Location selection for the furniture industry by using a goal programming model

Abstract

Keywords: Goal programming; facility location problem; furniture industry; Western Black Sea Region; Turkey.

1. Introduction

The furniture industry is a labor-intensive and dynamic sector. It includes the manufacturing of furniture parts and their assembly with appropriate finishing operations. Wood, medium density fiberboard, plywood, hardboard, and oriented strand board are some basic materials used in the furniture industry [1]. One of the countries that have abundant raw materials for furniture production is Turkey. The emergence of the furniture industry in Turkey dates back to the nineteenth century. The Turkish furniture industry has developed along with rapid globalization. The country's furniture industry is mainly divided into wooden furniture (massive and veneered), metal furniture, and others. The number of companies engaged in furniture production is 33,924 and the number of employees in the sector is 151,904 [2]. The furniture sector has a share of ̴10% of the Turkish manufacturing industry [3]. One of the most important problems faced by furniture manufacturing companies is location selection. Facility location selection is the determination of the best geographic location for a facility. The decision-making process includes the identification, analysis, evaluation, and selection among options [4]. Location selection is a vital strategic decision owing to its important effects on the economic operation of plants and the sustainable development of regions [5, 6]. *

Corresponding Author: e-mail: hilal.singer@hotmail.com, tel: (374) 254 10 00 / 4902 177

H. Singer, Ş. Özşahin / Sigma J Eng & Nat Sci 11 (2), 177-184, 2020

Wrong selection results in inadequate qualified work forces, unavailability of raw materials, increased operating expenses or disastrous effects due to political and societal interferences [7]. Hence, it is important to develop location strategies for business units such as factories, distribution centers, and stores. Facility location problems have been studied for many years. Many different decision-making methods have been used to solve these problems. Safari et al. [8] employed a fuzzy extension of the TOPSIS method for facility location selection. Cebi and Kahraman [9] selected an appropriate wind energy plant location by employing the Choquet integral. Ozgen and Gulsun [10] solved the capacitated multi-facility location problem by using the probabilistic linear programming approach and the fuzzy analytic hierarchy process (AHP). Chadawada et al. [11] utilized the AHP-QFD approach to select the best facility location. Güler et al. [12] used the goal programming (GP) approach to determine the optimal location of a feed factory. Mahmud et al. [13] determined the most appropriate location of a mango supplying business by employing the AHP method and the analytic network process (ANP). Bolturk and Kahraman [14] proposed the interval-valued intuitionistic fuzzy combinative distance-based assessment for wave energy facility location selection. Kheybari et al. [15] used the best-worst method to determine the optimal location of a bioethanol facility. Yücenur et al. [16] employed the step-wise weight assessment ratio analysis and the complex proportional assessment to select the best location for a biogas facility. Seker and Aydin [17] evaluated different locations for hydrogen production plants by using the Entropy-TOPSIS approach extended with interval-valued Pythagorean fuzzy sets. There are also some studies seeking solutions to such problems in the field of wood science. Azizi and Modarres [18] used the ANP method to evaluate different locations for plywood and veneer plants. Imren et al. [19] determined the optimal location of a furniture company by employing the AHP method. Azizi and Ramezanzadeh [20] employed the AHP method to select the best location for the particleboard industry. Üçüncü et al. [21] selected the best location for the furniture industry by employing the TOPSIS method. Azizi [22] used the TOPSIS method for the location selection of solar wood drying units. Yeşilkaya [23] utilized AHP, TOPSIS, and PROMETHEE to determine the optimal location of a paper factory. In the present study, the GP approach is employed for the location selection problem of a furniture manufacturing company in Turkey. Hence, this study contributes to the existing literature by introducing the use of the GP approach on determining the most appropriate location for the furniture industry. The study will help the furniture industry in improving the effectiveness of decision-making processes on the identification of the best facility location.

3. Application

The GP approach attempts to minimize the total deviation of targets. This approach considers all of the targets simultaneously by establishing an achievement function that minimizes deviations from targets [33]. Therefore, this study employs a GP model to determine the most appropriate facility location for furniture production. The study area is the Western Black Sea Region of Turkey. Kastamonu, Düzce, Bolu, Zonguldak, Bartın, Karabük, and Sinop are considered as candidate locations (see Figure 1). The criteria determined to evaluate the alternative locations are proximity to raw materials, the number of qualified individuals, proximity to markets, population, and distances to the provinces in the region. The proposed approach applied to the location selection problem of the furniture industry is displayed in Figure 3.

