Title Science and Technology Indonesia e-ISSN:2580-4391 p-ISSN:2580-4405 Vol. 7, No. 4, October 2022 Research Paper Greedy Reduction Algorithm as the Heuristic Approach in Determining the Temporary Waste Disposal Sites in Sukarami Sub-District, Palembang, Indonesia Sisca Octarina1,2, Fitri Maya Puspita2*, Siti Suzlin Supadi3, Nur Attina Eliza2 1Mathematics and Natural Sciences Doctoral Study, Sriwijaya University, Indralaya, 30662, Indonesia2Mathematics Department, Faculty of Mathematics and Natural Sciences, Sriwijaya University, Indralaya, 30662, Indonesia3Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, 50603, Malaysia *Corresponding author: fitrimayapuspita@unsri.ac.id AbstractWaste is one of the problems in Palembang, Indonesia. The amount of waste in Palembang increases proportionally to the populationyearly and can adversely affect the community. Therefore, we determine the optimal temporary waste disposal site (TWDS) tooptimize the problems. The set covering model is the proper model for solving the location and allocation problem. In this study, dataon the distance between each TWDS is needed in the set covering modeling. The novelty in this research is developing the 𝜌-medianproblem model, which is formed from the optimal solution of the set covering location problem (SCLP) model. Palembang consistsof 18 sub-districts, of which the Sukarami sub-district has the highest population density. This study discussed the determination ofstrategic TWDS in the Sukarami sub-district using the SCLP model, the 𝜌-median problem, and a heuristic approach, namely thegreedy reduction algorithm in solving the model. Based on the solution of the 𝜌-median problem model with LINGO 18.0 and the 𝜌-median problem solved by the greedy reduction algorithm, only three strategic TWDS were found for the Sukarami sub-district.The study results recommend a review of the existing TWDS and particularly the addition of a TWDS in Sukodadi and Talang Betutuvillages, respectively. KeywordsTWDS Location, Set Covering Location Problem, 𝜌-Median Problem, Greedy Reduction Algorithm Received: 4 July 2022, Accepted: 4 October 2022 https://doi.org/10.26554/sti.2022.7.4.469-480 1. INTRODUCTION Palembang is the second-largest and most populous city on the Sumatera island after Medan and Indonesia’s ninth most populous city. According to the Central Statistics Agency, in 2020, Palembang had around 8.5 million people with a popula- tion density of 92 people/km2 and 18 sub-districts. Sukarami sub-district is one of the sub-districts in Palembang, which has crowded public places daily, such as Hajj Dormitory, KM 5 Market, Pasaraya, hotels, and automotive companies or deal- ers. The waste volume increases every day. The increase in waste impacts the environment and public health (Puspita et al., 2018). Waste is an object that is no longer useful and arises from the community environment in solid form, both organic and inorganic. Waste can come from markets, factories, of- ces, institutions, public buildings, community settlements, or community yards (Bangun et al., 2022). The waste is collected in dierent temporary waste disposal sites (TWDS) in their respective locations (Yuliza et al., 2020). According to data from the Environment and Hygiene Ser- vice of Palembang City, TWDS are divided into several types: market TWDS, container TWDS, self-help TWDS, and un- ocial TWDS. Market TWDS is located in the market area, usually in a concrete square tub. Container TWDS is found in market areas and sometimes around community settlements, usually in bre containers. Self-help TWDS is located in resi- dential areas such as complexes, schools, buildings, or public places, usually in a concrete square tub. Unocial TWDS is generally located in community residential areas in front of the market, which are placed illegally. The waste collected at the TWDS will then be transported by dump truck to the nal disposal site (FDS) in stages according to the transportation schedule from each TWDS, which is dierent in each region. Several factors hinder the transportation process, including the waste transportation routes with longdistances between TWDS and disordered, the transportation equipment capacity, and the waste volume at each TWDS (Octarina et al., 2022b). In dealing with these problems, the set covering problem (SCP) model can be used to nd solutions to this TWDS optimization problem (Octarina et al., 2022b). https://crossmark.crossref.org/dialog/?doi=10.26554/sti.2022.7.4.469-480&domain=pdf https://doi.org/10.26554/sti.2022.7.4.469-480 Octarina et. al. Science and Technology Indonesia, 7 (2022) 469-480 Set covering is part of integer linear