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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Volume-7, Issue-6, November-December 2017 International Journal of Engineering and Management Research Page Number: 134-140

H. Mayyani1, B.P. Silalahi2, A. Aman3 1,2,3Department of Mathematics, Bogor Agricultural University, INDONESIA

ABSTRACT high traffic flow than the surrounding area. People prefer The public transportation service in Mataram City to use private vehicles like as motorcycles or private cars is currently in a fairly apprehensive condition. People prefer because they can easily be owned and operated. This to use private vehicles like as motorcycles or private cars. To conditions for a large city typically require a reliable overcome this, the government provides a public public transport service to accommodate the mobility transportation, that are more efficient, safe, convenient and needs of the population that also support the city's affordable, by public purchasing power i.e. Bus Rapid Transit (BRT). A good BRT operation can provide a high economic growth [8]. level of mobility with minimum operational costs. One way Responding to the problem, the Ministry of to minimize operational costs is optimizing the operating bus Transportation launched a development program of road- frequency. The optimal bus frequency is obtained when all based public transportation in urban areas. One of the the passanger demands have been covered. Therefore, this realization of the program is the procurement of Bus study aims to create a mathematical model to determine the Rapid Transit (BRT) for Mataram and surrounding areas. BRT frequency, to test this model with several test BRT of Mataram is also called Trans Mataram Metro bus. scenarios, and to apply this model on service system of BRT is one type of public transportation mode that is Trans Mataram Metro bus. The mathematical model of bus efficient, safe, convenient and affordable by people's frequency determination is formed into mixed integer linear programming (MILP). Five test scenarios were used to test purchasing power. The government hopes that BRT can the model by providing demand in different road segments. increase the the attractiveness of society to use public The result showed that the movement of the bus could cover transportation so that it can suppress the use of private all the demand in each segment of the road. The application vehicles. of the model of the service system of the Trans Mataram According to [1] a well-planned bus system can Metro bus resulted a total vehicle operational cost of Rp5 provide high mobility to most populations with the 208 880 772 with the lowest bus frequency on corridor 1, minimum operational costs. One way to minimize that is 36 times, while the highest frequency on corridor 5, operational costs is to optimize the determination of the that is 7492 times. operating bus frequency. The optimal bus frequency is

achieved when all the demand of passengers is covered. Keywords— bus frequency, Bus Rapid Transit, minimum Optimization problems in terms of minimizing or operational costs, mixed integer linear programming. 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 I. INTRODUCTION been conducted, among others [9], [5], [2], [3], [4], and [6]. The research generally has the objective function of The public transportation service in Mataram City minimizing costs and also route and frequency bus as its is currently in a fairly apprehensive condition. Currently decision variable. This research aims to make there are only 2 public transport routes operating in mathematical model of BRT frequency determination, to Mataram City whose service performance has been very test model with several test scenarios, and to apply the much decreased. Referring to the Detail Engineering model to Trans Mataram Metro bus service system. Design (DED) report of Trans Mataram Metro public transport interconnection, the average load factor of daily II. METHODOLOGY city transport operators is less than 46% and tends to be a collapse condition. However, when viewed from the This research was conducted from January to mobile activities within the city today, Mataram as the November 2017. This research is focused on the capital of West Nusa Tenggara province (NTB) shows a formulation of mathematical model of Bus Rapid Transit 134 Copyright © 2017. Vandana Publications. All Rights Reserved. www.ijemr.net ISSN (ONLINE): 2250-0758, ISSN (PRINT): 2394-6962

(BRT) operation that is determining the purpose function, = corridor; decision and constraints variable that are in accordance = terminal pair; with the assumptions specified. The model was further Set tested in several test scenarios using LINGO 11.0 = set of terminal pairs defined or software. The final step was applying the service system defined at the beginning, model of the bus trans mataram metro bus using the = the set of corridors passing through the potential data of public transport in 2017 as its passenger segment of the road segment m, data. = set of segments of road segments passed through corridor k. III. RESULT Parameter = vehicle operational cost in one trip Model Formulation from terminal i to terminal j in The general description of this problem is to corridor . determine the optimal bus frequency with demand of all = bus capacity, passenger that is fulfilled so the minimum vehicle = level of passenger service, operational cost was obtained. The formulation of the bus = the number of passengers passing corridor frequency determination problem can be through the road segment , modeled into the form of mixed integer linear = the adjacency matrix representing the programming (MILP). The formulation of the problem is set of the road segment passed in the given as follows: corridor k

