Frequency Determination of Bus Rapid Transit (BRT) Applied on Service System of Trans Mataram Metro Bus to Minimize the Operational Cost

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1 Volume-7, Issue-6, November-December 2017 International Journal of Engineering and Management Research Page Number: Frequency Determination of Bus Rapid Transit (BRT) Applied on Service System of Trans Mataram Metro Bus to Minimize the Operational Cost H. Mayyani 1, B.P. Silalahi 2, A. Aman 3 1,2,3 Department of Mathematics, Bogor Agricultural University, INDONESIA ABSTRACT The public transportation service in Mataram City is currently in a fairly apprehensive condition. People prefer to use private vehicles like as motorcycles or private cars. To overcome this, the government provides a public transportation, that are more efficient, safe, convenient and affordable, by public purchasing power i.e. Bus Rapid Transit (BRT). A good BRT operation can provide a high level of mobility with minimum operational costs. One way to minimize operational costs is optimizing the operating bus frequency. The optimal bus frequency is obtained when all the passanger demands have been covered. Therefore, this study aims to create a mathematical model to determine the BRT frequency, to test this model with several test scenarios, and to apply this model on service system of Trans Mataram Metro bus. The mathematical model of bus frequency determination is formed into mixed integer linear programming (MILP). Five test scenarios were used to test the model by providing demand in different road segments. The result showed that the movement of the bus could cover all the demand in each segment of the road. The application of the model of the service system of the Trans Mataram Metro bus resulted a total vehicle operational cost of Rp with the lowest bus frequency on corridor 1, that is 36 times, while the highest frequency on corridor 5, that is 7492 times. Keywords bus frequency, Bus Rapid Transit, minimum operational costs, mixed integer linear programming. I. INTRODUCTION The public transportation service in Mataram City is currently in a fairly apprehensive condition. Currently there are only 2 public transport routes operating in Mataram City whose service performance has been very much decreased. Referring to the Detail Engineering Design (DED) report of Trans Mataram Metro public transport interconnection, the average load factor of daily city transport operators is less than 46% and tends to be a collapse condition. However, when viewed from the mobile activities within the city today, Mataram as the capital of West Nusa Tenggara province (NTB) shows a high traffic flow than the surrounding area. People prefer to use private vehicles like as motorcycles or private cars because they can easily be owned and operated. This conditions for a large city typically require a reliable public transport service to accommodate the mobility needs of the population that also support the city's economic growth [8]. Responding to the problem, the Ministry of Transportation launched a development program of roadbased public transportation in urban areas. One of the realization of the program is the procurement of Bus Rapid Transit (BRT) for Mataram and surrounding areas. BRT of Mataram is also called Trans Mataram Metro bus. BRT is one type of public transportation mode that is efficient, safe, convenient and affordable by people's purchasing power. The government hopes that BRT can increase the the attractiveness of society to use public transportation so that it can suppress the use of private vehicles. According to [1] a well-planned bus system can provide high mobility to most populations with the minimum operational costs. One way to minimize operational costs is to optimize the determination of the operating bus frequency. The optimal bus frequency is achieved when all the demand of passengers is covered. Optimization problems in terms of minimizing or maximizing costs can be formed into linear functions with constraint functions in the form of linear equalities and/or linear inequalities [7]. Several similar studies have been conducted, among others [9], [5], [2], [3], [4], and [6]. The research generally has the objective function of minimizing costs and also route and frequency bus as its decision variable. This research aims to make mathematical model of BRT frequency determination, to test model with several test scenarios, and to apply the model to Trans Mataram Metro bus service system. 134 Copyright Vandana Publications. All Rights Reserved. II. METHODOLOGY This research was conducted from January to November This research is focused on the formulation of mathematical model of Bus Rapid Transit

