Ant Colony Optimization for Relocation Problem in Carsharing

Ant Colony Optimization for Relocation Problem in Carsharing 카쉐어링의 재배치 문제를 위한 개미 집단 최적화 알고리즘 저자 (Authors)

Ganjar Alfian, Umar Farooq, Jongtae Rhee

출처 (Source)

한국경영과학회 학술대회논문집 , 2013.5, 1859-1866 (8 pages)

발행처 (Publisher)

한국경영과학회 Korean Operations Research And Management Society

URL

http://www.dbpia.co.kr/Article/NODE07171241

APA Style

Ganjar Alfian, Umar Farooq, Jongtae Rhee (2013). Ant Colony Optimization for Relocation Problem in Carsharing. 한국경영과학회 학술대회논문집, 1859-1866.

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2013 한국경영과학회/대한산업공학회 춘계공동학술대회 논문집

카쉐어링의 재배치 문제를 위한 개미 집단 최적화 알고리즘

,

,

Ant Colony Optimization for Relocation Problem in Carsharing

Ganjar Alfian, Umar Farooq, Jongtae Rhee Department Industrial and Systems Engineering, Dongguk University {ganjar, umar, jtrhee}@dongguk.edu

Abstract An improved service of carsharing, one-way service enables customers use the vehicles from one station and return to other station. The common issue in one-way carsharing service is that the vehicle stock of each station become imbalance, thus will lead to the less customer satisfaction and less utilization of vehicles. Consequently, the relocation is used by the system to move the appropriate vehicle to high demand station in order to elevate customer satisfaction. This paper will demonstrate the Ant Colony Optimization for relocation in one-way carsharing system based on simulation model. Computational simulation result on commercially operational data of carsharing in South Korea is involved to solve relocation problem in one-way system. The result we have obtained in this study provide a clear insight into the impact of Ant Colony Optimization for relocation problem on utilization of system and high customer satisfaction. Keyword: one-way carsharing, relocation, Ant Colony Optimization.

1. Introduction As reported from previous research, the benefits of carsharing includes reducing in cost savings, reducing the negative impacts of private vehicle ownership and environmental impacts of auto use (e.g., congestion, energy consumption, vehicle emissions, and inefficient land use). The reduction of emission has been reported in North America as the result of the carsharing impact [6]. The carsharing system enables customers to access a carsharing operator website and easily make a car reservation via an internet or by phone. Basically, members subscribe to a carsharing operator which covers the cost of vehicle use, insurance, maintenance, and fuel. The information including travelled distances and rent duration are recorded and charged as a customer

bill [1]. The intelligent transportation system can play an important role in making a carsharing system user friendly, easy to manage, and efficient. Because of this benefit, a carsharing service is regarded as an alternative transportation paradigm that has become increasingly popular in many countries [2]. As can be seen from trip configuration point of view, it is usual to distinguish between one way system and round trip system. The traditional service such as a round-trip only allows users to use a vehicle and return it to the same station only. In the roundtrip service, even thought this service inconvenient for the users, but this type of system is less costly for the operator to implement it. Users are required to make reservation and specify a return time and adhere to it, or face a penalty. The up-to-date

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carsharing systems enable a vehicle to be driven among multiple stations: a one-way service. As opposed from previous, one-way service can provide convenience for customers, but it costly for operator to implement due to the complexity of management. The operator has to find the way in order to meet user demands otherwise loss in potential revenue for the operator and increased frustration for the customers, making carsharing a less attractive mode of transportation. The one-way service face a problem of uneven distribution of vehicles at the existing stations. The stations which are high demand of customer may not have enough vehicles while stations which are popular return points may end up with too many vehicles. The one-way system has challenge to be solved, such as relocation technique in order to meet user demands and increase potential revenue for operator. Since it is difficult to make a schedule of relocation to satisfy number of cars needed in demand station with respect to minimizing transportation cost, thus this paper propose ant colony optimization for solving relocation problem in carsharing. This paper is expected as extended version for relocation techniques which is already proposed such as shortest time, inventory balancing [4] and static relocation [1]. Computational simulation on commercially operational data of carsharing in South Korea are involved such as selecting location of stations, number of vehicles, VHT (Vehicle Hours Travel) and VKT (Vehicle Kilometers Travel) patterns. 2. Background 2.1. Relocation Problem in Carsharing A simulation approach is used for testing the relocation techniques, namely shortest time and inventory balancing, focusing on the problem of managing a team of people for moving the vehicles. Shortest time relocation involves a process to move a vehicle from a neighboring station in the shortest possible time. Inventory balancing relocation is an approach to moving a vehicle to a station with a shortage of cars from another station with an oversupply of cars [4]. Another simulation research proposed a static relocation to move a vehicle immediately after a customer requests the vehicle [1]. The results of the simulation experiment demonstrate that all of the aforementioned techniques have the potential to improve carsharing services in a realistic situation. In general, the simulation implementation will greatly assist a carsharing operator in evaluating their policies before implementing a service in a realistic situation.

