JURNAL RISET INFORMATIKA Vol. 5, No. 3. June 2023 P-ISSN: 2656-1743 |E-ISSN: 2656-1735 DOI: https://doi.org/10.34288/jri.v5i3.517 Accredited rank 4 (SINTA 4), excerpts from the decision of the DITJEN DIKTIRISTEK No. 230/E/KPT/2023 311 APPLICATION OF FUZZY C MEANS AND TOPSIS IN WAREHOUSE SELECTION AT PT WARUNG ISLAMI BOGOR Dewi Primasari-1, Khidir Zahid Muchtadiabillah-2*), Freza Riana-3 Teknik Informatika, Fakultas Teknik dan Sains Universitas Ibn Khaldun Bogor Bogor, Indonesia dewiprimasari9@gmail.com-1, khidirzahid@gmail.com-2*), zarianafre@gmail.com-3 (*) Corresponding Author Abstract PT Warung Islami Bogor needs a warehouse to store goods that come from suppliers. Currently, the selection of warehouses is still done manually and is subjective. It is feared that this will lead to inaccuracies in renting the warehouse. So an application is needed to assist companies in choosing a warehouse. The fuzzy C-Means method can be used to classify warehouse data based on the characteristics of each group. After obtaining the next group is to make a rating of each group. One method that can be used is the TOPSIS method. The TOPSIS method can be applied to this application to rank the data warehouses that have been grouped. In the selection of this warehouse, there are several criteria. The criteria used are price, building area, distance from the head office (HO), parking area, and number of floors. The calculation process is done by dividing the warehouse data into several groups and ranking them to obtain the best recommendations. This application uses the PHP programming language with the Laravel frameworkβ€”testing using a black box. Fuzzy C-Means and TOPSIS calculations show that Warehouse CCC is the best warehouse in Cluster 1 with a value of 0.797, and the Warehouse in Front of Gas Station Villa Bogor Indah is the best in Cluster 2 with a value of 0.613. Keywords: Cluster, Warehouse, Fuzzy C-Means, TOPSIS Abstrak PT Warung Islami Bogor membutuhkan sebuah gudang untuk menyimpan barang yang datang dari pemasok. Saat ini pemilihan gudang masih dilakukan secara manual dan bersifat subjektif. Hal ini dikhawatirkan akan menimbulkan ketidaktepatan dalam memilih gudang yang akan disewa. Sehingga dibutuhkan aplikasi untuk membantu perusahaan dalam memilih gudang. Metode Fuzzy C-Means dapat dilakukan untuk mengelompokkan data gudang berdasarkan karakteristik per tiap kelompok. Setelah didapatkan kelompok selanjutnya yaitu membuat peringkat dari tiap kelompok. Salah satu metode dapat digunakan adalah metode TOPSIS. Metode TOPSIS dapat diterapkan pada aplikasi ini untuk membuat peringkat dari data gudang yang sudah dikelompokkan. Pada pemilihan gudang ini ada beberapa kriteria. Adapun kriteria yang digunakan yaitu harga, luas bangunan, jarak dari head office (HO), luas parkir, dan jumlah lantai. Proses perhitungannya yaitu dengan cara membagi data gudang menjadi beberapa kelompok kemudian merangkingnya untuk memperoleh rekomendasi terbaik. Aplikasi ini dibangun menggunakan bahasa pemrograman PHP dengan framework Laravel. Pengujian menggunakan blackbox. Dari hasil perhitungan Fuzzy C-Means dan TOPSIS didapatkan bahwa Gudang CCC adalah gudang terbaik di kluster 1 dengan nilai 0.797 dan Gudang Depan Pom Bensin Villa Bogor Indah adalah gudang terbaik di kluster 2 dengan nilai 0.613. Kata kunci: Cluster, Gudang, Fuzzy C-Means, TOPSIS INTRODUCTION PT Warung Islami Bogor is one of the developing companies in Indonesia with a business that focuses on the trading sector of industrial packaging products. Starting from an idea to help fellow business people/producers find it challenging to get product packaging with plastic bottles to cover their production needs, in 2012, PT Warung Islami Bogor pioneered the company from a shop in Bogor to become a national company that continues to grow. PT Warung Islami Bogor specializes in distributing plastic bottle product packaging with a distribution network that spreads throughout Indonesia through