= a large number. Index = terminal; = road segment;

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 3. The number of passengers transported on the segment multiplication of the vehicle operational cost of each of road segment m does not exceed the bus capacity in corridor with the decision variable generated by the the corridor passing through the road segment for a model that is the bus frequency of each corridor. certain level of passenger service. Mathematically, the objective function of the problem is: 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. with . 5. No bus is moving from terminal i to terminal i. Constraints

The constraints on this issue are as follows: 6. If the bus trip does not pass through the corridor k 1. The total number of passengers transported in each then there is no bus frequency through the corridor. corridor k through the road segment m is equal to the

amount of demand passing through the road segment m. 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 © 2017. Vandana Publications. All Rights Reserved. www.ijemr.net ISSN (ONLINE): 2250-0758, ISSN (PRINT): 2394-6962

Model Test At each node there was a bus that stop to pick up The mathematical model test was performed in and discharge passengers. Node 1 was the initial terminal several test scenarios. The first example is a simple of departure while node 4 was the end terminal of bus network with 6 nodes and 8 segments of road segment stop. There were 6 possible corridors that could be passed shown in Figure 1. 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 Figure 1 An example of a road network costs are presented in Table 1. Table 1 Passenger demand data on road segment and corridor operational costs for each scenario Corridor operational costs - (IDR) 1 2 3 4 5 6 Skenario 1 300 200 100 400 700 1000 Passenger demand data on road segment (passanger) (1) (2) (3) (4) (5) (6) (7) (8) 0 0 0 0 0 1000 0 0 Corridor operational costs - (IDR) 1 2 3 4 5 6 3000 2000 100 4000 7000 2000 Skenario 2 Passenger demand data on road segment (passanger) (1) (2) (3) (4) (5) (6) (7) (8) 500 0 0 0 0 700 0 200 Corridor operational costs - (IDR) 1 2 3 4 5 6 100 2000 4000 100 7000 2000 Skenario 3 Passenger demand data on road segment (passanger) (1) (2) (3) (4) (5) (6) (7) (8) 200 300 400 100 400 0 0 500 Corridor operational costs - (IDR) 1 2 3 4 5 6 100 2000 100 10000 7000 2000 Skenario 4 Passenger demand data on road segment (passanger) (1) (2) (3) (4) (5) (6) (7) (8) 2000 220 440 0 0 300 0 100 Corridor operational costs - (IDR) 1 2 3 4 5 6 100 100 100 10000 7000 2000 Skenario 5 Passenger demand data on road segment (passanger) (1) (2) (3) (4) (5) (6) (7) (8) 2000 4000 440 0 0 500 1000 600

In scenario 1, the passengers demand was only traversed by two separate corridors. For example, the bus found on one road segment passed by two corridors. For passed through corridor 1 and corridor 4, then the example, the road segment 6 was traversed by corridor 3 passenger demand would be in all segments of road and corridor 6. In scenario 2, the passengers demand was segments traversed by corridor 1 and corridor 4, namely found on every road segment passed by one corridor. For (1), (2), (3), (4), (5) and (8). In scenario 4, the passengers example, the bus passed through corridor 3, so the demand was found on each segment of the road segment passengers demand was given to all segments of road passed by two corridors that had 1 road segment. For segment passed by corridor 3, i.e. the segment of road example, the bus through corridor 1 and corridor 3 had segment (1), (6) and (8). In scenario 3, the passangers intersection in the road segment (1), then the passenger demand was on each segment of the road segment demand would be in all road segments traversed by