programming related to optimization, which concerns the location-allocation prob- lems and aims to minimize the factors that aect the constraints in the model (Sitepu et al., 2022). SCP is one optimization problemincomputerscience (Crawfordetal.,2018). TheSCP application in daily life determines the waste vehicles routes, vehicle routes to pick up bus passengers at bus stops, scheduling ight crews, resource allocation, etc (Çalık and Fortz, 2019; Cubillos and Wøhlk, 2021; Roshanaei et al., 2017; Šarac et al., 2016). According to the model group, the SCP consists of the set covering location problem (SCLP), maximal covering location problem (MCLP), 𝜌-median problem, and 𝜌-center problem (Octarina et al., 2022a). The four models have a relationship in their solutions but dier in their objective func- tions. SCLP nds the optimum number of TWDS to serve all demand points (Jeong, 2017). MCLP aims to maximize the demand by a limited number of TWDS that can be served in standard time and p-median problem minimizes the distance between TWDS and sorts the routes (Guzmán et al., 2016). The 𝜌-center problem is the min-max multi-centre problem (Du et al., 2020). Previous research on SCP has been carried out (Crawford et al., 2018; Bangun et al., 2022; Çalık and Fortz, 2019; Daskin and Maass, 2019; Ahmadi-Javid et al., 2017; Kinsht and Petrunko, 2020; Kwon et al., 2020; Sitepu et al., 2019; Xu and Li, 2018). A greedy reduction algorithm (GRA) is an algorithm to solve optimization problems such as optimizing facility loca- tions, scheduling employee assignments, and scheduling lec- tures (Ardeshiri et al., 2015). In solving problems, GRA per- forms solutions based on a step-by-step solution in sequence so that the nal solution can be the most optimal (Binev et al., 2018). The advantage of GRA compared to other algorithms is that it can nd the best route in optimizing the distance, min- imize costs, and optimize the facility allocation point (Shao et al., 2020). Previous research by Puspita et al. (2018) used the GRA in optimizing TWDS and found a solution, namely 3 TWDS, to meet the six villages demands. Ardeshiri et al. (2015) implemented the GRA for mixtures of exponential families and found the optimal solution, even with a limited computational budget, can provide signicant results of 1%. Čertíková et al. (2020) concluded that greedy reduced basis algorithms could shorten the time and provide signicant solu- tions. This study determines the optimal TWDS in Sukarami sub-district using the SCP model and solved by GRA. This re- search’s novelty is in improving the 𝜌-median problem model from the optimal solution of the SCLP model. The model and algorithm are expected to optimize the number of TWDS to meet all demand points in the sub-district. The exact solutions obtained from SCP and the heuristic solution using GRA are expected to provide the best solution and can be considered for Palembang City in determining strategic TWDS in the Sukarami sub-district. 2. EXPERIMENTAL SECTION 2.1 Methods We discussed the method used in this research in this section. We also briey discuss SCLP, the 𝜌-median problem, and a short description of the GRA. The steps of this research are listed as follows: 1. CollectdataonTWDSnames, locations, andthenumber of TWDS in each village in the Sukarami sub-district from the Palembang City Environment and Hygiene Service (DLHK Palembang). 2. Describe the data used, namely: a. Check TWDS location points according to the actual TWDS location. b. Measure the distance between TWDS and TWDS and between TWDS and the village in the Sukarami sub-district using google maps. 3. Dene variables and parameters for the SCLP model and 𝜌-median problem. 4. Formulate the set covering model, namely the SCLP model and the 𝜌-median problem. 5. Find solutions to the SCLP model and 𝜌-median prob- lem using the LINGO 18.0. application 6. Solve the 𝜌-median problem model and implement the GRA to solve the 𝜌-median problem model. 7. Recapitulate the calculation results of the SCLP model and the 𝜌-median problem. 8. Analyze the results of the SCLP, 𝜌-median problem, and the GRA. 9. Make conclusions 2.2 Set Covering Location Problem (SCLP) SCLPis one of the optimization problems to nd the optimum TWDS placements so that it can serve all demand points on the waste transportation distribution system (Octarina et al., 2022a). The SCLP model can be systematically written as follows: Minimize ZSCLP = ∑︁ j𝜖  xj (1) subject to∑︁ j𝜖 J xj ≥ 1, ∀j𝜖 J (2) xj𝜖 {0,1}, ∀j𝜖 J (3) whereas ZSCLP = the number of TWDS location J = the set of TWDS location with index j The decision variables are: © 2022 The Authors. Page 470 of 480 Octarina et. al. Science and Technology Indonesia, 7 (2022) 469-480 xj = { 1; if the TWDS is allocated at j- th location 0; if the TWDS is not allocated at j-th location The objective function 1 minimizes the number of TWDS locations. Constraint 2 ensures that at least one TWDS can meet each demand point and Constraint 3 is the binary Con- straint. 