traditional and modern digital and internet-based channels. In its P-ISSN: 2656-1743 | E-ISSN: 2656-1735 DOI: https://doi.org/10.34288/jri.v5i3.517 JURNAL RISET INFORMATIKA Vol. 5, No. 3 June 2023 Accredited rank 4 (SINTA 4), excerpts from the decision of the DITJEN DIKTIRISTEK No. 230/E/KPT/2023 312 distribution, PT Warung Islami Bogor requires warehouses to accommodate goods coming from suppliers, and these goods will be sent back to stores owned by PT Warung Islami Bogor, scattered in various cities in Indonesia. A warehouse is a place or building used to hoard, and store goods, either in the form of raw materials, work in process, or finished products (R. Widowati & Septiawan, 2021). Inside the warehouse are essential components of the modern supply chain. The supply chain involves activities in various stages: sourcing, production, and distribution of goods, from handling raw materials and works in progress to finished products. A warehouse is part of a company's logistics system, which stores products and provides information regarding the status and condition of materials/supplies stored in the warehouse so that this information is always up-to-date and easily accessible to anyone concerned (D. Widowati & Ningtiyas, 2022). Selection of the current warehouse without using a specific calculation method. The General Affairs (GA) staff conducts a field survey and records the warehouse data into a memorandum, then gives the memo to the GA Supervisor, and the GA Supervisor forwards it to the Operations Manager for discussion with the board of directors. The selection of warehouses is only based on the needs criteria at that time, for example, only based on price or building area. Warehouse selection must be compared one by one with warehouse data that has been recorded, and the selection is subjective. To optimize the warehouse selection process, the fuzzy method is an alternative that can be used to group warehouse data. First of all, the data must be grouped using fuzzy clustering. Fuzzy clustering is a technique for determining optimal clusters in a vector space based on the standard Euclidian form for the distance between vectors. Several data clustering algorithms exist, including Fuzzy C-Means (Nugraha & Riyandari, 2020). Fuzzy C-Means (FCM) is a data clustering technique in which the existence of each data point in a cluster is determined by the degree of membership (Sanusi, Zaky, & Afni, 2020). The basic concept of FCM is to determine the cluster center that will mark each cluster's average location. With this method, the cluster center and membership degree are always repaired repeatedly so that it can be seen that the cluster center will move toward the correct location (Hidayat, Nazir, Candra, Sanjaya, & Syafria, 2023; Ningtyas, Nasution, & Syaripuddin, 2022). The FCM method allows dividing part of the data into two or more groups, comparing an object that divides into group members based on the division level (Adifia, Ulinnuha, & Khaulasari, 2023). FCM also has high accuracy and fast computation time (Rohmah & Saputro, 2020). After the data is grouped, the data must be ranked. There are several data ranking methods, one of which is TOPSIS. TOPSIS is a concept in which the best-chosen alternative has the shortest distance from the positive ideal solution and the longest from the negative ideal solution (Nasution & Hanum, 2020; Syafi’ie, Tursina, & Yulianti, 2019). This method is widely used in the MCDM concept to solve practical decision problems, and this is because the concept is simple and easy to understand, computationally efficient, and can measure the relative performance of decision alternatives in a simple mathematical form (Sembiring & Hasugian, 2021). After the data is ranked, the data will be presented by the manager to the management for consideration. To simplify this, we need an accurate system to make decision-making correctly. In this study, four previous studies will be used to support the