136 Copyright © 2017. Vandana Publications. All Rights Reserved. www.ijemr.net ISSN (ONLINE): 2250-0758, ISSN (PRINT): 2394-6962 corridor 1 and corridor 3, i.e. road segment (1), (2), 3), (6) Similarly, in Figure 3, scenario 2 produced the movement and (8). In scenario 5, the passengers demand was in the of bus passing corridor 3 with the maximum frequency of road segment that were intersected by three corridors. For bus in the corridor, that is 9 times, to obtain operational example, three corridors were used, namely 1, 2, and 3 cost of Rp1 800. corridor. Corridors 1 and 3 were intersected on road Scenario 3 on Figure 4 produced bus movement segment (1) while corridors 2 and 3 were intersected on through corridor 1 with 5 times bus frequency and road segment (2). The results of each scenario are through corridor 4 with 6 times bus frequency. The presented in Figures 2,3,4,5 and 6. 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 Figure 2 Scenario 1 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 Rp4 800. 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 3. 4000 passengers were located in road segment 2, 3000 passengers of them were transported through corridor 1 and 1000 of remaining passengers Figure 3 Scenario 2 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 Rp10 800. Model Applications on Service System of Trans Mataram Metro Bus In service system of Trans Mataram Metro Bus, Figure 4 Scenario 3 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 Figure 5 Scenario 4 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 Figure 6 Scenario 5 area in Mataram City that will start from Kebon Roek Terminal and end at South Lingkar Terminal (Plan). In Figure 2, scenario 1 produced the movement Corridor 7 was designed through urban areas in Kota of bus from node 1 to node 4 through corridor 3. The Mataram which will start from Kebon Roek Terminal and number of passengers transported in corridor 3 was 1000 end at South Lingkar Terminal (Plan-in according to people according to the number of passenger demand on Spatial Plan of Mataram City). Corridor 8 was designed the segment of the road segment (6) with the bus through the middle path of the urban area in Mataram frequency 12 times. We have the vehicle operational cost City which will start from South Lingkar Terminal (Plan) (VOC) of corridor 3 by Rp100, so the minimum and ended at North Lingkar Terminal (Plan). Corridor 9 operational cost for round trip buses is Rp24,000. 137 Copyright © 2017. Vandana Publications. All Rights Reserved. www.ijemr.net ISSN (ONLINE): 2250-0758, ISSN (PRINT): 2394-6962 was designed through the middle path of urban area in and ended at Terminal Mandalika. The Overall of Trans Mataram City which started from Kebon Roek Terminal Mataram Metro bus corridor can be seen in Figure 7.

Figure 7 Trans Mataram Metro bus corridor Based on service system of Trans Mataram in simpler form in Figure 8. Description of sketch of Metro Bus, Mataram City road network can be described Mataram road network can be seen in Table 2.

Figure 8 Sketch of the Mataram City road network

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 28 Majapahit 43 Mapak - Parampuan - Suryani Labuapi - Raya Lembar - Raya Kediri 14 Ahmad Yani 29 Airlangga 15 Energi 30 Sriwijaya

Based on the road segments passed by each VOC ware Rp235.36 and 75 passengers respectively. corridor that had been made by NTB Provincial Therefore, the VOC of each corridor could be obtained by Transportation Department, the road segment passed by multiplying the VOC per seat / km by the number of each corridor could be seen in Table 3. Vehicle capacities per bus and the length of the corridor. The operational cost (VOC) per seat / km and capacity of this VOC results of each corridor are presented in Table 3.

Table 3 Road segments and VOC per corridor Length VOC per Corridor Terminal Road Segment (km) corridor (Rp) 1 Senggigi – Mandalika 1-2-14-25 22.039 389 032.40 Mandalika - Kebun 2 4-7-15-34-43-42-33-25 25.183 444 530.30 Roek Mandalika - Kebun 4-7-15-34-36-38-40-41- 3 18.575 327 885.90 Roek 42-33-25 Mandalika - Kebun 4 5-6-14-25 11.028 194 666.30 Roek 1-3-7-8-9-10-12-23-24- 5 Senggigi - Narmada 25-26-25-24-22-20-18- 25.759 454 697.90 27-16-8-7-3-1 Kebun Roek - Lingkar 6 5-11-19-29-37-38-40 12.477 220 244.00 Selatan Kebun Roek - Lingkar 5-11-19-29-28-35-34-36- 7 19.777 349 103.60 Selatan 38-40 Sayang-sayang – 8 13-21-31-39-40 8.53 150 571.60 Lingkar Selatan 4-7-8-9-17-27-28-30-32- Kebun Roek - 9 33-25-33-32-30-28-16-8- 11.789 208 099.40 Mandalika 7-4

The demand of passengers on each road segment users of public transport in Mataram City in 2017. The was calculated based on the survey results of potential data are presented in Table 4.