2.3 𝜌-Median Problem The 𝜌-median problem nds 𝜌 TWDS at location j to mini- mize the distance (Ahmadi-Javid et al., 2017). The 𝜌-median problem can be formulated as follows: Minimize Zp−median = ∑︁ i𝜖I ∑︁ j𝜖 J di jxi j (4) Subject to:∑︁ i𝜖 J xi j = 1, ∀i𝜖I (5)∑︁ i𝜖  yj = p (6) xi j ≤ yi , ∀i𝜖I , ∀j𝜖 J (7) yj𝜖 {0,1}, ∀j𝜖 J (8) xi j𝜖 {0,1}, ∀i𝜖I , ∀j𝜖 J (9) whereas Z𝜌−Median =the total of minimum distance from the demand point to the TWDS I =the set of demand point with index i J =the set of TWDS location with index j p =the number of TWDS for facility allocation di j =the distance between the i-th and the j-th location (metre) The decision variables are: yj = { 1; if the TWDS is allocated at j-th location 0; if the TWDS is not allocated at j-th location xi j = { 1; if the TWDS is allocated at j-th location 0; if the TWDS is not allocated at j-th location Equation4obtains theminimumdistancefromthedemand point to the nearest facility TWDS. Whereas, Constraint 5 indicates the demand for each TWDS placement. Constraint 6 sets the maximum number of TWDS. Constraint 7 suggests thateveryTWDSplacementshouldbegiventhesamefacilities, and Constraints 8 and 9 indicate that the problem is a binary integer. 2.4 Greedy Reduction Algorithm (GRA) GRA is an algorithm commonly used to solve optimization problems, determining the optimal facility point. Several fac- tors in optimizing the location include the distance between the facility locations and the location quality. GRA is an algorithm used to solve optimization problems sequentially, producing a local optimum at each step and producing the best nal solu- tion in a global optimum solution (Sanchez-Oro and Duarte, 2018). According to Muliyadi (2017), the Greedyalgorithm has several important elements, the candidate set, solution set, selection function, feasibility function, and objective function. In this study, we implemented GRA to solve the 𝜌-median problem in getting the nal solution. The steps of GRA are as follow: 1. Form a distance matrix D with size m×n. 2. Look for the dominating matrix value in all existing ma- trix columns, provided that the dominating column has a smaller value than the other column values or dik ≤ dil; ∀ i≠ k and ∀ i ≠ l. 3. Compare all columns with the dominant value from the selected column. 4. Find the optimum value by comparing the entry values between the selected dominant column. 5. Compare the selected dominant column pair with each column to looks for the optimum value. 6. Analyze the results of each step and recapitulate the re- sults. 3. RESULT AND DISCUSSION TWDS data in the Sukarami sub-district was obtained from DLHK Palembang, which was surveyed and grouped based on the TWDS location points in each village. Table 1 shows the distribution of TWDS based on village location points. There is only one TWDS in Talang Jambe Village, TWDS Talang Jambe, next to Public Cemetery. Kebun Bunga village has 6 TWDS and Sukarami has 8 TWDS. Suka Bangun, Suka Jaya, Sukodadi, and Talang Betutu villages do not have any TWDS. Next, the denition of variables for SCLP and the 𝜌-median problem model can be seen in Table 2. The distance between each TWDS was obtained through direct measurements of the location with Google Maps. Table 3 states the distance between each TWDS (di j) in the Sukarami sub-district (in meters). The number labelled in yellow is the maximum distance between each TWDS based on DLHK Palembang provisions, which is less than 500 meters. Table 3 states that the distance from TWDS Kolonel H Burlian beside Hotel DE Premium (x1) to TWDS Naskah (x2) is 610 meters, and so on. Using the data in Tables 2 and 3, we formulate the SCLP model. Minimize ZSCLP =x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8+ x9 + x10 + x11 + x12 + x13 + x14 + x15 (10) Subject to © 2022 The Authors. Page 471 of 480 Octarina et. al. Science and Technology Indonesia, 7 (2022) 469-480 Table 1. TWDS Based on Village Location Points No Village Names TWDS Names 1 Talang Jambe TWDS Talang Jambe next to Public Ceme- tery 2 Kebun Bunga • TWDS Letjen Harun Sohar in front of Honda Dealer • TWDS Letjen Harun Sohar in front of Hajj Dormitory • TWDS Letjen Harun Sohar in front of Al-Hikmah Mosque • TWDS Letjen Harun Sohar in front of Talang Kedondong • TWDS Letjen Harun Sohar in front of Auto 2000 TAA • TWDS Bambu Kuning