research that will be carried out. The first study was written by Giovan Meidy Susanto et al. with the title Android Smartphone Selection Reference System Using the Fuzzy C- Means and TOPSIS Methods in 2020. This study discusses the Fuzzy C-Means and TOPSIS algorithms to provide references for selected Android smartphones. The results of the Fuzzy C-Means and TOPSIS calculations can group Android smartphones into three clusters, then testing is carried out using White-Box Testing, and the results are that all functions in the software can run properly. The weakness of this system is that it does not discuss lifestyle needs in choosing Android(Susanto, Kosasi, David, Gat, & Kuway, 2020). The second study was written by Erlita Faridatul Himah and Raden Sulaiman, titled Implementing Fuzzy C-Means and TOPSIS Methods in Evaluating the Financial Performance of Banking Companies in Indonesia Based on Financial Ratios for 2021. This study discusses financial performance in the banking sector, which needs to be evaluated for company performance. Banking in Indonesia is based on financial ratios to determine a company's financial condition. The results of the discussion above are cluster rankings using the Fuzzy C-Means and TOPSIS methods. In calculating company performance evaluations using the Fuzzy C-Means and TOPSIS methods, a displacement index is obtained: the average number of companies in an inappropriate classification of 1.23 and the error rate of 25.65% (Himah & Sulaiman, 2021). JURNAL RISET INFORMATIKA Vol. 5, No. 3. June 2023 P-ISSN: 2656-1743 |E-ISSN: 2656-1735 DOI: https://doi.org/10.34288/jri.v5i3.517 Accredited rank 4 (SINTA 4), excerpts from the decision of the DITJEN DIKTIRISTEK No. 230/E/KPT/2023 313 The third study was written by Yuliadarnita et al. titled Management of Distribution of Assistance for SMEs Cooperative Office Using the FCM and TOPSIS Methods in 2023. this study discusses the management of aid distribution so that it can be given accurately. Fuzzy C-Means is used to classify eligible and ineligible recipients, and TOPSIS is used to sort by turnover and the number of employees. The results of calculations using Fuzzy C-Means and TOPSIS show that SMEs in Bedeng Bata deserve assistance (Yuliadarnita, Dwi Wardana, & Toyib, 2023). Christian Sri Kusuma Aditya wrote the fourth study titled Selection of Representative Sentences with the Integration of Fuzzy C-Means Clustering and TOPSIS (FCM- TOPSIS) for Document Summarization in 2020. In this study, discussing text documents is a much- needed source of information, but document collections in large numbers can hurt users who need a relatively long time to sort. A summary is needed for the essence without changing the context of information from a text document. The discussion above shows that this study integrates Fuzzy C-Means with the TOPSIS method to get summary results from text documents (Christian S. K. Aditya, 2021). What this research has in common with previous research is the method used, namely Fuzzy C-Means and TOPSIS, and what distinguishes this research from previous research is the research object, namely the selection of warehouses with price criteria, building area, distance from HO, parking area, and floors. RESEARCH METHODS The research method applied is by conducting interviews and direct observation of PT Warung Islami Bogor. More details can be seen in Figure 1. Time and Place of Research This research starts from March 2022 to June 2022 at PT Warung Islami Bogor. Research Target / Subject In this research, the target/subject is the HRD Manager, and then the interview stages are carried out in the information of variables, criteria, and alternatives. Procedure The research method is described in Figure 1. The analysis begins with the stages of observation, interviews, and literature application. Furthermore, the design is carried out using UML. The next stage is coding using the PHP programming language with the Laravel framework. Other