The relocation we used in here is based on periodically relocation i.e. for every six hours the relocation is triggered. To implement vehicle relocations, the operator sets vehicle inventory thresholds at each station. This threshold is based on the prediction of customer demand each station. The system will calculate the total of vehicle which exceed the threshold value in some station and total car needed which below the threshold in other station. In addition, the system will prompt the operator (staff) to move a vehicle from high volume to low volume car station. As the impact, to move the vehicle from oversupply car station to shortage car station, the transportation cost must be considered. A new relocation technique using ant system algorithm is proposed in this paper to solve the relocation problem in one-way scheme in order to minimize the transportation cost. A typical network flow in single-stage transportation problem such as number of sources which has specified commodity demand at each of a number of destinations, and the transportation cost between each source-destination pair is known. The problem is to find the optimal distribution plan for shipments from sources to destinations that minimizes the total transportation cost. Since cost is closely associated with distance, an operator might attempt to find the minimum distance traveled by a number of vehicles in order to satisfy its customer demand. In addition, the relocation problem in carsharing is closely related to the single-stage transportation problem above but with little different model. In transportation problem, the commodity is sent from a central location is determined for each vehicle, while in the carsharing relocation consider vehicle itself as commodity with the additional staff in order to drive/move the car from oversupply car station to the shortage car station. The total cost which considered in here is equal to the transportation cost between two stations and the relocation cost of the staff. The relocation problem in carsharing can be considered as an instance of the transportation problem. The formulation of the problem can be seen as follows. ai = Number of vehicle available to be relocated at departure station i (i = 1, 2, . . . , m), = Number of vehicle required at destination station j (j = 1, 2, . . . , n), A = set of routes from departure to destination station, = Unit transportation cost from source i to destination j (i = 1, 2, . . . , m; j = 1, 2, . . . , n).

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The relocation problem in one-way carsharing can be formulated as min-cost-flow problems with one node per departure stations and one node per destination station. Edges correspond to elements of A. The vehicles available to be relocated by departure station are given by ai and the vehicles required at destination station are given by . Since this is a min-cost-flow problem, basic feasible solutions assign integer values to variables. The number of available car and the demand must be equal, thus the total product availability is equal to the total product requirements. = where the decision variables is = Number of vehicles to be relocated from departure station i to destination station j (i = 1, 2, . . . , m; j = 1, 2, . . . , n) The relocation problem in carsharing is trying to find minimal cost of relocation plan, as can be seen as follow. Minimize z =

(

subject to:

)

(− ) = -bj (j = 1, 2, . . . , n), xi j ≥ 0 (i = 1, 2, . . . , m; j = 1, 2, . . . , n) = ai

(i = 1, 2, . . . , m),

(1)

(2) (3)

substance called pheromone. As an ant travels, it deposits a constant amount of pheromone that other ants can follow. Each ant moves in a somewhat random fashion, but when an ant encounters a pheromone trail, it must decide whether to follow it. If it follows the trail, the ant’s own pheromone reinforces the existing trail, and the increase in pheromone increases the probability of the next ant selecting the path. Therefore, the more ants that travel on a path, the more attractive the path becomes for subsequent ants. Additionally, an ant using a short route to a food source will return to the nest sooner and therefore, mark its path twice, before other ants return. This directly influences the selection probability for the next ant leaving the nest. Over time, as more ants are able to complete the shorter route, pheromone accumulates faster on shorter paths and longer paths are less reinforced. In transportation problem, the research about Ant Colony Optimization has been applied [3,7]. The algorithm successfully finds the optimal distribution plan for shipments from sources to destinations that minimizes the total transportation cost. In addition, based on Ant Colony Optimization developed by previous researches above, we customized it for relocation problem in carsharing. Finding the minimum distance of number vehicle in departure station i that must satisfy requirement of destination station j is the main similarity previous research problems and ours. As initial implementation, the following parameters are set up before the algorithm starts:

Expression (1) represents the minimization of the total distribution cost, assuming a linear cost structure for relocation. Equation (2) states that the amount of car being relocated from departure station i to all possible destinations should be equal to the total availability, ai , at that departure station. Equation (3) indicates that the amounts of car being relocated to destination station j from all possible departure station should be equal to the requirements, , at that destination station.

number of ants; number of iterations; parameter controlling the magnitude of τ (the parameter for an ant to represent the pheromone intensity from the ith edge to the jth edge in the next stage); parameter controlling the magnitude of η (the profitability of selecting jth edge from the next stage by the ith edge in the current stage);

N IT α

β

ρ Q τ

3. Methodology

(t=0)

=∑

evaporation rate; parameter controlling the pheromone increment amount (constant); initial amount of pheromone in each edge in the graph, where a is total departure and b is total destination station.

Table 1. parameter for ACO

3.1. Ant Colony Optimization for Relocation ACO is based on the behavior of real ants and possesses enhanced abilities such as memory of past actions and knowledge about the distance to other locations. In nature, an individual ant is unable to communicate or effectively hunt for food, but as a group, ants possess the ability to solve complex problems and successfully find and collect food for their colony. Ants communicate using a chemical

These parameters are tuned parameters obtained from experimental results. In this paper finding the optimum combination of parameters is considered. At each construction step the probability ant k at time t, currently in departure station i, chooses to be allocated to destination station j is defined as follow.

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P (t) = ∑

τ ( )α η ( )β

!∈#$ ( ) τ !

( )α η ! ( )β

if j ∈ J (i) otherwise 0 (4)

where the heuristic function ) is

*+

destination. If any element in the matrix is zero, it shows that there is no allocation (there is no relocation need).

means trying

to find the shortest relocation time (transportation cost) from stations i to j while the , is the pheromone concentration from i to j. -. (/) represents the feasible neighborhood of ant k when being at edge i, i.e. the set of destination station that ant k has not allocated yet. This ACO based relocation system can be considered as the combination of two previous relocation techniques called shortest time (finding the shortest destination) and inventory balancing (moving car from oversupply station to shortage car station)[4].

1 2 F 3 4

Proceeding to the next iteration, the pheromone concentration will be updated according to the quality of the constructed tour solutions (objective function value) and the evaporation rate ρ as shown , (0 + 1) = (1 − 3), (0) + ∆,

.

(5)

In the above equation, represents the additional deposit of pheromone in the iteration t+1 based on the total cost of the allocation done by the all ants through the tour in the iteration t. The term ∆, . is the increased pheromone on the link (i, j) of the allocation done by ant k. For the pheromone increment updating rule, an antweight strategy is given in equation (6). ∆,

.

6

= 5 789 :; global optimum. Update global optimum as local optimum. End each time IT Final feasible distribution-relocation which has global optimum.

The parameter q is random variable while q0 is determined to measure the importance between exploitation versus exploration. Both variable is range between 0-1, in our experiment we set q0=0.5 which indicate the balance between exploitation and

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3.2. Korea Case Study The carsharing pilot project began in the campus area at Dongguk University with faculty members, students and residents near campus as the first trial members since November 2011 until June 2012. In this paper, upgrading service i.e. one way service is proposed to elevate customer satisfaction. Thus the simulation must be developed first in order to minimize the negative impact of the one-way service in South Korea. The discrete-event simulation is used in this paper and the travelling time based on carsharing dataset must be set to obtain good results. More details about input parameters are shown in Table 2. Input Parameters Total operated cars Total Stations

Operation time Service

Relocation or transportation cost (cij) The relocation time (how long the time needed for staff to move the car) in simulation should consider the real traffic velocity in Seoul city at current time. The traffic dataset has been collected from Seoul Metropolitan Police Agency [8], thus the expected relocation time or transportation cost can be collected base on the real situation. Figure 2a shows some part of our real stations in Seoul City. The average of hourly traffic flow around the area can be seen in Figure 2b. In addition, the averages of daily traffic in weekend show less in traffic compare to the weekdays while the average congestion about less than 15km/hour. The real time information above are considered as input thus Table 3 as adjacency matrix of real time transportation cost can be obtained. Station 1 -

1 2 3 4 5

Destination 2 3 10 15 13 -

4 12 13 24 -

5 20 17 17 28 -

Table 3. Example Adjacency Matrix the average of transportation cost (in minutes) at Wednesday 6:00 PM

Values 25 cars 5 station, each station has about 10 parking stalls. 5 parking stalls are occupied by vehicles and the 5 rest are free. 6 days Roundtrip, One way, with reservation and defined returning time.