Arah Rumah Sakit Pelabuhan 3 Sukarami • TWDS Batujajar • TWDS Naskah • TWDS Kolonel H Burlian behind Mitra Bangunan Bus Stop • TWDS Kolonel H Burlian beside Lorong Dharma Agung • TWDS Kolonel H Burlian Simpang SMP 40 Palembang • TWDS Kolonel H Burlian beside Hotel DE Premium • TWDS Kolonel H Burlian in front of Bank BRI • TWDS Kolonel H Burlian beside Indo- maret Bus Stop 4 Suka Bangun - 5 Suka Jaya - 6 Sukodadi - 7 Talang Betutu - x1 ≥ 1 (11) x2 + x4 ≥ 1 (12) x3 ≥ 1 (13) x3 + x4 + x5 ≥ 1 (14) x4 + x5 + x6 ≥ 1 (15) x5 + x6 ≥ 1 (16) x7 + x8 ≥ 1 (17) x9 + x10 ≥ 1 (18) x11 ≥ 1 (19) x12 + x13 ≥ 1 (20) x14 ≥ 1 (21) x15 ≥ 1 (22) x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15𝜖 {0,1} (23) Model 10 states that the objective function minimizes the number of TWDS to satisfy all demand points. Constraints (11) to (22) state that each TWDS must meet at least one request point. Constraint (23) states that the variables x1 to x(15) are binary. The optimal solution of the model is attached in Table 4. Table 2. The Denition of Variabless Variable The Denition of Variables x1 TWDS Kolonel H Burlian beside Hotel DE Premium x2 TWDS Naskah x3 TWDS Batujajar x4 TWDS Kolonel H Burlian beside Lorong Dharma Agung x5 TWDS Kolonel H Burlian Simpang SMPN 40 Palembang x6 TWDS Kolonel H Burlian behind Mitra Bangunan Bus Stop x7 TWDS Kolonel H Burlian beside Indomaret Bus Stop x8 TWDS Kolonel H Burlian in front of Bank BRI x9 TWDS Letjen Harun Sohar in front of Hajj Dormitory x10 TWDS Letjen Harun Sohar in front of Al-Hikmah Mosque x11 TWDS Letjen Harun Sohar in front of Talang Kedondong x12 TWDS Letjen Harun Sohar in front of Honda Dealer x13 TWDS Letjen Harun Sohar Auto 2000 TAA x14 TWDS Bambu Kuning Arah Rumah Sakit Pelabuhan x15 TWDS Talang Jambe next to Public Cemetery y1 Talang Jambe Village y2 Kebun Bunga Village y3 Sukarami Village y4 Suka Bangun Village y5 Suka Jaya Village y6 Sukodadi Village y7 Talang Betutu Village Table 4 states the optimal solution of the model using LINGO 18.0 software. In the solver status section, the model class is PILP(Pure IntegerLinearProgramming), which means the model is solved in PILP form. State means the resulting solution is globally optimal. The infeasibility of the model is 0. Iterations in the model are 0, meaning that the solution value has been obtained without iteration in programming. The ex- tended solver status section shows that the method used in this case is the branch and bound. The objective value is 10, which means that the optimal number of locations in the model is ten facility locations. Generated memory used (GMU) is 22K, meaning the total memory allocation used is 22K. Elapsed runtime (ER) shows the total time to complete the model on LINGO 18.0, 2 seconds. The optimal variable values of the SCLP model are attached in Table 5. Variables with 0 value mean that there are no facilities placed at the location, and variables with one value mean that there are facilities placed at the location. In Table 5, it can be seen that there are ten variables with one value, namely the variables x1, x3, x4, x6, x8, x10, x11, x13, x14, x15 which means that the candidate locations should be in 10 TWDS locations, as shown in Table 6. The distance between TWDS and villages in the Sukarami sub-district can be seen in Table 7. d11 shows that the distance between Jambe village and TWDS Kolonel H Burlian beside HotelDEPremiumis7,400meters, d13 showsthat thedistance between Jambe village and TWDS Batujajar is 5,800 meters, and so on. Based on the data in Table 7, the 𝜌-median problem model is Minimize © 2022 The Authors. Page 472 of 480 Octarina et. al. Science and Technology Indonesia, 7 (2022) 469-480 Table 3. The Distance between Each TWDS i\ j di j 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 0 610 2090 750 940 1330 2205 2330 3280 3360 4230 5010 5290 6490 7170 2 610 0 1480 380 570 960 1980 1960 2910 2990 3860 4640 4920 6120 6800 3 2090 1480 0 1850 2040 2430 3200 3430 4380 4460 5330 6110 6390 7590 8270 4 750 380 1850 0 190 580 1600 1580 2530 2610 3480 4260 4540 5740 6420 5 940 570 2040 190 0 390 1410 1390 2340 2420 3290 4070 4350 5550 6230 6 1330 960 2430 580 390 0 1020 1000 1950 2030 2900 3680 3960 5160 5840 7 2205 1980 3200 1600 1410 1020 0 200 1070 1150 2020 2800 3030 4230 4910 8 2330 1960 3430 1580 1390 1000 200 0 950 1030 1900 2680 2960 4160 4840 9 3280 2910 4380 2530 2340 1950 1070 950 0 80 950 1730 2010 3210 3890 10 3360 2990 4460 2610 2420 2030 1150 1030 80 0 870 1650 1930 3130 3810 11 4230 3860 5330 3480 3290 2900 2020 1900 950 870 0 780 1060 2260 2940 12 5010 4640 6110 4260 4070 3680 2800 2680 1730 1650 780 0 280 1480 2160 13 5290 4920 6390 4540 4350 3960 