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An object-oriented evaluation framework for dynamic vehicle routing problems under real-time information
Expert Systems with Applications 38 (2011) 12548–12558
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Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
An object-oriented evaluation framework for dynamic vehicle routing problems under real-time information Tsai-Yun Liao a,⇑, Ta-Yin Hu b a b
Graduate Institute of Marketing and Logistics/Transportation, National Chiayi University, No. 580, Sinmin Rd, Chiayi City 60054, Taiwan, ROC Department of Transportation and Communication Management Science, National Cheng Kung University, Taiwan, ROC
a r t i c l e
i n f o
Keywords: Logistics management Vehicle routing problem Vehicle assignment Real-time information Sweep method Tabu search
a b s t r a c t The dynamic vehicle routing problems (DVRP) is an extension of vehicle routing problems (VRP) in order to consider possible variations of travel times in the network. In this research, a two-stage framework for solving dynamic vehicle routing problem is proposed. In the first stage, the sweep method is adopted in vehicle assignment. In the second stage, a tabu search algorithm is implemented to improve routes under real-time information. The framework is implemented in an object-oriented approach and possible benefit from real-time information is illustrated through numerical simulation. The simulation-assignment model, DynaTAIWAN is applied in numerical simulation to evaluate real-time routing strategies in a traffic network. Numerical experiments are conducted in a 50 Nodes Network and a Taichung City. The results show that positive benefits could be achieved through utilization of real-time information with careful design. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction As the advancement of information technology (IT), the competition of businesses has been changed from single entity to a whole supply chain. Logistics management has been one of the most important parts in the supply chain management (Chopra & Meindl, 2001). More and more distribution centers (DC) have been established to provide the flexibility of sales and supply. Major daily operation issues in distribution centers are routes and schedules of trucks. The IT applications in commercial vehicle operations (CVO), especially in communication and information technologies, allow the study of dynamic vehicle routing problems under new and updated information, such as real-time traffic conditions, vehicle status, and new coming demands (Gendreau, Cuertin, Potvin, & Tailiard, 1999; Ghiani, Guerriero, Laporte, & Musmanno, 2003; Hu, Liao, & Lu, 2003; Psaraftis, 1995). Two major operational benefits of CVO include: (1) dynamically assign vehicles to time-sensitive demands, and (2) efficiently reroute vehicle according to current traffic conditions. However, critical problems, involved in obtaining these benefits, include vehicle assignment and vehicle routing problem (VRP) in real time. Vehicle assignment and routing problems have been studied for several decades (Bodin, Golden, Assad, & Ball, 1983; Powell & Spivey, 2004). Although most real-world vehicle routing problems
⇑ Corresponding author. Tel.: +886 5 2732935; fax: +886 5 2732932. E-mail address: [email protected] (T.-Y. Liao). 0957-4174/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2011.04.041
are dynamic, and the traditional methodologies for this class of problems has been based on adaptations of static algorithms. These static routing strategies are developed under static travel time, but they do not consider real-time traffic flow conditions. Dynamic vehicle routing problems (DVRP) need to consider real-time information as well as demands, and thus information attributes are important to the DVRP. DVRP is an extension of VRP in order to consider possible variations of travel times in the network. A vehicle fleet of fixed capacities has to serve customers of fixed demand from a central depot. Customers must be assigned to vehicles and the vehicles are routed so that the total time spent on the routes is minimized. The travel time between two customers or between a customer and the depot depends on the traffic network characteristics as well as traffic conditions. In this research, a two-stage framework for solving DVRP is proposed. In this framework, DVRP is divided into vehicle assignment and real-time route improvement. In both stages, simple algorithms are integrated in a complicated environment. In the first stage, the sweep method is adopted in vehicle assignment process. In the second stage, a tabu search algorithm is implemented to improve routes under real-time information. The advantages of the proposed framework are (1) each stage is modularized, (2) these simple algorithms provide positive benefits and (3) the framework is easy to be implemented. The contributions of this research include the integration of two existing algorithms, the implementation in an object-oriented approach, and the illustration of possible benefits of real-time information.