applications are the Google Chrome application as a browser, MySQL as a database development application, and Apache as a web server. The testing phase is carried out using a black box to test the suitability of the application with the functionality or functional capabilities of the system. The Fuzzy C-Means algorithm generates calculation clusters, and the TOPSIS algorithm generates recommendation values. Figure 1. Research Methods Data, Instruments, and Data Collection Techniques The data used in this research is warehouse data at PT Warung Islami Bogor. Warehouse data can be seen in Table 1. Table 1. Warehouse Data No Code Variable 1 W1 Warehouse in Front of Gas Station Villa Bogor Indah 2 W2 Warehouse in Front of Puri Nirwana 3 W3 Warehouse KM 36 4 W4 Warehouse 88 5 W5 Warehouse Welding Workshop 6 W6 Warehouse CCC 7 W7 Warehouse PT. Grasindo 8 W8 Warehouse Kacang Garuda 9 W9 Warehouse Kedung Halang 10 W10 Warehouse PT. Nugratama Dayamitra 11 W11 Warehouse Nurdhin 12 W12 Warehouse Hj. Nasrul P-ISSN: 2656-1743 | E-ISSN: 2656-1735 DOI: https://doi.org/10.34288/jri.v5i3.517 JURNAL RISET INFORMATIKA Vol. 5, No. 3 June 2023 Accredited rank 4 (SINTA 4), excerpts from the decision of the DITJEN DIKTIRISTEK No. 230/E/KPT/2023 314 The criteria used for this research can be seen in Table 2, and details can be seen in Table 3. Table 2. Criteria Data No Code Variable 1 C1 Price 2 C2 Building Area 3 C3 Distance from HO 4 C4 Parking Area 5 C5 Floor Table 3. Details of the criteria data No Ware house C1 (mon th/ye ar) C2 (m2) C3 (km) C4 (m2 ) C 5 1 W1 200 500 3,3 150 2 2 W2 200 300 1,5 150 2 3 W3 355 600 11,9 300 2 4 W4 460 1500 2,8 500 1 5 W5 180 300 2,8 150 1 6 W6 279 1200 3,3 500 2 7 W7 653 1600 3,2 150 1 8 W8 921 1650 0,8 400 1 9 W9 406 720 11,1 360 2 10 W10 868 1800 10,1 500 1 11 W11 607 600 12,7 700 1 12 W12 962 1400 15,2 546 1 Data analysis technique with Fuzzy C-Means The first stage is Warehouse Data Grouping Using Fuzzy C-Means. 1. Input data to be clustered X is a matrix of size n x m (n = number of data samples, m = attributes of each data). Xij = sample data i (𝑖 = 1,2, . . . , 𝑛), attribute j (𝑗 = 1,2, . . . , π‘š). 2. Define: a. Number of cluster = 𝒄; b. Power = π’˜; c. Maximum Iteration = Maxlter; d. The smallest expected error = 𝜺; e. Initial objective function P0 = 0; f. Initial iteration = 𝑑 = 1; 3. Generate random numbers πœ‡π‘–π‘˜ , 𝑖 = 1,2, . . . , 𝑛; π‘˜ = 1,2, . . . , 𝑐; as the elements of the initial partition matrix U. Count the sum of each column (attribute): 𝑸𝒋 = βˆ‘ ο­π’Šπ’Œ 𝒄 π’Œ=𝟏 ............................................................... (1) with 𝑗 = 1,2, . . . , π‘š. Calculate:  π’Šπ’Œ = ο­π’Šπ’Œ 𝑸𝒋 ......................................................................... (2) 4. Compute the cluster center k: π‘‰π‘˜π‘— , with π‘˜ = 1,2, . . . , 𝑐; and 𝑗 = 1,2, . . . , π‘š. π‘½π’Œπ’‹ = βˆ‘ ((ο­π’Šπ’Œ) π’˜βˆ—π‘Ώπ’Šπ’‹) 𝒏 π’Š=𝟏 βˆ‘ (ο­π’Šπ’Œ) π’˜π’ π’Š=𝟏 ................................................... (3) 5. Compute the objective function on iteration t, Pt. 𝑷𝒕 = βˆ‘ βˆ‘ ([βˆ‘ (π‘Ώπ’Šπ’‹ βˆ’ π‘½π’Œπ’‹) πŸπ’Ž 𝒋=𝟏 ](ο­π’Šπ’Œ) π’˜)π’„π’Œ=𝟏 𝒏 π’Š=𝟏 ... (4) 6. Compute the change in the partition matrix:  π’Šπ’Œ = [βˆ‘ (π‘Ώπ’Šπ’‹βˆ’π‘½π’Œπ’‹) πŸπ’Ž 𝒋=𝟏 ] βˆ’πŸ π’˜βˆ’πŸ βˆ‘ [βˆ‘ (π‘Ώπ’Šπ’‹βˆ’π‘½π’Œπ’‹) πŸπ’Ž 𝒋=𝟏 ] βˆ’πŸ π’˜βˆ’πŸπ’„ π’Œ=𝟏 .................................... (5) with: 𝑖 = 1,2, . . . , 𝑛; and π‘˜ = 1,2, . . . , 𝑐. 7. Check stop condition: If: (|𝑃𝑑 βˆ’ 𝑃𝑑 βˆ’ 1| < πœ€) or (𝑑 > π‘€π‘Žπ‘₯πΌπ‘‘π‘’π‘Ÿ) then stop; If not: 𝑑 = 𝑑 + 1, repeat step 4. Data analysis technique with TOPSIS The next step is to rank using the TOPSIS. 1. Create a normalized decision matrix; 2. Create a weighted normalized decision matrix; 3. Determine the positive ideal solution matrix & negative ideal solution matrix; 4. Determine the distance between the value of each alternative with the positive ideal solution matrix & negative ideal solution matrix; 5. Determine the preference value for each alternative. RESULTS AND DISCUSSION Warehouse Data Grouping Using Fuzzy C-Means The first stage is Warehouse Data Grouping Using Fuzzy C-Means. 