Figure 3. The procedure for location selection Several objectives are defined to establish the mathematical model. The objectives involved in this study are as follows: Goal 1: Minimizing the distance between the facility and the source of raw materials Goal 2: Minimizing the distance between the facility and the market Goal 3: Minimizing the distance of the facility to the provinces in the region Goal 4: Minimizing the distance between the facility and the skilled-labor abundant locations Goal 5: Minimizing the distance between the facility and the densely populated places Once the objectives of the study are defined, the mathematical model is formulated. The mathematical formulation of the proposed GP model and the notations employed in this model are presented below. Notations i, j : provinces k: goals 1 if there is a facility at location i 𝑥𝑖 = { 0 otherwise dij: Distance between facility location i and province j 𝑟𝑖 : The distance of facility location i to the source of raw materials 𝑚i : The distance of facility location i to the market 𝑢i : The distance of facility location i to the provinces 𝑏𝑗 : The number of qualified individuals in province j ℎ𝑗 : The population of province j 𝑃𝑘 : Priority level 𝑑𝑘+ : Positive deviation variable for the kth goal 𝑑𝑘− : Negative deviation variable for the kth goal Mathematical Model Min Z = ∑5k=1 𝑃𝑘 𝑑𝑘+

∑7i=1 𝑟i 𝑥𝑖 + 𝑑1− − 𝑑1+ = 0 ∑7i=1 𝑚i 𝑥𝑖 + 𝑑2− − 𝑑2+ = 0 ∑7i=1 𝑢i 𝑥𝑖 + 𝑑3− − 𝑑3+ = 0 ∑7𝑗=1 𝑏𝑗 ∑7i=1 𝑑ij 𝑥𝑖 + 𝑑4− − 𝑑4+ = 0

H. Singer, Ş. Özşahin / Sigma J Eng & Nat Sci 11 (2), 177-184, 2020

Equation (4) is the objective function of the GP model. The aim of the GP model is to minimize the sum of the positive deviations. Constraint (5) attempts to minimize the distance between the facility and the source of raw materials. Constraint (6) tries to minimize the distance between the facility and the market. Constraint (7) ensures a low distance between the facility and the provinces in the region. Constraint (8) attempts to minimize the distance of the facility location to the skilled-labor abundant locations. Constraint (9) tries to minimize the distance between the facility and the densely populated places. Constraint (10) indicates that the facility will be located in only one location. Lastly, constraints (11) and (12) ensure the non-negativity and binary restrictions on the decision variables. The GP model described above is used to determine the best facility location. The codes required to solve the facility location selection problem are written in GAMS. The results of the analysis are summarized in Table 2. From Table 2, it is possible to see that the solutions obtained by the GP model are x6 = 1 and x1 = x2 = x3 = x4 = x5 = x7 = 0. The results indicate that Karabük is the best place for building a furniture manufacturing plant. Table 2. The results of the GP model Variable x1 x2 x3 x4 x5 x6 x7

Marginal 4.7423E+8 4.2018E+8 4.0485E+8 3.4066E+8 3.9870E+8 3.3145E+8 8.5451E+8

The demand for furniture products has increased in parallel with the increase in human population. Furniture manufacturing companies should choose the most suitable location to meet their customers’ expectations at minimum costs and to support their long-term competitive structures. In order to select the best location, decision-makers should apply an appropriate method. The contribution of this paper is the presentation of an effective approach for solving the location selection problem of furniture manufacturing companies. With the help of GP, decisionmakers could get an alternative ranking list in solving the problem.

4. Conclusion

Selection of the most appropriate location for the furniture industry is an important phase in the construction process because the results of this decision can have long-term effects on various factors such as profitability, accessibility, and sustainability. Developing a location selection model is needed for decision-makers to avoid undesired negative results. In this study, a GP model is proposed to determine an appropriate location for the Turkish furniture industry. Kastamonu, Düzce, Bolu, Zonguldak, Bartın, Karabük, and Sinop are evaluated using the following criteria: proximity to raw materials, the number of qualified individuals, proximity to markets, population, and distances to the provinces in the region. The proposed model is solved via an optimization tool. Based on the results of this study, it can be said that Karabük is the most 182

appropriate location. Consequently, the proposed GP model can present a road map for decisionmakers to make a dispassionate and objective location selection. In further research, this model can be combined with different decision-making methods to have an integrated decision support system that may assist decision-makers for the evaluation of candidate locations.

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