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The solution approach is experimented through numerical experiments in an evaluation framework in which assigning and routing operations could be simulated in a realistic traffic environment. The simulation-assignment model, DynaTAIWAN (Hu, Liao, Chen, Huang, & Chiang, 2007), is applied to evaluate assigning and routing strategies in a traffic network. Numerical experiments are conducted in a 50 Nodes Network and a Taichung City Network to explore the simulation framework for dynamic fleet management problem under real-time information supply strategies. This paper is organized as follows: the next section briefly describes some related research. The research framework and solution algorithms are discussed in the third section. The simulation model, DynaTAIWAN, is discussed in the fourth section, followed by numerical experiments and analysis. Concluding comments are given in the last section.
2. Literature review The fleet management problem includes two types of subproblems: fleet assignment problem and routing problem (Bramel & Simchi-Levi, 1997). Assume a dispatcher uses a fleet of vehicles of limited capacity to serve a set of demands. First, the dispatcher must decide how to partition the demands into groups that can be served by a vehicle. Second, the dispatcher must decide what sequence to use so as to minimize cost. VRP is the problem of constructing vehicles routes of minimum total cost starting and ending at a depot, such that each node is visited by one vehicle, and satisfying some constraints, such as capacity, duration, and time windows. Since VRP problem is NP-Hard, different solution techniques, including heuristics, mathematical programming based heuristics, meta-heuristics, and polyhedral combinatorics based optimization algorithms, are applied to obtain acceptable solutions within a reasonable time frame. For dynamic assignment problem, Powell and Spivey (2004) described a set of network assignment models, from deterministic to stochastic models, and also presented a hybrid model. Brown and Graves (1981) presented an integer linear programming formulation of a real-time routing and scheduling problem for petroleum tank trucks. The model developed truck tours for known (deterministic) customer demands. Gavish (1981) described an optimization-based, hierarchical model for real-time routing scheduling. All of these papers presented optimal algorithms or near optimal heuristics for use in a real-time environment. The underlying models do not incorporate forecasted demands and/or real travel time. With the advancement of communication and information technologies, real-time traffic conditions as well as dynamic demands are possible to obtain during the vehicle’s journey, thus a realistic vehicle routing problem is defined as DVRP. Psaraftis (1995) addressed some basic characteristics of DVRP, and pointed out that computer and communication technologies, such as electronic data interchange (EDI), geographic information systems (GIS), global positioning systems (GPS), and Intelligent Transportation Systems (ITS), have significantly enhanced the possibilities for efficient dynamic routing. Possible information attributes might include evolution of information (static/dynamic), quality of information (known-deterministic/forecast/probabilistic/unknown), availability of information (local/global), and processing of information (centralized/decentralized) (Psaraftis, 1995). These information attributes might have great impact on how to develop and design an efficient and good dynamic vehicle routing algorithms. Under on-line VRP consideration, Ghiani et al. (2003) listed several possible applications for this type of problems: dynamic fleet management, couriers, rescue and repair service companies, dial-a-ride system, taxi cab service, emergency services. Possible DVRP can be classified as follows (Hu et al., 2003):
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1. On-line VRP Demand information is not known when vehicles are assigned, and demand information is revealed on-line. Thus, the problem focuses on how to incorporate new demands into existing and/ or new vehicle routes in order to minimize total travel cost. 2. DVRP under real-time information Another category of DVRP is vehicle routing under real-time traffic conditions, such that vehicles could be efficiently rerouted according to current traffic conditions. 