2 (BRT) operation that is determining the purpose function, decision and constraints variable that are in accordance with the assumptions specified. The model was further tested in several test scenarios using LINGO 11.0 software. The final step was applying the service system model of the bus trans mataram metro bus using the potential data of public transport in 2017 as its passenger data. III. RESULT Model Formulation The general description of this problem is to determine the optimal bus frequency with demand of all passenger that is fulfilled so the minimum vehicle operational cost was obtained. The formulation of the bus corridor frequency determination problem can be modeled into the form of mixed integer linear programming (MILP). The formulation of the problem is given as follows: Index = terminal; = road segment; Set Parameter = corridor; = terminal pair; = set of terminal pairs defined or defined at the beginning, = the set of corridors passing through the segment of the road segment m, = set of segments of road segments passed through corridor k. = vehicle operational cost in one trip from terminal i to terminal j in corridor. = bus capacity, = level of passenger service, = the number of passengers passing through the road segment, = the adjacency matrix representing the set of the road segment passed in the corridor k = a large number. Decision variabel = Bus travel frequency is used from terminal i to terminal j for corridor, = { = bus travel frequency in corridor k through the segment of road segment m = the number of passengers transported in the corridor k through the road segment m Objective Function The objective function of this problem is to minimize the vehicle operational cost by the multiplication of the vehicle operational cost of each corridor with the decision variable generated by the model that is the bus frequency of each corridor. Mathematically, the objective function of the problem is: with. Constraints ( ) The constraints on this issue are as follows: 1. The total number of passengers transported in each corridor k through the road segment m is equal to the amount of demand passing through the road segment m. 3. The number of passengers transported on the segment of road segment m does not exceed the bus capacity in the corridor passing through the road segment for a certain level of passenger service. 4. The bus frequency from terminal i to terminal j is equal to the frequency of bus returning from terminal j to terminal i for each corridor k. 5. No bus is moving from terminal i to terminal i. 6. If the bus trip does not pass through the corridor k then there is no bus frequency through the corridor. 7. Constraints of nonnegativity { } 2. The bus frequency passing through the road segment m is no more than the bus frequency passing through each corridor k from terminal i to terminal j. 135 Copyright Vandana Publications. All Rights Reserved.

3 Model Test The mathematical model test was performed in several test scenarios. The first example is a simple network with 6 nodes and 8 segments of road segment shown in Figure 1. Figure 1 An example of a road network At each node there was a bus that stop to pick up and discharge passengers. Node 1 was the initial terminal of departure while node 4 was the end terminal of bus stop. There were 6 possible corridors that could be passed from node 1 to node 4, namely corridor 1 which passed through the road segment (1) - (2) - (3), corridor 2 which passed through the road segment (1) - (2) - (7) (8), corridor 4 which passed through the road segment (4) - (5) - (8), the corridor 5 which passed through the road segment 4, - (5) - (7) - (3) and corridor 6 which passed through the road segment (1) - (6) - (7) - (3). There were five scenarios to test the validity of the model. Passenger demand data on road segment and corridor operational costs are presented in Table 1. Table 1 Passenger demand data on road segment and corridor operational costs for each scenario Skenario Skenario Skenario Skenario Skenario In scenario 1, the passengers demand was only found on one road segment passed by two corridors. For example, the road segment 6 was traversed by corridor 3 and corridor 6. In scenario 2, the passengers demand was found on every road segment passed by one corridor. For example, the bus passed through corridor 3, so the passengers demand was given to all segments of road segment passed by corridor 3, i.e. the segment of road segment (1), (6) and (8). In scenario 3, the passangers demand was on each segment of the road segment traversed by two separate corridors. For example, the bus passed through corridor 1 and corridor 4, then the passenger demand would be in all segments of road segments traversed by corridor 1 and corridor 4, namely (1), (2), (3), (4), (5) and (8). In scenario 4, the passengers demand was found on each segment of the road segment passed by two corridors that had 1 road segment. For example, the bus through corridor 1 and corridor 3 had intersection in the road segment (1), then the passenger demand would be in all road segments traversed by 136 Copyright Vandana Publications. All Rights Reserved.