1. Input warehouse data to be clustered based on Table 3 in the form of xij matrix as follows: [ π‘₯11 π‘₯21 β‹― β‹― π‘₯111 π‘₯121 π‘₯12 π‘₯22 β‹― β‹― π‘₯112 π‘₯122 π‘₯13 π‘₯23 β‹― β‹― π‘₯113 π‘₯123 π‘₯14 π‘₯24 β‹― β‹― π‘₯114 π‘₯124 π‘₯15 π‘₯25 β‹― β‹― π‘₯115 π‘₯125] ο€­ i is warehouse data amounting to 12 (n=12) ο€­ j is criterion data amounting to 5 (m=5) 2. Initialization : a. Number of cluster = 2; b. Power = 2; c. Maximum iteration = 100; d. The smallest expected error = 10-2; e. Initial objective function = 0; f. Initial iteration = 1; JURNAL RISET INFORMATIKA Vol. 5, No. 3. June 2023 P-ISSN: 2656-1743 |E-ISSN: 2656-1735 DOI: https://doi.org/10.34288/jri.v5i3.517 Accredited rank 4 (SINTA 4), excerpts from the decision of the DITJEN DIKTIRISTEK No. 230/E/KPT/2023 315 3. Generate random numbers (πœ‡π‘–π‘˜ ) How to calculate the initial πœ‡π‘–π‘˜ Matrix: a. Generate the random value of the partition matrix [ πœ‡11 β‹― β‹― β‹― πœ‡111 πœ‡121 πœ‡12 β‹― β‹― β‹― πœ‡112 πœ‡122] b. Calculate the number of each line (attribute) [ 0,316 β‹― β‹― β‹― 0,912 0,365 0,765 β‹― β‹― β‹― 0,179 0,727] β†’ 1,081 β‹― β‹― β‹― β‹― β‹― Contoh baris ke 1 : πœ‡π‘–1 + πœ‡π‘–2 = 𝑄𝑗 0,316 + 0,765 = 1,081 c. Calculate the matrix element. πœ‡π‘–π‘˜ ο€­ πœ‡π‘–1 𝑄𝑗 = πœ‡π‘–1 0,316 1,081 = 0,292 ο€­ πœ‡π‘–1 𝑄𝑗 = πœ‡π‘–1 0,765 1,081 = 0,708 𝑄𝑗 Is the number of degrees of membership in line = 1: 0,292 + 0,708 = 1 So that the value of the first-row initial partition matrix is obtained: 0,292 0,708 Thus, for rows 2 to 12, the initial partition matrix is obtained in Table 4. Table 4. Initial ππ’Šπ’Œ matrix ππ’ŠπŸ ππ’ŠπŸ 0,292 0,125 0,620 0,514 0,112 0,921 0,205 0,545 0,129 0,410 0,836 0,334 0,708 0,875 0,380 0,486 0,888 0,079 0,795 0,455 0,871 0,590 0,164 0,666 4. Calculate cluster centroid (π‘£π‘˜π‘— ) For the first cluster center: Is known πœ‡11 2 = (0,292)2 = 0,085, and so on until the warehouse to 12 So that βˆ‘ (πœ‡π‘–1) 𝑀𝑛 𝑖=1 = 2,944 Calculate the first warehouse value for the 1st criterion : πœ‡11 2 Γ— π‘₯11 = (0,292) 2 Γ— 200 = 17,034, and so on until the warehouse to 12 So that βˆ‘ ((πœ‡π‘–1) 𝑀 Γ— π‘₯𝑖1) 𝑛 𝑖=1 = 1502,124 Calculate the first warehouse value for the 2nd criterion : πœ‡11 2 Γ— π‘₯12 = (0,292) 2 Γ— 500 = 42,584, and so on until the warehouse to 12 So that βˆ‘ ((πœ‡π‘–1) 𝑀 Γ— π‘₯𝑖2) 𝑛 𝑖=1 = 3142,911 Calculate the first warehouse value for the 3rd criterion : πœ‡11 2 Γ— π‘₯13 = (0,292) 2 Γ— 3,3 = 0,281, and so on until the warehouse to 12 So that βˆ‘ ((πœ‡π‘–1) 𝑀 Γ— π‘₯𝑖3) 𝑛 𝑖=1 = 21,273 Calculate the first warehouse value for the 4th criterion : πœ‡11 2 Γ— π‘₯14 = (0,292) 2 Γ— 150 = 12,775, and so on until the warehouse to 12 So that βˆ‘ ((πœ‡π‘–1) 𝑀 Γ— π‘₯𝑖4) 𝑛 𝑖=1 = 1453,435 Calculate the first warehouse value for the 5th criterion : πœ‡11 2 Γ— π‘₯15 = (0,292) 2 Γ— 2 = 0,170, and so on until the warehouse to 12 So that βˆ‘ ((πœ‡π‘–1) 𝑀 Γ— π‘₯𝑖5) 𝑛 𝑖=1 = 4,293 Calculate the central value for the 1st cluster : 𝑉11 = 510,301 𝑉12 = 1067,708 𝑉13 = 7,227 𝑉14 = 493,760 𝑉15 = 1,458 And so on for the 2nd cluster center, so the cluster center is obtained in Table 5. Table 5. 1st Iteration Cluster Center π‘½π’Œπ’‹ π’™π’ŠπŸ π’™π’ŠπŸ π’™π’ŠπŸ‘ π’™π’ŠπŸ’ π’™π’ŠπŸ“ Cluster 1 510,301 1067,708 7,227 493,760 1,458 Cluster 2 455,540 890,706 5,889 279,577 1,448 5. Compute Objective Function For the 1st cluster, calculate the 1st warehouse value for the 1st criterion. So the objective function is obtained in Table 6. P-ISSN: 2656-1743 | E-ISSN: 2656-1735 DOI: https://doi.org/10.34288/jri.v5i3.517 JURNAL RISET INFORMATIKA Vol. 5, No. 3 June 2023 Accredited rank 4 (SINTA 4), excerpts from the decision of the DITJEN DIKTIRISTEK No. 230/E/KPT/2023 316 Table 6. 