied. Then, the values obtained by dividing each element of the resulting vector by the corresponding component of W are averaged and calculated as in Eq. 7 (Saaty 1994).

(7)

Step 6: Consistency Check

The consistency Indicator (CI) was calculated utilizing Eq. 8 using the coefficient λ. In the last step of this stage, CI and the Random Value Index (RI) corresponding to the number of relevant factors given in Table 5 were processed, as seen in Eq. 9, to obtain the CR value (Saaty 2008). At this stage, the desired CR value is less than 0.1 (Aczel and Saaty 1983).

(8)

(9)

Table 5. Random Value Indices

PROMETHEE Method

The PROMETHEE method was first introduced by L. P. Brans at a conference in Canada in 1982 (Brans 1982). This method initially provided a partial ranking of decision alternatives with PROMETHEE I and a complete ranking with PROMETHEE II. Subsequently, Brans and Mareschal expanded the methodology by introducing different versions into the literature (Brans et al. 1986; Mareschal and Brans 1988; Brans and Mareschal 1992; Brans and Mareschal 2005). A fundamental distinction of PROMETHEE from other Multi-Criteria Decision Making (MCDM) methods is its ability to allow the decision-maker to specify different preference functions for each criterion. This feature eliminates the necessity of evaluating all criteria similarly, thus providing flexibility and customization options.

The PROMETHEE method was performed in 6 stages.

Step 1: First, the data matrix reflecting the importance of the criteria was created. In the data matrix, w = (w₁,w₂,…, w_k) represents the criteria weights, c = (f₁, f₂,…, f_k), and A = (a, b, c,…) represent the criteria and the evaluated alternatives, respectively.

Step 2: Six different preference functions, namely Ordinary, U-Type, V-Type, Level, Linear, and Gaussian, were identified as defined by Brans and Vincke for the criteria determined in the previous stage.

First Type Preference Function (Usual or Ordinary): If the decision maker had no preference regarding the relevant evaluation criterion, that criterion’s preference function was determined as the First Type (Usual or Ordinary) Preference Function.

Second Type Preference Function (U Type): If the decision maker used a preference judgment for decision alternatives with a value higher than the value determined by the relevant evaluation criterion, the preference function to be selected was identified as the Second Type (U Type) preference function.

Third Type Preference Function (V Type): This function was used for decision alternatives with an above-average evaluation criterion; however, when the decision-makers did not want to neglect the values below this value, the Third Type (V Type) Preference Function was selected.

Fourth Type Preference Function (Level): In cases where a specific range of values was determined for an evaluation criterion, and the preference was made according to these values, the Fourth Type (Level) Preference Function was selected.

Fifth Type Preference Function (Linear): In the cases where one of the above-average value alternatives was used for an evaluation criterion, the Fifth Type (Linear) Preference Function was the appropriate option.

Sixth-Type Preference Function (Gaussian): When the choice was made considering the deviation values from the mean, the Sixth-Type (Gaussian) Preference Function was selected.

Step 3: Based on the preference functions defined in the previous step, the shared preference functions for the pairs of alternatives were determined per the relations given in Eqs. 10 and 11,

(10)

(11)

where represents the value obtained by alternative a for any criterion j, while denotes the value difference between alternatives a and b for criterion j. In this study, a linear function type has been employed for all criteria used in city and district selection, and the values for have been calculated as shown in Eq. 12. The p and q values included in the model for each criterion are provided in Figs. 7 and 13. The Visual PROMETHEE software recommended these p and q values based on the data characteristics. Fig. 3 gives a schematic representation of the shared preference functions.

(12)

Fig. 3. Schematic representation of preference functions

Step 4: Based on the determined ordinary preference functions, preference indices for each pair of alternatives were calculated using Eq. 13 for pairs of alternatives evaluated with k criteria with weight w_i (i = 1, 2,…,k) in the alternative set.

(13)

Step 5: The alternatives’ positive (ϕ+) and negative (ϕ-) superiorities were determined using Eqs. 14 and 15. The schematic structure of positive and negative superiority for a generic alternative is shown in Fig. 4. Positive and negative supremacy structures were constructed for all alternatives.

(14)

(15)

Fig. 4. Schematic representation of positive and negative supremacies

Step 6: In this step, partial priorities were determined with PROMETHEE I. Partial priorities were used to assess the preferability of alternatives over each other, alternatives that are indistinguishable from each other, and alternatives that cannot be compared. Equations 16 to 21 were used to determine the partial priorities of the alternative pairs.

If any of the following conditions were met, alternative a was preferred to alternative b.

If the following condition was met, alternative a was indistinguishable from b.

If any of the following conditions were met, alternative a could not be compared with alternative b.