4 corridor 1 and corridor 3, i.e. road segment (1), (2), 3), (6) and (8). In scenario 5, the passengers demand was in the road segment that were intersected by three corridors. For example, three corridors were used, namely 1, 2, and 3 corridor. Corridors 1 and 3 were intersected on road segment (1) while corridors 2 and 3 were intersected on road segment (2). The results of each scenario are presented in Figures 2,3,4,5 and 6. Figure 2 Scenario 1 Figure 3 Scenario 2 Figure 4 Scenario 3 Figure 5 Scenario 4 Figure 6 Scenario 5 In Figure 2, scenario 1 produced the movement of bus from node 1 to node 4 through corridor 3. The number of passengers transported in corridor 3 was 1000 people according to the number of passenger demand on the segment of the road segment (6) with the bus frequency 12 times. We have the vehicle operational cost (VOC) of corridor 3 by Rp100, so the minimum operational cost for round trip buses is Rp24,000. Similarly, in Figure 3, scenario 2 produced the movement of bus passing corridor 3 with the maximum frequency of bus in the corridor, that is 9 times, to obtain operational cost of Rp Scenario 3 on Figure 4 produced bus movement through corridor 1 with 5 times bus frequency and through corridor 4 with 6 times bus frequency. The results were based on the passenger demand in each road segment passed by corridors 1 and 4. Therefore, a minimum operational cost of Rp2 200 was required. On the other hand, scenario 4 in Figure 5 explained that there was a division of the number of passengers transported to the corridor passing through the intersected road segment. Total of 2000 passengers on road segment 1 are transported through corridor 1 as many as 1664 passengers and 336 passengers are transported through corridor 3 with frequency at corridor 1 of 20 times and 4 times in corridor 3. Therefore the minimum operational cost that is resulted is Rp Finally scenario 5 in Figure 6 explained that the bus moves through corridors 1,2, and 3 with an optimal frequency of 36 times through corridors 1, 12 times through corridor 2, and 6 times through corridor passengers were located in road segment 2, 3000 passengers of them were transported through corridor 1 and 1000 of remaining passengers through corridor 2. While 600 passengers on the road segment (8) were transported, 96 passengers of them were transported through corridor 2 and 504 of remaining passengers through corridor 3 so the minimum operational cost was of Rp Model Applications on Service System of Trans Mataram Metro Bus In service system of Trans Mataram Metro Bus, there were 6 terminals, namely Senggigi, Roek Garden, Sayang-Sayang, Mandalika, Narmada, and South Ring. The terminals were connected by 9 corridors that had been made by Transportation Department of NTB Province. Corridor 1 was designed through the main tourism area of Senggigi Beach and ends at Mandalika Terminal. Corridor 2 was designed through trading and service areas that was begun from Mandalika Terminal and ended at Kebon Roek Terminal. Corridor 3 was designed through the south circle road of Mataram City that was begun from Mandalika Terminal and ended at Kebon Roek Terminal. Corridor 4 was designed through the north circle road of Mataram City that was begun from Terminal Mandalika and ended at Kebon Roek Terminal. Corridor 5 was designed through the tourism area of Senggigi, commercial and office areas in Mataram City that ended at Narmada Terminal which is also a tourist area. Corridor 6 was designed through an urban area in Mataram City that will start from Kebon Roek Terminal and end at South Lingkar Terminal (Plan). Corridor 7 was designed through urban areas in Kota Mataram which will start from Kebon Roek Terminal and end at South Lingkar Terminal (Plan-in according to Spatial Plan of Mataram City). Corridor 8 was designed through the middle path of the urban area in Mataram City which will start from South Lingkar Terminal (Plan) and ended at North Lingkar Terminal (Plan). Corridor Copyright Vandana Publications. All Rights Reserved.

5 was designed through the middle path of urban area in Mataram City which started from Kebon Roek Terminal and ended at Terminal Mandalika. The Overall of Trans Mataram Metro bus corridor can be seen in Figure 7. Figure 7 Trans Mataram Metro bus corridor Based on service system of Trans Mataram Metro Bus, Mataram City road network can be described in simpler form in Figure 8. Description of sketch of Mataram road network can be seen in Table 2. Figure 8 Sketch of the Mataram City road network 138 Copyright Vandana Publications. All Rights Reserved.