3. On-line VRP under real-time information In order to corporate possible coming demands and current traffic conditions, on-line VRP problems can also developed with consideration of real-time information. In order to consider travel time variations, different approaches have been developed. Malandraki and Daskin (1992) used a step function to represent time-dependent issue and develop a heuristic approach. Stochastic VRP (SVRP) has been proposed to consider such travel time variations (Gendreau, Laporte, & Séguin, 1996; Laporte, Louveaux, & Mercure, 1992). Due to the difficulties of capturing the variation of travel time in a traffic network, simulation models have been used to generate realistic travel time and applied in different routing strategies. Hu (2001) provided an evaluation framework under the consideration of real-time information, and the vehicle routing strategies are solved through a heuristic approach. Hu et al. (2003) applied a SVRP approach in a chance-constrained formulation (Laporte et al., 1992) and the SVRP solution formulation is solved through branch-and-bound technique by CPLEX. Ichoua, Gendreau, and Potvin (2003) proposed time-dependent vehicle speed model to consider possible travel time variation for different time intervals and links, and the approach is solved through a parallel tabu search heuristic. Fleischmann, Gnutzmann, and Sandvob (2004) used dynamic information and dynamic path calculation, and propose three different heuristics to solve DVRP. According to Laporte, Gendreu, Potvin, and Semet (2000), the tabu search heuristics have proved to be the most successful meta-heuristic approach. The tabu search algorithm, a memorybased search strategy, attempts to guide the local search method to continue its search beyond a local optimum. The algorithm keeps a tabu list of moves or solutions that have been made or visited in the past. The purpose of the tabu list is to record a number of most recent moves and prohibit any repetition or cycling. A number of researchers have applied the tabu search algorithm on VRP. Gendreau et al. (1999) proposed a tabu search heuristic approach to the dynamic VRP and implemented on a parallel computer platform to increase the computational effort. Liao (2004) addressed the DVRP problem and implemented a tabu search heuristic algorithm. 3. Framework for DVRP under real-time information A two-stage framework for solving DVRP is proposed in this research, namely, vehicle assignment and real-time vehicle route improvement. Several key issues and algorithms are discussed in detail in this section. These issues include the solution algorithm, the sweep method for vehicle assignment, and the tabu search algorithm for real-time route updating process. 3.1. Solution framework for DVRP under real-time information According to the basic formulation, the research aims at developing a solution approach for the DVRP under real-time information, and the solution strategy is then evaluated in a realistic traffic simulation framework. Basic inputs of the framework include vehicles with associated attributes, traffic network descriptions, and other data, such as
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Step 2: Vehicle assignment Vehicle assignment is implemented through the sweep method. The demand nodes are clustered into several groups according to sweep angles and the sweep is performed for each node. After the sweep method, vehicles are assigned to serve these groups one by one. The number of vehicles is equal to the number of groups. Step 3: Traffic simulation In DynaTAIWAN, vehicles are generated according to the timedependent origin-destination (OD) demands, and the current best paths are assigned to these vehicles. General vehicles and commercial vehicles are loaded into the network according to their departure times. The routes for commercial vehicles are the output from the sweep method. The vehicles are moved in the network, and thus detailed vehicle movements can be simulated and real-time information can be generated and provided to distribution centers. Step 4: Real-time information generation In DynaTAIWAN, travel time on links as well as at junctions is calculated based on simulated traffic flow distributions. An all-pair shortest path algorithm, the Floyd–Warshall Algorithm,
traffic control. Within this framework, vehicles, including commercial or other special vehicles, could be sent out by dispatchers to handle specific demands. The simulation-assignment model, DynaTAIWAN (Hu et al., 2007), is used to simulate mixed traffic flow patterns, and real-time information is processed to design dynamic dispatching strategies, and the results are assigned back to commercial vehicles. The solution approaches for the DVRP are implemented in two phases: pre-trip route assignment and real-time route updating. The initial route is generated according to the sweep method. Then, the dynamic route information is provided to commercial vehicles to achieve real-time route updating. The overall research structure is depicted in Fig. 1. The algorithmic steps are further described as follows: Step 1: Initialization Prepare input data for vehicle route assignment and simulation. The input data include network data, demand data, vehicle capacity, and time-dependent origin-destination (OD) trip tables.
Time Dependent OD Trip
Network Geometric Data
VRP Data
Vehicle Assignment : The Sweep method
Vehicle Assignment
Initial Route Generation
Commercial Vehicles
DynaTAIWAN
Floyd-Warshall Algorithm Real-Time Route Updating : Tabu Search
New Routing
Real-Time Roue Update
Yes
No No
Stop Yes End
Fig. 1. Research framework for DVRP under real-time information.