3030 2960 2010 1930 1060 280 0 1200 1880 14 6490 6120 7590 5740 5550 5160 4230 4160 3210 3130 2260 1480 1200 0 1230 15 7170 6800 8270 6420 6230 5840 4910 4840 3890 3810 2940 2160 1880 1230 0 Table 4. Optimal Solution of SCLP Model Solver Status Model Class PILP State Global Optimal Objective 10 Infeasibility 0 Iterations 0 Extended Solver Status Solver Type Branch and Bound Best Objective 10 Objective Bound 10 Steps 0 Active 0 Update Interval 2 GMU (K) 22 ER (sec) 2 Table 5. Variable Value of SCLP Model Variable Value Variable Value Variable Value x1 1 x6 1 x11 1 x2 0 x7 0 x12 0 x3 1 x8 1 x13 1 x4 1 x9 0 x14 1 x5 0 x10 1 x15 1 Table 6. TWDS Candidate Locations Variable Name of TWDS x1 TWDS Kolonel H Burlian beside Hotel DE Premium x3 TWDS Batujajar x4 TWDS Kolonel H Burlian beside Lorong Dharma Agung x6 TWDS Kolonel H Burlian behind Mitra Bangunan Bus Stop x8 TWDS Kolonel H Burlian in front of Bank BRI x10 TWDS Kolonel H Burlian in front of Bank BRI x11 TWDS Letjen Harun Sohar in front of Talang Kedondong x13 TWDS Letjen Harun Sohar in front of Auto 2000 TAA x14 TWDS Bambu Kuning Arah Rumah Sakit Pelabuhan x15 TWDS Talang Jambe next to Pub- lic Cemetery © 2022 The Authors. Page 473 of 480 Octarina et. al. Science and Technology Indonesia, 7 (2022) 469-480 Table 7. The Distance between TWDS and Villages i\j di j 1 3 4 6 8 10 11 13 14 15 1 7400 5800 5900 6500 5500 4200 3600 3100 1900 1320 2 3200 2400 2410 2000 1000 4200 1510 1900 3300 3680 3 1700 1900 900 500 950 2300 3050 3800 5200 5580 4 1800 2800 2400 2900 4000 5300 6150 5400 6800 7280 5 1100 1600 1500 1900 3000 4300 4750 4100 5500 5820 6 5600 6000 4900 4400 3400 3800 4050 4900 6300 6780 7 10000 8400 9500 9100 8000 6700 6050 5800 4900 3980 ZP−Median =7400y11 + 5800y13 + 5900y14 + 6500y16+ 5500y18 + 4200y110 + 3600y111 + 3100y113+ 1900y114 + 1320y115 + 3200y21 + 2400y23+ 2410y24 + 2000y26 + 1000y28 + 900y210+ 1510y211 + 1900y213 + 3300y214 + 3680y215+ 1700y31 + 1900y33 + 900y34 + 500y36 + 950y38+ 2300y310 + 3050y311 + 3800y313 + 5200y314+ 5580y315 + 1800y41 + 2800y43 + 2400y44+ 2900y46 + 4000y48 + 5300y410 + 6150y411+ 5400y413 + 6800y414 + 7280y415 + 1100y51+ 1600y53 + 1500y54 + 1900y56 + 3000y58+ 4300y510 + 4750y511 + 4100y513 + 5500y514 + 5820y515 + 5600y61 + 6000y63 + 4900y64+ 4400y66 + 3400y68 + 3800y610 + 4050y611+ 4900y613 + 6300y614 + 6780y615 + 10000y71+ 8400y73 + 9500y74 + 9100y76 + 8000y78+ 6700y710 + 6050y711 + 5800y713 + 4900y714+ 3980y715 (24) Subject to y11 + y13 + y14 + y16 + y18 + y110 + y111 + y113+ y114 + y115 = 1 (25) y21 + y23 + y24 + y26 + y28 + y210 + y211 + y213+ y214 + y215 = 1 (26) y31 + y33 + y34 + y36 + y38 + y310 + y311 + y313+ y314 + y315 = 1 (27) y41 + y43 + y44 + y46 + y48 + y410 + y411 + y413+ y414 + y415 = 1 (28) y51 + y53 + y54 + y56 + y58 + y510 + y511 + y513+ y514 + y515 = 1 (29) y61 + y63 + y64 + y66 + y68 + y610 + y611 + y613+ y614 + y615 = 1 (30) y71 + y73 + y74 + y76 + y78 + y710 + y711 + y713+ y714 + y715 = 1 (31) x1 + x3 + x4 + x6 + x8 + x10 + x11 + x13 + x14+ x15 = 10 (32) y11, y21, y31, y41, y51, y61, y71 ≤ x1 (33) y13, y23, y33, y43, y53, y63, y73 ≤ x3 (34) y14, y24, y34, y44, y54, y64, y74 ≤ x4 (35) y16, y26, y36, y46, y56, y66, y76 ≤ x6 (36) y18, y28, y38, y48, y58, y68, y78 ≤ x8 (37) y110, y210, y310, y410, y510, y610, y710 ≤ x10 (38) y111, y211, y311, y411, y511, y611, y711 ≤ x11 (39) y113, y213, y313, y413, y513, y613, y713 ≤ x13 (40) y114, y214, y314, y414, y514, y614, y714 ≤ x14 (41) y115, y215, y315, y415, y515, y615, y715 ≤ x15 (42) y11, y21, y31, y41, y51, y61, y71, y13, y23, y33 y43, y53, y63, y73, y14, y24, y34, y44, y54, y64, y74, y16, y26, y36, y46, y56, y66, y76, y18, y28, y38, y48, y58, y68, y78, y110, y210, y310, y410, y510, y610, y710, y111, y211, y311, y411, y511, y611, y711, y113, y213, y313, y413, y513, y613, y713, y114, y214, y314, y414, y514, y614, y714, y115, y215, y315, y415, y515, y615, y715𝜖 {0,1} (43) x1, x3, x4, x6, x8, x10, x11, x13, x14, x15𝜖 {0.1} (44) Model 24 minimizes the distance between the village and TWDS, Constraints 25 - 31 are the limitation of demand points ineachvillage, andConstraint32states that thenumbers of facility locations are 10 locations. Constraints 33 to 42 are limitations for location requests. Constraints 43 ensure that the variable limitation for village and TWDS are non-negative and integer. The solution of the model obtained using the LINGO 18.0 software is attached in Table 8. Table 8 in the extended solver status section shows the method used in this case is the Branch and Bound method. The objective value obtained is 13000. GMU is 53K, which means the amount of memory allocation used is 53K. ER shows the total time used to complete the model on