6 Table 2 Sketch description of the Mataram city road network No. Name of road segment No. Name of road segment No. Name of road segment 1 Raya Senggigi 16 Majapahit 31 Bung Hatta 2 Pariwisata (Gunung Sari) 17 Suprapto 32 Brawijaya - Dr. Wahidin Mambalan 3 Saleh Sungkar 18 Pendidikan 33 Teguh Faisal 4 Adi Sucipto 19 Airlangga 34 Dr. Sujono 5 Adi Sucipto 20 Catur Warga 35 TGH M. Rais - TGH Ali Batu 6 Jendral Sudirman 21 Bung Karno 36 Dr. Sujono 7 Energi 22 Panca Usaha 37 Gajah Mada 8 Langko 23 Salaparang 38 Dr. Sujono 9 Langko 24 Selaparang 39 Bung Karno 10 Langko 25 Sandubaya 40 Dr. Sujono 11 Udayana 26 Sandubaya 41 Dr. Sujono 12 Pejanggik 27 Suprapto 42 Teguh Faisal 13 Imam Bonjol - Ade Irma Suryani 14 Ahmad Yani 29 Airlangga 15 Energi 30 Sriwijaya 28 Majapahit 43 Mapak - Parampuan - Labuapi - Raya Lembar - Raya Kediri Based on the road segments passed by each corridor that had been made by NTB Provincial Transportation Department, the road segment passed by each corridor could be seen in Table 3. Vehicle operational cost (VOC) per seat / km and capacity of this VOC ware Rp and 75 passengers respectively. Therefore, the VOC of each corridor could be obtained by multiplying the VOC per seat / km by the number of capacities per bus and the length of the corridor. The VOC results of each corridor are presented in Table 3. Table 3 segments and VOC per corridor Corridor Terminal Segment Length VOC per (km) corridor (Rp) 1 Senggigi Mandalika Mandalika - Kebun Roek Mandalika - Kebun Roek Mandalika - Kebun Roek Senggigi - Narmada Kebun Roek - Lingkar Selatan Kebun Roek - Lingkar Selatan Sayang-sayang Lingkar Selatan Kebun Roek - Mandalika The demand of passengers on each road segment was calculated based on the survey results of potential users of public transport in Mataram City in The data are presented in Table Copyright Vandana Publications. All Rights Reserved.

7 Segment Tabel 4 passengers every segment of the road Segmen Segment Segment The calculation result using LINGO 11.0 software had been obtained that the total of the minimum operational cost of Trans Mataram Metro bus was Rp The optimal bus frequency of corridor 1 until corridor 9 were 36, 620, 1410, 486, 7492, 1564, 776, 486, and 1284 times respectively. The passing bus frequency in corridor 1 was lowest than other corridors, hence the other corridors could be modified by eliminating corridor 1. That elimination was no problem because a road segment was passed by corridor 1, the another corridors was also passed so the passengers on that road segment could still be covered. IV. CONCLUSION Bus operation problems can be formulated into a mathematical model to determine the frequency of Bus Rapid Transit (BRT) in the form of mixed integer linear programming (MILP). In addition, the optimal bus frequency of each corridor can also be known the number of passengers transported in each road segment by each corridor. In the testing model using 5 test scenarios by providing demand in different road segments, it is found that the bus movement can cover all demands in each road segment. The model application of the service system of Trans Mataram Metro bus generates the minimum total of vehicle operating cost of Rp with the lowest bus frequency through corridor 1 which is 36 times, while the highest bus frequency passes corridor 5 is 7492 times. REFERENCES [1] Advani M and Tiwari G Review of Capacity Improvement Strategies for Bus Transit Service. Indian Jouernal of Transport Management [2] Aman A, Nurisma, Hanum F, and Bakhtiar T Buses Dispatching Problem in Urban Transport System. Far East Journal of Mathematical Science. 96(4): doi: b2015 _393_ 408. [3] Chien S, Yang Z, and Hou E A Genetic Algorithm Approach for Transit Route Planning and Design. ASCE Journal of Transportation Engineering. 127(3): [4] Ekowicaksono I Masalah Penentuan Koridor Bus dalam Meminimumkan Biaya Operasional [skripsi]. Bogor (ID): Institut Pertanian Bogor. [5] Making SRM, Silalahi BP, and Bukhari F Multi Depot Vehicle Routing Problem dengan Pengemudi Sesekali. Jurnal Matematika dan Aplikasinya. 17(1 JULI 2018): [6] Ngamchai S and Lovell DJ Optimal Time Transfer in Bus Transit Route Network Design using a Genetic Algorithm. ASCE Journal of Transportation Engineering. 129(5): [7] Silalahi BP and Dewi MS Comparison of Sensitivity Analysis on Linear Optimization Using Optimal Partition and Optimal Basis (in The Simplex Method) at Some Cases. Indonesian Mathematical Society. (Apir): [8] Sufiani A, Alvinsyah, and Hadian E Potensi dan Kendala Pengembangan Angkutan Umum Masal di Kota Mataram dan Sekitarnya [Internet]. [downloaded on November 27, 2016]. Available on: artikel/potensi-dan- kendala-pengembangan-angkutanumum-masal-di-kota-mataram-dan-sekitarnya.html. [9] Wihartiko FD, Buono A, Silalahi BP Integer Programming Model for Optimizing Bus Timetable Using Genetic Algorithm. IOP Conf. Series: Materials Science and Engineering 166 (2017) doi: / x/166/1/ Copyright Vandana Publications. All Rights Reserved.