On-line Route Improvement
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is applied to calculate travel time from node to node in order for paths and/or routes updating process. In practice, flow movements and possible travel time information could be gathered through vehicle detectors (VD) and other possible surveillance measures. Step 5: Commercial vehicle route updating process Upon receiving real-time information, distribution centers update routes based on current traffic conditions. The route updating is implemented based on the tabu search algorithm. Step 6: Updating If new routes for commercial vehicles are determined, the commercial vehicles are assigned to new routes according the received information. If no new route is generated, then go to step 7. Step 7: Stop rule If the simulation is terminated, travel statistics are summarized. Otherwise, go to step 3 and continue the simulation process.
Initialization
Select the Reference Point
Calculate theAngle
Sorting by Angle Value
3.2. Vehicle assignment: the sweep method Vehicle dispatching center usually arrange one commercial vehicle for one specific zone; therefore, demand nodes in neighborhood are clustered together. Although several approaches have been developed to efficiently solve the problem, the sweep method is chosen due to the capability to group neighboring nodes. The sweep method (Gillett & Miller, 1974) constructs a solution in two stages. First, it assigns nodes to vehicles and then it sequences the order in which each vehicle visits the nodes assigned to it. It is assumed that the problem is Euclidean, an ordering can easily be obtained by numbering the vertices in increasing order of the angle between the line linking the vertex to a reference point (e.g. the depot) and an arbitrary axis passing through the chosen reference point. Demand nodes are added to a route as they are swept. Our implementation uses two reference points: the depot location and the customer location. Every demand nodes are set to be one of the reference points, thus n possible solutions are obtained. Among all possible route combinations, the strategy with the minimum cost is selected as an initial solution for real-time updating. The algorithmic steps, as shown in Fig. 2, are described. Step 1: Initialization Obtain input data, such as demand nodes and associated coordinates, vehicle capacity, and travel times from nodes to nodes. Step 2: Selection of the reference point Select a reference point from N, the set of demand nodes. Step 3: Angle calculation Calculate the polar coordinates, from the two reference points, the depot and the selected reference point. Step 4: Sorting Obtain an ordering in increasing order of the angle. Step 5: Vehicle assignment and routing Select demand nodes in sequence, and check the loads and vehicle capacity. If the load is less than the remaining capacity, assign the demand node to the vehicle. Step 6: Check If all the demand nodes have been scanned, then stop. If the demand load exceeds the remaining vehicle capacity, dispatch another vehicle and go to step 5. Step 7: Reference point reselection Select the next node as the reference point and repeat the process from step 3 to step 6. 3.3. Real-time route updating: the tabu search algorithm The tabu search algorithm is applied in the real-time route updating process. The process considers unvisited demand nodes
Route Generation
Choose Next Demand Node
Less than Vehicle Capacity
Yes
No No
Have all Nodes been served?
Yes Finished Reference Point Selection?
No
Select the Next Reference Point
Yes Select the Route with Minimum Cost
Stop Fig. 2. The sweep algorithm.
and generates possible solutions through the 2-opt exchange method. These possible solutions are evaluated through tabu lists and aspiration criteria. The detailed flowchart is illustrated in Fig. 3, and the steps are summarized as follows: Step 1: Initialization Input demand nodes, associated demands, and initial routes. Step 2: Travel time matrix updating Update the travel time matrixes generated from DynaTAIWAN.
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Step 10: If there are remaining demand nodes, go to step 2. Otherwise, stop the algorithm. In order to operate the tabu search algorithms, several parameters are determined numerically (Liao, 2004). The parameters include number of iterations, and the size of tabu list.
Step 3: Route improvement Routes (candidate lists) are generated through 2-opt exchange method. Step 4: Route selection Select the best routes from possible candidates. Step 5: Tabu list check If the link used in the selected route is in the tabu list, check the aspiration level. If yes, go to step 6. If not, the candidate route is not considered, go to step 4. Step 6: Update information Update route information, current solution, and tabu list. Step 7: Stop criteria If the solutions satisfy the stop criteria, stop. Otherwise, go back to step 3. Step 8: Route conversion Update the vehicle’s routes.