LINGO 18.0, 2 seconds. The optimal solutions are y115=y210=y36= y41= y51=y68=y715=1 which mean 1. The demand in Talang Jambe village (y1) is located at © 2022 The Authors. Page 474 of 480 Octarina et. al. Science and Technology Indonesia, 7 (2022) 469-480 Table 8. Optimal Solutions of 𝜌-Median Problem Model Solver Status Model Class PILP State Global Optimal Objective 13000 Infeasibility 0 Iterations 0 Extended Solver Status Solver Type Branch and Bound Best Objective 13000 Objective Bound 13000 Steps 0 Active 0 Update Interval 2 GMU (K) 53 ER (sec) 2 TWDS Talang Jambe next to Public Cemetery (x15) 2. The demand in Kebun Bunga village (y2) is located at TWDS Letjen Harun Sohar infront of Al-Hikmah Mosque (x10) 3. The demand in Sukarami villag (y3) is located at TWDS Kolonel H Burlian behind Mitra Bangunan bus stop (x6) 4. The demand in Suka Bangun village (y4) is located at TWDS Kolonel H Burlian beside Hotel DE Premium (x1) 5. The demand in Suka Jaya villagex (y5) is located at TWDS Kolonel H Burlian beside Hotel DE Premium (x1) 6. ThedemandinSukodadivillage (y6) is locatedatTWDS Kolonel H Burlian in front of Bank BRI (x8) 7. The demand in Talang Betutu village (y7) is located at TWDS Talang Jambe next to Public Cemetery (x15) The TWDS obtained from the 𝜌-median problem model is solved by GRA in the next stage. The steps of GRA are as follows: Step 1: D =  7400 5800 5900 6500 5500 4200 3600 3100 1900 1320 3200 2400 2410 2000 1000 900 1510 1900 3300 3680 1700 1900 900 500 950 2300 3050 3800 5200 5580 1800 2800 2400 2900 4000 5300 6150 5400 6800 7280 1100 1600 1500 1900 3000 4300 4750 4100 5500 5820 5600 6000 4900 4400 3400 3800 4050 4900 66300 6780 10000 8400 9500 8000 6700 6050 5800 4900 3980  Determine the distance matrix D between villages and TWDS in the Sukarami sub-district. Step 2 : Compare matrix columns to get the dominating column by comparing each entry in the matrix column. Column 1 7400 3200 1700 1800 1100 5600 10000  Column 3 5800 2400 1900 2800 1600 6000 8400  Compare the matrix column 1 with the matrix column 3. The matrix column 1 is the column with the dominant value because column 1 has more dominant values than column 3. Column 3 5800 2400 1900 2800 1600 6000 8400  Column 4 5900 2410 900 2400 1500 4900 8500  Compare the matrix column 3 with the matrix column 4. The matrix column 4 is the column with the dominant value because column 4 has more dominant values than column 3. The column comparison continues until the comparison of columns 1 and 15. Based on the results of the column comparison, it is found that columns 8, 10, and 11 are more dominant than other columns. Thus, columns 8, 10, and 11 are solutions for the 𝜌-median model. Step 3: Compare each column entry with the dominating result column, nd, and add the smallest dominant value. Comparison with column 8 Column 1 and 8 7400 3200 1700 1800 1100 5600 10000   5500 1000 950 4000 3000 3400 8000  −→ We add the smallest dominant value from each row of column 1 and 8, so 5500+1000+950+1800+1100+3400+ 8000=21750 Column 3 and 8 5800 2400 1900 2800 1600 6000 8400   5500 1000 950 4000 3000 3400 8000  −→ We add the smallest dominant value from each row of column 3 and 8, so 5500+1000+950+2800 +1600+3400+ 8000= 23250 Thecomparisoncontinuesuntil thecomparisonofcolumns 15 and 8. The dominant results from comparing each column with matrix column 8 are attached in Table 9. © 2022 The Authors. Page 475 of 480 Octarina et. al. Science and Technology Indonesia, 7 (2022) 469-480 Table 9. The Dominant Results from Comparing Each Column with Matrix Column 8 Column 1 3 4 6 10 11 13 14 15 8 21,750 23,250 22,700 23,200 23,150 22,510 21,250 19,150 17,650 Based on Table 9, the minimum value of the comparison between columns 8 and 1 is 21,750. The minimum value of the comparison between columns 8 and 3 is 23,250 and continues until the minimum value of columns 8 and 15. The least value is in column 15, as the solution of facility location (8,15). Comparison with column 10 Column 1 and 10 7400 3200 1700 1800 1100 5600 10000   4200 900 230 5300 4300 3800 6700  −→ We add the smallest dominant value from each row of column 1 and 10, so 4200+900+1700+1800 +1100+3800 +6700=20200 Column 3 and 10 5800 2400 1900 2800 1600 6000 2400   4200 900 2300 5300 4300 3800 6700  −→ We add the smallest dominant value from each row of column 3 and 10, so 4200+900+1900+2800+1600+ +3800+6700=21900 Thecomparisoncontinuesuntil thecomparisonofcolumns 15 and 10. The dominant results from comparingeach column with matrix column 10 are attached in Table 10. Based on Table 10, the minimum value of the comparison between columns 10 and 1 is 20,200. The minimum value of the comparison