1st Iteration Objective Function [βˆ‘ (π’™π’Šπ’‹ βˆ’ π’Ž 𝒋=𝟏 π‘½π’Œπ’‹) 𝟐 ] (ππ’ŠπŸ π’˜ ) [βˆ‘ (π’™π’Šπ’‹ βˆ’ π’Ž 𝒋=𝟏 π‘½π’Œπ’‹) 𝟐 ] (ππ’ŠπŸ π’˜ ) 45715,076 117726,384 12551,624 330051,563 107755,691 13737,417 50103,957 99067,354 10194,818 348477,762 60226,013 1104,689 17662,799 353573,876 153477,066 167159,649 2496,727 28886,814 111846,019 363532,067 189050,165 7669,505 35392,487 260336,977 6. Calculate the new partition (πœ‡π‘–π‘˜ ) matrix How to calculate the new U partition matrix : Table 7. 1st Iteration Partition ππ’Šπ’Œ Matrix [βˆ‘ (π‘₯𝑖𝑗 βˆ’ π‘š 𝑗=1 π‘‰π‘˜π‘—) 2 ] βˆ’1 π‘€βˆ’1 [βˆ‘ (π‘₯𝑖𝑗 βˆ’ π‘š 𝑗=1 π‘‰π‘˜π‘—) 2 ] βˆ’1 π‘€βˆ’1 βˆ‘ [βˆ‘ (π‘₯𝑖𝑗 βˆ’ π‘š 𝑗=1 𝑐 π‘˜=1 π‘‰π‘˜π‘—) 2 ] βˆ’1 π‘€βˆ’1 0,00000186 0,00000426 0,00000612 0,00000124 0,00000232 0,00000356 0,00000357 0,00001052 0,00001408 0,00000528 0,00000238 0,00000766 0,00000122 0,00000226 0,00000349 0,00001407 0,00000570 0,00001977 0,00000237 0,00000179 0,00000416 0,00000194 0,00000124 0,00000317 0,00000668 0,00002625 0,00003293 0,00000151 0,00000096 0,00000246 0,00000369 0,00000352 0,00000721 0,00000315 0,00000170 0,00000486 7. Check the stop condition. |𝑃𝑑 βˆ’ 𝑃0| = |2887796,499 βˆ’ 0| = 2887796,499 In 1st iteration, the conditions have not been met because (|𝑃𝑑 βˆ’ 𝑃0| > πœ€), and (𝑑 < π‘€π‘Žπ‘₯πΌπ‘‘π‘’π‘Ÿ), then the process continues to 2nd iteration until the conditions are met. The process stops at the 10th iteration because of the condition. (|𝑃𝑑 βˆ’ 𝑃𝑑 βˆ’ 1| < πœ€) Has been met. In other experiments, different cluster positions may be obtained due to the random initial initialization of the partition matrix, but this does not affect the final result. In the 10th iteration, the cluster center and the new πœ‡π‘–π‘˜ Matrix is obtained in Table 8: Table 8. 10th Iteration Cluster Center π‘½π’Œπ’‹ π’™π’ŠπŸ π’™π’ŠπŸ π’™π’ŠπŸ‘ π’™π’ŠπŸ’ π’™π’ŠπŸ“ Cluster 1 739,094 1554,222 6,214 427,274 1,074 Cluster 2 307,721 521,034 6,791 284,492 1,715 From Table 8, the following information is obtained: a. Cluster 1 contains warehouse data which has a price of around IDR 739,094,000; an average building area of 1,554.222 m2; the distance from HO is about 6,214 km; an average parking area of 427,274 m2; and an average of 1 floor. This cluster is a cluster with a higher price but with a larger building area. b. Cluster 2 contains warehouse data which has a price of around IDR 307,721,000; an average building area of 521,034 m2; the distance from HO is about 6,791 km; an average parking area of 284,492 m2; and an average of 2 floors. This cluster has a lower price but a smaller building area. Table 9. New ππ’Šπ’Œ matrix No Ware house The degree of data membership in the cluster The most significant degree of membership in the cluster 1 2 1 W1 0,020 0,980 2 2 W2 0,039 0,961 2 3 W3 0,008 0,992 2 4 W4 0,923 0,077 1 5 W5 0,041 0,959 2 6 W6 0,597 0,403 1 7 W7 0,938 0,062 1 8 W8 0,975 0,025 1 9 W9 0,063 0,937 2 10 W10 0,960 0,040 1 11 W11 0,211 0,789 2 12 W12 0,935 0,065 1 The new πœ‡π‘–π‘˜ The matrix table shows the degree of membership of the data warehouse in each cluster. The most significant degree of membership shows the highest tendency of the data warehouse to become a member of the cluster. From Table 9, the following information is obtained : a. Based on the largest membership in Cluster 1, there are 6 data warehouses in Cluster 1, namely the warehouse: 4, 6, 7, 8, 10, dan 12. b. Based on the most significant degree of membership in cluster 2, there are 6 data warehouses in cluster 2, namely the warehouse 1, 2, 3, 5, 9, dan 11. JURNAL RISET INFORMATIKA Vol. 5, No. 3. June 2023 P-ISSN: 2656-1743 |E-ISSN: 2656-1735 DOI: https://doi.org/10.34288/jri.v5i3.517 Accredited rank 4 (SINTA 4), excerpts from the decision of the DITJEN DIKTIRISTEK No. 230/E/KPT/2023 317 Warehouse Data Ranking Using TOPSIS After the data is grouped, the data must be ranked. 