Tabel 4 Demand passengers every segment of the road Road Road Road Road Demand Demand Demand Demand Segment Segmen Segment Segment 1 28059 12 97105 23 68137 34 66067 2 1402 13 19107 24 68137 35 29334 3 78285 14 16574 25 119609 36 58668 4 130475 15 79915 26 294954 37 35709 5 92963 16 50559 27 26656 38 35709 6 19107 17 24676 28 81060 39 8950 7 208760 18 1980 29 92094 40 35801 8 128844 19 92094 30 24676 41 8950 9 128844 20 1980 31 8950 42 17900 10 97105 21 8287 32 21155 43 24363 11 92094 22 34682 33 39056

The calculation result using LINGO 11.0 8.doi:http://dx.doi.org/10.17654/FJMSFe b2015 _393_ software had been obtained that the total of the minimum 408. operational cost of Trans Mataram Metro bus was Rp5 [3] Chien S, Yang Z, and Hou E. 2001. A Genetic 208 880 772. The optimal bus frequency of corridor 1 Algorithm Approach for Transit Route Planning and until corridor 9 were 36, 620, 1410, 486, 7492, 1564, 776, Design. ASCE Journal of Transportation Engineering. 486, and 1284 times respectively. The passing bus 127(3):200-207. frequency in corridor 1 was lowest than other corridors, [4] Ekowicaksono I. 2012. Masalah Penentuan Koridor hence the other corridors could be modified by Bus dalam Meminimumkan Biaya Operasional [skripsi]. eliminating corridor 1. That elimination was no problem Bogor (ID): Institut Pertanian Bogor. because a road segment was passed by corridor 1, the [5] Making SRM, Silalahi BP, and Bukhari F. 20017. another corridors was also passed so the passengers on Multi Depot Vehicle Routing Problem dengan Pengemudi that road segment could still be covered. Sesekali. Jurnal Matematika dan Aplikasinya. 17(1 JULI 2018):75-86. IV. CONCLUSION [6] Ngamchai S and Lovell DJ. 2003. Optimal Time Transfer in Bus Transit Route Network Design using a Bus operation problems can be formulated into a Genetic Algorithm. ASCE Journal of Transportation mathematical model to determine the frequency of Bus Engineering. 129(5):510-521. Rapid Transit (BRT) in the form of mixed integer linear [7] Silalahi BP and Dewi MS. 2014. Comparison of programming (MILP). In addition, the optimal bus Sensitivity Analysis on Linear Optimization Using frequency of each corridor can also be known the number Optimal Partition and Optimal Basis (in The Simplex of passengers transported in each road segment by each Method) at Some Cases. Indonesian Mathematical corridor. In the testing model using 5 test scenarios by Society. (Apir):82-90. providing demand in different road segments, it is found [8] Sufiani A, Alvinsyah, and Hadian E. 2016. Potensi that the bus movement can cover all demands in each dan Kendala Pengembangan Angkutan Umum Masal di road segment. The model application of the service Kota Mataram dan Sekitarnya [Internet]. [downloaded on system of Trans Mataram Metro bus generates the November 27, 2016]. Available on: http://iutri.org/ minimum total of vehicle operating cost of Rp5 208 880 artikel/potensi-dan- kendala-pengembangan-angkutan- 772 with the lowest bus frequency through corridor 1 umum-masal-di-kota-mataram-dan-sekitarnya.html. which is 36 times, while the highest bus frequency passes [9] Wihartiko FD, Buono A, Silalahi BP. 2017. Integer corridor 5 is 7492 times. Programming Model for Optimizing Bus Timetable Using Genetic Algorithm. IOP Conf. Series: Materials Science and Engineering 166 (2017) 012016.

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