between columns 10 and 3 is 21,900 and continues until the minimum value of columns 10 and 15. The least value is in column 1, as the solution of facility location (10,1). Step 4 : Compare the selected dominant column pair with each column and nd the optimum value. For pairs of columns (8,15) with columns 1,3,4,6,10,11,13,14 Column (8,15) with column 1  5500 1000 950 4000 3000 3400 8000   1320 3680 5580 7280 5820 6780 3980   7400 3200 1700 1800 1100 5600 10000  −→ We add the smallest dominant value from each row of column 8,15, and 1, so 1320+ 1000+950+1800 +1100 +3400+3980= 13550 Column (8,15) with column 3  5500 1000 950 4000 3000 3400 8000   1320 3680 5580 7280 5820 6780 3980   5800 2400 1900 2800 1600 6000 8400  −→ We add the smallest dominant value from each row of column 8,15, and 3, so 1320+1000 +950+2800 +1600+3400 +3980= 15050 Thecomparisoncontinuesuntil thecomparisonofcolumns (8,15) and 14. The dominant results from comparing each column with matrix column (8,15) are attached in Table 11. Figure 1. The Strategic TWDS in Sukarami Sub-District Based on Table 11, the minimum value of the comparison between columns (8,15) and 1 is 13,550. The minimum value of the comparison between columns (8,15) and 3 is 15,050 and continues until the minimum value of columns (8,15) and 14. The least value is in column 1, as the solution of facility location (8,15,1). For pairs of columns (8,15,1) with columns 3,4,6,10,11,13, © 2022 The Authors. Page 476 of 480 Octarina et. al. Science and Technology Indonesia, 7 (2022) 469-480 Table 10. The Dominant Results from Comparing Each Column with Matrix Column 10 Column 1 3 4 6 8 11 13 14 15 10 20,200 21,900 20,400 20,900 23,150 26,250 25,300 23,400 21,900 Table 11. The Dominant Results from Comparing Each Column with Matrix Column (8,15) Column 1 3 4 6 10 11 13 14 (8,15) 3,550 15,050 14,500 15,000 17,550 17,650 17,650 17,650 14 Column (8,15,1) with column 3  5500 1000 950 4000 3000 3400 8000   1320 3680 5580 7280 5820 6780 3980   7400 3200 1700 1800 1100 5600 10000   5800 2400 1900 2800 1600 6000 8400  −→ We add the smallest dominant value from each row of column 8,15, 1 and 3, so 1320+1000+ 950+1800 +1100+3400 +3980= 13550 Column (8,15,1) with column 4  5500 1000 950 4000 3000 3400 8000   1320 3680 5580 7280 5820 6780 3980   7400 3200 1700 1800 1100 5600 10000   5900 2410 900 2400 1500 4900 9500  −→ We add the smallest dominant value from each row of column 8,15, 1 and 4, so 1320+1000+900+1800+ 1100+3400+3980= 13550 Thecomparisoncontinuesuntil thecomparisonofcolumns (8,15,1) and 14. The dominant results from comparing each column with matrix column (8,15,1) are attached in Table 12. Based on Table 12, the minimum value of the comparison between columns (8,15,1) and 3 is 13,550. The minimum value of the comparison between columns (8,15,1) and 4 is 13,550 and continues until the minimum value of columns (8,15,1) and 14. The least value is in column 6 which is 13,100. For pairs of columns (10,1) with columns 3,4,6,8,11,13,14, 15 Column (10,1) with column 3  4200 900 2300 5300 4300 3800 6700   7400 3200 1700 1800 1100 5600 10000   5800 2400 2400 1900 2800 1600 6000  −→ We add the smallest dominant value from each row of column 8,1, and 3, so 14200 +900+1700+1800 +1100+3800+6700 = 20200 Column (10,1) with column 4  4200 900 2300 5300 4300 3800 6700   7400 3200 1700 1800 1100 5600 10000   5900 2410 900 2400 1500 4900 9500  −→ We add the smallest dominant value from each row of column 8,1, and 4, so 4200+ 900+9001800+1100+ 3800+6700= 19400 Thecomparisoncontinuesuntil thecomparisonofcolumns (10,1) and 15. The dominant results from comparing each column with matrix column (10,1) are attached in Table 13. Based on Table 13, the minimum value of the comparison between columns (10,1) and 3 is 20,200. The minimum value of the comparison between columns (10,1) and 4 is 19,400 and continues until the minimum value of columns (10,1) and 15. The least value is in column 15 which is 14,600. Step 5 : Analyze the results of each step. Based on steps 1 to 4, it is found that the completion of the rst pair of columns is 8,15,1,6 and the second pair of columns is 10,1,15 with the following explanation: 1. 8 is matrix column 8, which shows TWDS Kolonel H Burlian in front of Bank BRI. 2. 15 is matrix column 15, which shows TWDS Talang Jambe next to Public Cemetery. 3. 1 is matrix column 1, which shows TWDS Kolonel H Burlian beside Hotel DE Premium. 4. 6 is matrix column 6, which shows TWDS Kolonel H Burlian behind Mitra Bangunan Bus Stop. 5. 10 is matrix column 10, which shows TWDS Letjen Harun Sohar in front of Al-Hikmah Mosque. 6. 1 is matrix column 1, which shows TWDS Kolonel H Burlian beside Hotel DE Premium. 