1. Create a normalized decision matrix. Table 10. Warehouse Data Cluster 1 No Ware house C1 C2 C3 C4 C5 1 W4 460 1500 2,8 500 1 2 W6 279 1200 3,3 500 2 3 W7 653 1600 3,2 150 1 4 W8 921 1650 0,8 400 1 5 W10 868 1800 10,1 500 1 6 W12 962 1400 15,2 546 1 Table 11. Warehouse Data Cluster 2 No Ware house C1 C2 C3 C4 C5 1 W1 200 500 3,3 150 2 2 W2 200 300 1,5 150 2 3 W3 355 600 11,9 300 2 4 W5 180 300 2,8 150 1 5 W9 406 720 11,1 360 2 6 W11 607 600 12,7 700 1 For cluster 1 Calculate the first warehouse value for the 1st criterion: π‘₯11 2 = 4602 = 211.600 Calculate the first warehouse value for the 2nd criterion: π‘₯11 2 = 2792 = 77.841 Calculate the first warehouse value for the 3rd criterion: π‘₯11 2 = 6532 = 426.409 Calculate the first warehouse value for the 4th criterion: π‘₯11 2 = 9212 = 848.241 Calculate the first warehouse value for the 5th criterion: π‘₯11 2 = 8682 = 753.424 Calculate the first warehouse value for the 6th criterion: π‘₯11 2 = 9622 = 925.444 βˆ‘ π‘₯𝑖𝑗 2π‘š 𝑖=1 = 3.242.959 π‘Ÿ11 = 0,255 And so on until the sixth warehouse. To obtain a normalized decision matrix, in Table 12. Table 12. Normalized Decision Matrix Cluster 1 No Ware house π‘Ÿπ‘–π‘— π‘Ÿπ‘–π‘— π‘Ÿπ‘–π‘— π‘Ÿπ‘–π‘— π‘Ÿπ‘–π‘— 1 W4 0,255 0,398 0,147 0,451 0,333 2 W6 0,155 0,319 0,173 0,451 0,667 3 W7 0,363 0,425 0,168 0,135 0,333 4 W8 0,511 0,438 0,042 0,361 0,333 5 W10 0,482 0,478 0,530 0,451 0,333 6 W12 0,534 0,372 0,798 0,492 0,333 In the same way for the second cluster, so that in the second cluster, a normalized decision matrix is obtained. Table 13. Table 13. Normalized Decision Matrix Cluster 2 No Ware house π‘Ÿπ‘–π‘— π‘Ÿπ‘–π‘— π‘Ÿπ‘–π‘— π‘Ÿπ‘–π‘— π‘Ÿπ‘–π‘— 1 W1 0,228 0,387 0,156 0,170 0,471 2 W2 0,228 0,232 0,071 0,170 0,471 3 W3 0,404 0,465 0,563 0,340 0,471 4 W5 0,205 0,232 0,132 0,170 0,236 5 W9 0,462 0,557 0,525 0,408 0,471 6 W11 0,691 0,465 0,601 0,794 0,236 2. Create a weighted normalized decision matrix. The weight to be used is based on Table 3 Calculate normalized weights : 𝑀𝑖𝑗 = 4+3+2+2+2 = 13 Calculate the normalized weight for the 1st criterion: 𝑀1 = 4 Γ· 13 = 0,308 And so on until the 5th criterion Calculate the first warehouse value : 𝑦11 = 𝑀1 Γ— π‘Ÿ11 = 0,308 Γ— 0,255 = 0,079 And so on until the sixth warehouse. So we get a weighted normalized decision matrix in Table 14. Table 14. Weighted Normalized Decision Matrix Cluster 1 No Ware house 𝑦𝑖𝑗 𝑦𝑖𝑗 𝑦𝑖𝑗 𝑦𝑖𝑗 𝑦𝑖𝑗 1 W4 0,079 0,092 0,023 0,069 0,051 2 W6 0,048 0,074 0,027 0,069 0,103 3 W7 0,112 0,098 0,026 0,021 0,051 4 W8 0,157 0,101 0,006 0,055 0,051 5 W10 0,148 0,110 0,082 0,069 0,051 6 W12 0,164 0,086 0,123 0,076 0,051 In the same way, for the second cluster, so that in the second cluster a weighted normalized decision matrix is obtained in Table 15. Table 15. Weighted Normalized Decision Matrix Cluster 2 No Ware house π‘Ÿπ‘–π‘— π‘Ÿπ‘–π‘— π‘Ÿπ‘–π‘— π‘Ÿπ‘–π‘— π‘Ÿπ‘–π‘— 1 W1 0,070 0,089 0,024 0,026 0,073 2 W2 0,070 0,054 0,011 0,026 0,073 3 W3 0,124 0,107 0,087 0,052 0,073 4 W5 0,063 0,054 0,020 0,026 0,036 5 W9 0,142 0,129 0,081 0,063 0,073 6 W11 0,213 0,107 0,092 0,122 0,036 3. Determine the positive ideal solution matrix & negative ideal solution matrix. If the criterion is a benefit, the most significant value is calculated by calculating the positive ideal solution matrix. If the criterion is cost, then the P-ISSN: 2656-1743 | E-ISSN: 2656-1735 DOI: https://doi.org/10.34288/jri.v5i3.517 JURNAL RISET INFORMATIKA Vol. 5, No. 3 June 2023 Accredited rank 4 (SINTA 4), excerpts from the decision of the DITJEN DIKTIRISTEK No. 230/E/KPT/2023 318 smallest value is taken. The result of the negative ideal solution matrix is taken as the smallest value if the criterion is beneficial. If the criterion is cost, then the most significant value is taken. So we get the matrix of positive and negative ideal solutions in Table 16. Table 16. Matrix of Positive and Negative Ideal Solutions Cluster 1 π’šπ’‹ + 0,048 0,110 0,006 0,076 0,103 π’šπ’‹ βˆ’ 0,164 0,074 0,123 0,021 0,051 In the same way, in the second cluster, so that in the second cluster the positive and negative ideal solution matrices are obtained in Table 17. Table 17. Matrix of Positive and Negative Ideal Solutions Cluster 2 π’šπ’‹ + 0,063 0,129 0,011 0,122 0,073 π’šπ’‹ βˆ’ 0,213 0,054 0,092 0,026 0,036 4. Determine the