3.4. DynaTAIWAN DynaTAIWAN (Hu et al., 2007) is an integrated dynamic simulation-assignment model for ITS applications in Taiwan. DynaTAIWAN is structured based on the concept of simulationassignment method. The DynaTAIWAN is composed of two layers, namely simulation-layer and real-time control layer. The simulation layer is designed to simulate traffic flow patterns according to assumed tripmaker characteristics and/or under a set of given conditions; the real-time control layer receives real-time vehicle
Start
Determine the demand node Real-time travel time matrix
Initial Routes Generate all move from the candidate list Determine the best move
Spatial tabu list Yes
No
Does the move be tabu
No
Yes Satisfy with aspiration level
Reject the move
Update
Satisfy with stopping criterion Yes
No
Route switch
Yes
Does it have demand node No Stop
Fig. 3. The tabu search algorithm with real-time information.
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compiler C++ is chosen for the simulation core due to its efficiency; the object-oriented language Java is chosen for the GUI due to its capability of cross-platform capabilities. The sequence diagram defines message passing and interrelationship of objects and classes. In Fig. 4, the sequence diagram for simulation process is illustrated. Classes involved in this process include CTimer (simulation timer class), CNet (network class), CVehicle (vehcile class), CPath (path class), CQueue (queue class) and CLink (link class). According to the sequence diagram, the simulation process is summarized as follows:
information and forecast short-term traffic flow patterns. One of the key features of DynaTAIWAN is its ability to model mixed traffic flows in both urban streets and freeways. 4. Program implementation 4.1. Object-oriented system analysis The framework is analyzed and designed through objectoriented approach via UML (Unified Modeling Language) (Booch, Rumbaugh, & Jacobson, 1999; Fowler & Scott, 2000), and the model is implemented in C++ to inherit object-oriented characteristics. The object-oriented approach provides the capabilities to enhance the correspondence between objects and their semantic representation and to allow the user to control the levels of detail and summarize and aggregate data during decision-making. UML is a visual modeling language adopted as a standard for object-oriented modeling and design in software development by the Object Management Group (OMG). UML consists of a set of diagrams that are used to represent models of a system in diagrammatic notation through stages of development. The latest release is UML 1.3 which this paper refers to (UML 2.0 has been official announced in March, 2005). The implementation of DynaTAIWAN includes two parts: simulation core and graphic user interface (GUI). The object-oriented
:CTimer
:CNet
TempEntry:CQueue
:CVehicle
1. CTimer initiates the simulation process. 2. CNet calculates number of vehicles at this time interval, denoted as C. 3. TempEntry: generates and stores these new vehicles. 4. Setup vehicle and behavior attributes for new vehicles. 5. Calculate the capacity for LinkEntry, and move generated vehicle entities to LinkEntry. 6. Calculate the capacity for Link i, and load the vehicles onto the network. 7. Calculate the average speed for Link i. 8. Move the car and motorcycle according the average speed and adjusted speed. 9. Obtain path information from CPath, and determine the entering Link j.
LinkEntry:CQueue
i:CLink
Waiting:CQueue
INTOO:CQueue
:CPath
j:CLink
Count Vehicle-Entry() Vehicle Generated() Set Tripmakers' Attributes() Calculate Revenue Capacity()
Vehicle Added() Calculate Revenue Capacity()
Vehicle Generated()
Compute Vehicle Average Speed() move() check path()
Arrive Stop Line() Calculate Outflow()
Vehicle Added() Vehicle Added() Calculate Revenue Capacity() Repeat Until Arrive the Destination()
Arrive Destintion()
Fig. 4. Sequence diagram of simulation process.
Vehicle Generated()
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Fig. 5. The overall program structure.
Fig. 6. 50-node test network.
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N15-NR
N15-R3
N15-R5
Fig. 7. Routes for 15 demand nodes in peak loading pattern.