7. 15 is matrix column 15, which shows TWDS Letjen Harun Sohar in front of Auto 2000 TAA. The solution of the 𝜌-median problem model that GRA solved is shown in Table 14. Based on Table 14, the demand in Talang Jambe village will be located at TWDS Kolonel H Burlian in front of Bank BRI. The demand in Kebun Bunga village will be located at TWDS Talang Jambe next to Public Cemetery, and so on. The comparisons of 𝜌-median calculation results using LINGO 18.0 software and GRA are shown in Table 15. Based on the comparison of the calculation results from © 2022 The Authors. Page 477 of 480 Octarina et. al. Science and Technology Indonesia, 7 (2022) 469-480 Table 12. The Dominant Results from Comparing Each Column with Matrix Column (8,15,1) Column 3 4 6 10 11 13 14 (8,15,1) 13,550 13,550 13,100 13,450 13,550 13,550 13,550 Table 13. The Dominant Results from Comparing Each Column with Matrix Column (10,1) Column 3 4 6 8 11 13 14 15 (10,1) 20,200 19,400 19,000 19,050 18,950 18,200 16,100 14,600 Table14. The Solution of The 𝜌-Median Problem Model Using GRA No Village Solution of GRA 1 Talang Jambe TWDS Kolonel H Burlian in front of Bank BRI 2 Kebun Bunga TWDS Talang Jambe next to Public Cemetery 3 Sukarami TWDS Kolonel H Burlian beside Hotel DE Premium 4 Suka Bangun TWDS Kolonel H Burlian behind Mitra Bangunan Bus Stop 5 Suka Jaya TWDS Letjen Harun Sohar infront of Al- Hikmah Mosque 6 Sukodadi TWDS Kolonel H Burlian beside Hotel DE Premium 7 Talang Betutu TWDS Letjen Harun Sohar in front of Auto 2000 TAA Table 15. The Comparisons of 𝜌-Median Solution Using LINGO 18.0 software and GRA No Demand Recommended TWDS Locations LINGO 18.0 GRA 1 Talang Jambe Village TWDS Talang Jambe next to Public Cemetery TWDS Kolonel H Burlian in front of Bank BRI 2 Kebun Bunga Village TWDS Letjen Harun Sohar in front of Al- Hikmah Mosque TWDS Talang Jambe next to Public Cemetery 3 Sukarami Village TWDS Kolonel H Burlian behind Mitra Bangunan Bus Stop TWDS Kolonel H Burlian beside Hotel DE Pre- mium 4 Suka Bangun Village TWDS Kolonel H Burlian beside Hotel DE Pre- mium TWDS Kolonel H Burlian behind Mitra Bangunan Bus Stop 5 Suka Jaya Village TWDS Kolonel H Burlian beside Hotel DE Pre- mium TWDS Letjen Harun Sohar in front of Al- Hikmah Mosque 6 Sukodadi Village TWDS Kolonel H Burlian in front of Bank BRI TWDS Kolonel H Burlian beside Hotel DE Pre- mium 7 Talang Betutu Village TWDS Talang Jambe next to Public Cemetery TWDS Letjen Harun Sohar in front of Auto 2000 TAA © 2022 The Authors. Page 478 of 480 Octarina et. al. Science and Technology Indonesia, 7 (2022) 469-480 Table 15 with Table 1, it turns out that there is a discrepancy between the demand in each village and the specied TWDS. According to LINGO solutions, the appropriate TWDS for Talang Jambe Village should be placed at TWDS Talang Jambe next to Public Cemetery. Whereas, based on the GRA, the appropriate TWDS is TWDS Kolonel H Burlian in front of Bank BRI. Dierences in solutions also occur in other villages. By analyzing the optimal solution from LINGO 18.0, GRA, and the current locations of TWDS, this research recommends the strategic TWDS as follows. 1. TWDS Talang Jambe next to Public Cemetery will serve the demand in Talang Jambe village. 2. TWDSLetjenHarunSoharinfrontofAl-HikmahMosque will serve the demand in Kebun Bunga and Suka Jaya village. 3. TWDS Kolonel H Burlian beside Hotel DE Premium will serve the demand in Sukarami and Suka Bangun village. 4. We recommend to add some new TWDS in Sukodadi and Talang Betutu village. 4. CONCLUSION From the results and discussion, we only got three strategic TWDSintheSukaramiSub-District. Byanalyzing theoptimal solution from LINGO 18.0, GRA, and the current locations of TWDS, this research recommends TDWS Talang Jambe next to Public Cemetery, TWDS Kolonel H Burlian in front of Bank BRI, TWDS Letjen Harun Sohar in front of Al-Hikmah Mosque, TWDS Letjen Harun SoharAuto 2000 TAA, TWDS Kolonel H Burlian behind Mitra Bangunan Bus Stop, and TWDS Kolonel H Burlian beside Hotel DE Premium. We also recommended adding some new TWDS in Sukodadi and Talang Betutu villages because no TWDS is serving these two villages now. The strategic TWDS can be seen in Figure 1. We can use other heuristic approaches for further research and add additional constraints to improve the model. 5. 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Bulletin of Electrical Engineering and Informatics, 9(5); 2074–2081 © 2022 The Authors. Page 480 of 480 INTRODUCTION EXPERIMENTAL SECTION Methods Set Covering Location Problem (SCLP) -Median Problem Greedy Reduction Algorithm (GRA) RESULT AND DISCUSSION CONCLUSION ACKNOWLEDGMENT