distance between the value of each warehouse with the positive ideal solution matrix & negative ideal solution matrix. Calculate the distance between the values of each warehouse and the positive ideal solution matrix for the first warehouse : 𝐷1 + = 0,065. And so on until the sixth warehouse. Calculate the distance between the values of each warehouse and the negative ideal solution matrix for the first warehouse: 𝐷1 βˆ’ = 0,142 And so on until the sixth warehouse. To get the distance between warehouses, here can be seen in the matrix of positive and negative ideal solutions in Table 18. Table 18. Warehouse Distance with Positive and Negative Ideal Solution Matrix Cluster 1 No Warehouse 𝐷𝑖 + 𝐷𝑖 βˆ’ 1 W4 0,065 0,142 2 W6 0,042 0,167 3 W7 0,101 0,113 4 W8 0,123 0,125 5 W10 0,136 0,075 6 W12 0,174 0,056 In the same way for the second cluster, so that in the second cluster, the distance between the warehouse and the positive and negative ideal solution matrices is obtained in Table 19. Table 19. Warehouse Distance with Positive and Negative Ideal Solution Matrix Cluster 2 No Warehouse 𝐷𝑖 + 𝐷𝑖 βˆ’ 1 W1 0,105 0,166 2 W2 0,122 0,168 3 W3 0,122 0,113 4 W5 0,127 0,166 5 W9 0,121 0,116 6 W11 0,175 0,110 5. Determine the preference value for each alternative For the 1st warehouse : 𝑉1 = 0,142 0,065+0,142 = 0,686 And so on until the sixth warehouse. So that the preference value is obtained which can be seen in Table 20. Table 20. Preference Value Cluster 1 No Warehouse 𝑉𝑖 1 W4 0,686 2 W6 0,797 3 W7 0,528 4 W8 0,503 5 W10 0,357 6 W12 0,244 In the same way as the second cluster, the second cluster gets the preference value in Table 21. Table 21. Preference Value Cluster 2 No Warehouse 𝑉𝑖 1 W1 0,613 2 W2 0,579 3 W3 0,481 4 W5 0,566 5 W9 0,489 6 W11 0,385 6. Based on the order of choice, the warehouse with the best preference value is the best. These results can be seen in Table 22. Table 22. Final Results Ranking Cluster 1 No Warehouse 𝑉𝑖 1 W6 0,797 2 W4 0,686 3 W7 0,528 4 W8 0,503 5 W10 0,357 6 W12 0,244 JURNAL RISET INFORMATIKA Vol. 5, No. 3. June 2023 P-ISSN: 2656-1743 |E-ISSN: 2656-1735 DOI: https://doi.org/10.34288/jri.v5i3.517 Accredited rank 4 (SINTA 4), excerpts from the decision of the DITJEN DIKTIRISTEK No. 230/E/KPT/2023 319 Table 23. Final Results Ranking Cluster 2 No Warehouse 𝑉𝑖 1 W1 0,613 2 W2 0,579 3 W5 0,566 4 W9 0,489 5 W3 0,481 6 W11 0,385 In Table 23, it can be explained that the recommended warehouse data for cluster 1 is the CCC Warehouse, with the highest value of 0.797. And for cluster 2, namely the warehouse in front of the Villa Bogor gas station, with a value of 0.613. System Implementation Figure 2-5 is the result of the display of the warehouse selection application. Figures 2 and 3 show the criteria and warehouse data, while Figures 4 and 5 are the calculation process pages. 1. Criteria Data Figure 2. Criteria Data 2. Warehouse Data Figure 3. Warehouse Data 3. Calculation Process Figure 4. Calculation Process 4. Calculation Result Detail Page Figure 5. Calculation Result Detail Page CONCLUSIONS AND SUGGESTIONS Conclusion The conclusion that can be drawn from this research is that this application can group warehouse data into two clusters. With the characteristics of the first cluster, the price is higher but with a larger building area, and the characteristics of the second cluster are cheaper but with a smaller building area. The results of grouping data must be ranked to obtain recommended data warehouses. The warehouse selection application can run according to the needs desired by the company and has been implemented at PT Warung Islami Bogor. Suggestion Thanks to the newly added warehouse data import capability, companies no longer need to manually enter warehouse data into the system. Meanwhile, the Subtractive Clustering with Fuzzy C- Means algorithm is used to increase speed. REFERENCES Adifia, N. N. N., Ulinnuha, N., & Khaulasari, H. (2023). 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