10. When vehicles reach the stop line, Link i calculates outflow capacity and stores the possible leaving vehicles into waiting queues. 11. Vehicles in Link i waiting queue is assigned to each downstream Link j INTOO queue. 12. Calculate possible capacity for Link j and move vehicles from INTOO queue to Link j. 4.2. Program structure The evaluation framework is implemented in object-oriented approach, and five major modules are developed. The overall program structure is shown in Fig. 5. These modules are described hereafter: 1. Input module In the evaluation framework, required data sets include timedependent O–D trip tables, VRP data, and network data. The VRP data include number of commercial vehicles, number of demand nodes to be served, and the location of the depot. The time-dependent O–D trip tables and network data are primarily used in the simulation to reflect realistic traffic environment. 2. Vehicle assignment module The vehicle assignment module processes the sweep algorithm to calculate initial routes for commercial vehicles, and these initial routes are assigned to commercial vehicles. 3. Traffic simulation module The main purpose of the module is to simulate vehicle’s movements in realistic traffic conditions. Simulated vehicles include passenger cars, motorcycles, and commercial vehicles. Passenger cars and motorcycles are generated though O–D tables and commercial vehicles are generated according to the VRP data. During the simulation, link travel costs are estimated for every simulation interval and a travel time matrix from node to node is calculated based on the Floyd–Warshall algorithm, the all pair shortest path algorithm. The travel time matrix is used in the route updating module to calculate new routes for commercial vehicles. 4. Route updating module The module uses the tabu search algorithm to re-calculate optimal routes for commercial vehicles based on real-time travel costs. The algorithm updates service sequence and paths between each pair of demand nodes. 5. Output module The module keeps track updated routes and travel time information for each vehicle.
Data and message are passed among these modules through several functions, and the message passing functions are described as follows: 1. Vehicle assignment module The module obtains commercial vehicles information through VRPdata() function, and generates initial routes for each vehicle. The initial route information is passed to DynaTAIWAN to simulate vehicle’s movements and to route updating module through AssignResult() function. 2. Traffic simulation module Traffic simulation module is constructed based on DynaTAIWAN. DynaTAIWAN obtains basic input data through Demand() function, and commercial vehicles from AssignResult() function. Real-time link travel cost and travel time matrix are stored in CostResult() function. The route updating module can retrieve cost values through CostResult() function. 3. Route updating module Based on the data from AssignResult() and CostResult() functions, the route updating module re-calculates optimal routes for commercial vehicles, and new routes are updated through RouteResultUpdate() function. 5. Numerical experiments Two networks, a 50-node test network and a real Taichung City Network, with different factors are experimented to illustrate the proposed approach and to investigate possible benefits from realtime route updating strategies. General assumptions for both networks are summarized as follows:
Table 1 The results for 15 demand nodes in peak loading pattern. Experiment
Vehicle
Number of links in the route
Travel time (min)
Improvement (%)
N15-NR
1 2 3
11 12 16
11.10 12.34 14.10
– – –
N15-R3
1 2 3
11 12 16
11.34 12.34 14.10
2.16 0 0
N15-R5
1 2 3
11 12 16
11.10 12.34 14.10
0 0 0
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Fig. 8. The Taichung City Network in DynaTAIWAN.
III-N10 -NR
I II -N10-R5
III-N10-R10
III-N10-R15
Fig. 9. Routing strategies for 10 demand nodes in the Taichung City Network.