Table 2. Input parameter for simulation -

-

Departure

exploration. As explained in the algorithm above, at the end of iteration ACO will produce the minimum cost feasible-allocation distribution. This calculation for allocation-distribution is always used by our simulation model for every time the relocation being triggered, it aims to increase the customer satisfaction and reduce the transportation cost.

Travel time distribution Based on the Korea carsharing dataset [5], the travelling time of customers is between 30 minutes and 6 hours while the average of VHT (Vehicle Hours Travel) by customers is between 2-3 hours. The dataset also provides detail about the trip behavior of the carsharing member during the whole day and grouped into three clusters; morning, afternoon and night which majority of trips are made at night. The VKT (Vehicle Kilometers Travel) shows that the majority of trips made by carsharing members are short-distance trips, less than 100 km and average between 20-30 km. In addition, the dataset shows that the major peak occurs on the weekends, which mean customers prefer travelling during the weekend, starting from Friday night until Sunday midnight. A trip generator has been developed to transform the distribution into artificial reservation data. The trip generator randomly generate the round trip and one way service. The reason is Korea carsharing dataset in this study is round trip only, thus information regarding total percentage of one way reservation in real service is not possibly presented.

3.3. Simulation Implementation In this paper, a simulation model is presented in order to evaluate round trip and basic scheme oneway service. The simulation tool is designed to be as realistic as possible for a carsharing reservation system. The reservation acceptance rate and the vehicle utilization rate are presented to evaluate the performance of round trip and one-way system with or without ant colony relocation model. The vehicle utilization rate is very important for a carsharing operator in order to optimize the time operation of cars, which can gain profit, the formula can be seen as follow. Utilization ratio =

LMLNO PQRSTOQ MUQVNLQW

LMLNO PQRSTOQ UMXXSYOZ MUQVNLQW [\LSO T[VVQ\L LS]Q

On the other hand, the reservation acceptance rate is important to customers because it can provide a benchmark to reveal customer satisfaction, the formula can be seen as follow. Acceptance ratio

=

LMLNO NTTQULQW VQXQVPNLSM\

LMLNO VQXQVPNLSM\ ]NWQ [\LSO T[VVQ\L LS]Q

We upgraded our simulation model, not only support for roundtrip but also one way service. This simulation tool will check the event from the calendar sequentially from the earliest event until the last event, and the simulation tool will implement the

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task based on the calendar. For instance, if the CurrentTime is 08.00 and that time is actually the calling time, the simulation tool will check whether there is a vehicle available at that time or not, and if at least one vehicle and destination space are available, the simulation tool will assign a vehicle to the reservation and change the status of that vehicle from "parked" to "booked” for the reservation time. In addition, if the CurrentEvent is at the starting time of a reservation, the simulation tool will change the status of the vehicle from "booked" to "on road". Moreover, if the CurrentEvent is at the ending time, the status of the vehicle on the road is changed to "parked" again. This status also happen for station, if the parking stall in station is parked by car then the

status is “parked” and “booked” if there is reservation made to the station and “free” if there is no car parked at parking stall. The reservation system in this simulation tool is basically the same idea as the common reservation system in carsharing services. The system checks customer reservations sequentially, and if there is a vehicle available at a departure and at least free parking stall at destination station, then the system will assign the vehicle to that reservation otherwise it will be rejected (see Figure. 3). The simulation tool is used for all 24 hours in 6 days for roundtrip and one way service. The simulation will show the average vehicle utilization rate and reservation acceptance rate for every step number of hours in 6 days.

Figure 2a. Location of stations

Figure 2b. Average hourly traffic flow

Figure 3. Simulation Model

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Figure 4a. Number of vehicle used

Figure 4b. Number of vehicle relocated

Figure 5a. The utilization rate

Figure 5b. The acceptance rate

4. Result and Discussion 4.1. Number of vehicle relocated per time As can be seen from the simulation result, the implementation of ACO for relocation gave the significant result to the vehicle used (increasing number of vehicle used). First, this situation is affected by the relocation decision itself. The system predict the total car needed to be relocated or total car needed in every station based on the customer demand in each station. By using relocation, the high demand station will get additional car, thus it also will elevate the customer satisfaction. Second, the efficiency ACO relocation in order to minimize cost for transportation will lead to high probability of customer getting certain car. The result in figure 4a present the number of vehicle used versus the time (in hour), the data show that ACO relocation leading in vehicle used compare to without relocation.

