www.ijemr.net ISSN (ONLINE): 2250-0758, ISSN (PRINT): 2394-6962 Volume-7, Issue-6, November-December 2017 International Journal of Engineering and Management Research Page Number: 134-140 Frequency Determination of Bus Rapid Transit (BRT) Applied on Service System of Trans Mataram Metro Bus to Minimize the Operational Cost 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.