Step 7: In this step, the absolute priorities of the alternatives were calculated according to the PROMETHEE II procedure using Eq. 24. The exact ranking was determined by evaluating all alternatives on the same plane with the calculated complete priority values. The superiority or indifference decision of the alternatives was determined with the help of Eqs. 22 to 24:

AHP and PROMETHEE MCDM methods were also simultaneously deployed for the study’s district selection phase. A final decision was made by choosing the most feasible location for establishing the facility among potential districts based on the same evaluation steps outlined above. Following Phase 4 of the study, the venturing company identified four alternative industrial zones (Dudullu O.I.Z., Kimyacilar O.I.Z., Beylikduzu O.I.Z., and Ikitelli O.I.Z.) within the determined city according to the attractiveness of the existing investment incentives, as shown in Fig. 1 (Phase 5). A final decision regarding the most feasible district in the best city alternative was reached through the Borda Count method by aggregating the results of the MCDM analysis.

Borda Count Method

The “Borda Count Method,” which has been essential in developing modern electoral systems, was first introduced as a voting technique by Jean-Charles De Borda (1784) (Lumini and Nanni 2006).

The method’s underlying principle ranks the alternatives based on an aggregate performance score called the Borda Score. This study used the Borda Count method as a data aggregation technique, enabling scientists to combine the independent rankings generated by the AHP and PROMETHEE methods into a more valid single ranking. In the Borda scores calculation procedure, each alternative received n–1 point for a first preference, n–2 for a second preference, and so on. Zero points were assigned to the least preferred alternative, where n is the number of alternatives. The best alternative was determined by arranging the obtained Borda Scores from the largest to the smallest.

To represent the order given to the i^th alternative by the th decision maker (classifier), the Borda Score for the ith alternative was calculated as shown in Eq. 25.

After deciding where the facility would be established, the sixth and seventh phases of the study, which were identifying the departments for the production and assembly facility and planning the final facility layout, were initiated. The CORELAP (Closeness Rating and Layout Planning) method has been selected for the facility’s internal layout planning. CORELAP is a constructive algorithm that optimizes inter-departmental relationships. The rationale for choosing this method is its ability to minimize material handling costs and workflow durations in the internal layout planning of production and assembly facilities, thereby enhancing production efficiency. The sections subject to the interior arrangement optimization study were determined in cooperation with the architectural project team and the company’s technical consultants. The plant was determined to be established upon a land area of approximately 7400 m². It involved seven interconnected but independent sections with various area requirements: a production and assembly facility (2688 m²), a finished goods warehouse (832 m²), a raw material warehouse (468 m²), a cafeteria (168 m²), a recyclable collection zone (128 m²), and a social interaction zone called MSD (72 m²). Within the scope of this study, the production and assembly facility were subject to in-plant layout planning efforts. At the end of deliberate discussions, a consensus was reached, and the team experts agreed upon 13 distinct departments for the production and assembly facility. The optimization work focused on placing these departments within the allocated land parcel of 2688 m². Agreed upon facility design involved Quality Control (96 m²), Shop-Floor (1736 m²), Production Planning (80 m²), Administrative Offices (48 m²), Maintenance and repair (120 m²), Accounting (60 m²), Human Resources (80 m²), Sales (108 m²), R&D (84 m²), Logistics (40 m²), Occupational Health and Safety (36 m²), Restrooms (32 m²), and Meeting Room (168 m²). An inter-departmental relationship diagram has been created, and the Corelap 01 software package has been utilized for the internal arrangement of the facility. This approach facilitated optimizing spatial relationships and the effective placement of departments based on their interaction levels.

CORELAP Method

CORELAP is one of the first computerized organization algorithms (Heragu 1997). This method helps plan the first part to be placed in the layout by converting the attribute type input data to the quantity type input data. According to the created relationship diagram, successive sections were included in the layout in consecutive order. In-plant layout optimization was carried out in two stages through the CORELAP algorithm. The department selection order was determined in the first and second stages, and the final layout was reached by following the department placement procedure. The relationship values shown in Table 6 and the Total Closeness Rating (TCR) calculated based on these relationship values were used in the department selection order process and placement procedure of the departments.

Table 6. The Verbal and Numeric Scales Used in the Identification of the Relationship of Departments with Each Other

RESULTS

As a product of the first two phases of the study, the most favorable and feasible city alternative was identified for the commercial bedroom furniture manufacturing facility. The criteria to be used in city selection and the hierarchical structure of alternatives are shown in Fig. 5.

Fig. 5. The hierarchical structure of the city selection problem

The criteria weights used in the city selection procedure were determined according to the hierarchical structure shown in Fig. 5, and these weights are given in Fig. 6.