In other hand, the relocation leads to the negative impact, the additional cost for relocation. Operator has to pay the staff in order to move/drive the car from oversupply car to the shortage car station. As increasing vehicle relocated it will also lead to the high cost for operator. In figure 4b show the total number of vehicle needed to be relocated versus the time (in hour). To sum up, even though the relocation lead to the high vehicle used but it will create additional cost for relocation. In this paper, six hourly relocation period is considered carefully in order to reduce relocation cost. This status of car should be free car; it means there is no reservation made to the car in the future.

4.2. Utilization ratio and Acceptance Ratio As previously explained, the ant colony optimization for relocation show significant result in vehicle used thus it leads to high utilization ratio of

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vehicle. Since operator needs to maximize vehicle operated, this situation give the advantage or profit for operator. Figure 5a show that ACO for relocation lead to the high utilization ratio compare to without relocation scheme. In addition, the application of ant colony optimization for relocation leads to the high acceptance rate as well. This result affected by the effectiveness of relocation which minimize the transportation cost thus it enable the high chance of customer to get available vehicle. The detail comparison of acceptance ratio with and without relocation can be seen in figure 5b. To sum up, the application of ACO based relocation will lead to high customer satisfaction, operator profit but also lead to additional cost for relocation. 5. Conclusion In this paper, the ant colony optimization for relocation is presented in order to solve relocation problem in one way carsharing service. The result show that ACO give the significant result by finding the optimal distribution plan of relocation from oversupply car station to the shortage car station thus it lead to minimum cost for transportation. The commercial carsharing dataset of Korea Carsharing such as: VHT, VKT, Time of day and Day of week are tested while the traffic dataset of Seoul city also used to increase the result of simulation. The discrete event simulation is developed and run to analyze the acceptance rate and the utilization rate based on the dataset distribution in 6 days. Based on the simulation data result, the ACO for relocation give the significant result by increasing both acceptance and utilization rate. Later, the ACO relocation can be considered by operator in order to optimize the profit and customer satisfaction. Lastly, limitations were evident in this paper. First, there are no relocation constraints (i.e., number of relocation staff is set to ∞). Later, the additional predictive relocation for predicting total car needed to be relocated can be considered in this simulation for future work. Also, the comparison with existing relocation should be presented in the future.

6. References [1] Barth, M., and M. Todd.1999. Simulation model Performance Analysis of a Multiple Station Shared Vehicle System. Transportation Research Part C: Emerging Technologies7(4): 237-259. [2] Barth, M., J. Han, and M. Todd. 2001. Performance Evaluation of a Multi-Station Shared Vehicle System. Proceedings of the 4th IEEE International Conference on Intelligent Transportation Systems,1218–1223, Oakland (CA), USA. [3] Chan, F.T.S. and N.Kumar. 2009. Effective allocation of customers to distribution centres: a multiple ant colony optimization approach. Robotics and Computer Integrated Manufacturing 25(1):1-12. [4] Kek, A.G.H., R.L.Cheu, and M.L. Chor. 2006. Relocation Simulation Model for MultipleStation Shared-Use Vehicle Systems. Transportation Research Record: Journal of the Transportation Research Board 1986: 81–88. [5]

Wesharecar. 2013. Korean Carsharing Reservation System. http://www.wesharecar.co.kr. Accessed March 26, 2013.

[6] Martin, E., and S. Shaheen. 2011. Greenhouse Gas Emission Impacts of Carsharing in North America. IEEE Transactions on Intelligent Transportation Systems 12(4): 1074-1086. [7] Panicker, V.V., R. Vanga and R. Sridharan. 2013. Ant Colony optimization algorithm for distribution-allocation problem in a two-stage supply chain with fixed transportation charge. International Journal of Production Research 51(3):698-717. [8] Seoul Metropolitan Police. 2013. Traffic Information Center. http://www.spatic.go.kr/wwwen/main.dev. Accessed March 26, 2013. [9] Socha, K and M. Dorigo. 2008. Ant colony optimization for continuous domains. European Journal of Operational Research 185(3):11551173.

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