T.-Y. Liao, T.-Y. Hu / Expert Systems with Applications 38 (2011) 12548–12558 Table 2 Summary statistics for 10 demand nodes in the Taichung City Network. Experiment
Vehicle
Number of links in the route
Travel time (min)
Improvement (%)
III-N10-NR
1 2
23 19
31.20 25.30
– –
III-N10-R5
1 2
23 19
31.10 25.30
0.32 0
III-N10-R10
1 2
23 19
31.20 25.30
0 0
III-N10-R15
1 2
23 19
31.10 25.30
0.32 0
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from numerical experiments. The size of the tabu list is set to 2.375 N. The maximum iteration is set to 2000. 3. The results are evaluated in an improvement index, written as follows:
Improvement Percentage ¼ ðNRITT RITTÞ=NRITT 100% ð1Þ NRITT: Travel time of commercial vehicles without real-time information. RITT: Travel time of commercial vehicles with real-time information. 5.1. Experiments and results for the 50-node test network
Table 3 Summary statistics for the Taichung City Network. Experiment
Vehicle
Number of links in the route
Travel time (min)
Improvement (%)
III-N20-NR
1 2
31 29
46.84 69.76
– –
III-N20-R5
1 2
30 29
37.70 29.77
19.51 57.33
III-N20-R10
1 2
30 31
27.80 71.80
40.65 2.92
III-N20-R15
1 2
31 31
46.84 67.92
0 2.64
1. Commercial vehicles follow the new routes assigned by the dispatching center. 2. Since no experience has been made for the tabu search algorithm on the DVRP, several important parameters are selected
Fig. 6 depicts the test network used in the current study. The network, which consists of a freeway surrounded by a street network, includes 50 nodes and 172 links. Consequently, the network has 32 origin nodes and 10 destination nodes. All arcs are one-directional and have two lanes in each direction except the entrance and exit ramps that connect the street network to the freeway, these are directed arcs with one lane as shown in the figure. Each link is 500 m long. The freeway links have a free speed of 100 kph and all other links have a 50 kph free speed. The maximum bumper-to-bumper and jam densities are assumed to be 167 vehicles/km and 120 vehicles/km respectively for all links of the network. Different car and motorcycle OD trip matrices are applied in these experiments. In these experiments, 15 demand nodes with a fixed depot are considered, and a peak loading pattern is assumed. The peak loading pattern is generated to capture possible dynamic traffic peak pattern. There are 10 time intervals within 50 min, the total
III-N20-NR
III-N20-R5
III-N20-R10
III-N20-R15
Fig. 10. Routing strategies for the Taichung City Network.
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number of vehicles is about 31,800, the average travel time is about 14.57 min, and the average travel distance is about 2.42 km. In these experiments, real-time travel time information is provided for a certain intervals, including 3 and 5 min, in order to reflect the journey time for commercial vehicles. N15-NR, N15-R3, and N15-R5 represent 15 demands nodes without real-time information, with 3-min and 5-min real-time information updating intervals, respectively. The results are shown in Fig. 7 and Table 1. Under this scenario, the travel times of commercial vehicles remain about the same. The routes in most of the experiments remain the same and the improvement is not significant. 5.2. Numerical experiments and results for the Taichung City Network Numerical experiments are conducted in a Taichung City Network, as shown in Fig. 8, which includes 122 demand zones, 707 nodes and 2309 links. There are two sets of experiments: 10 and 20 demand nodes with a fixed depot. All these demand nodes are randomly picked up from CBD of the Taichung Network. The initial solution, as shown in Fig. 9, is generated from the sweep method. A peak traffic loading pattern is assumed, the total number of vehicles is about 73,140, the average travel time is about 32.31 min, and the average travel distance is about 5.70 km. In these experiments, real-time travel time information is provided for a certain intervals, including 5, 10 and 15 min. The notations of N10-NR, N10-R5, N10-R10 and N10-R15, N20-NR, N20-R5, N20-R10 and N20-R15 represent 10 and 20 demands nodes without real-time information, with 5-min and 10-min and 15-min real-time information updating intervals, respectively. 1. 10 Demand nodes The results for 10 demand nodes are summarized in Table 2 and Fig. 9. The improvement of real-time information is insignificant for different real-time information updating intervals. It indicates that traffic situation might not be congested. 2. 20 Demand nodes The results are summarized in Table 3 and Fig. 10. Through the real-time route updating, travel time could be greatly reduced in most of the cases. If the updating interval is 5 min, the percentages of saving for both vehicles are 19.51% and 57.33%, respectively. If the updating interval is 10 min, the percentages of saving for both vehicles are 40.65% and 2.92%, respectively. The results show that the best updating interval is about 5 min and it provides flexibility to switch to better routes. In Fig. 10, the final routes are slightly varied from one case to another, and this might indicate that links with high congestion are avoided during the real-time route updating process. From a series of experiments, it seems that number of demand nodes might be an important factor for real-time route updating process. When the number of demand nodes increases, the possible switching number also increases and it is more likely to obtain efficient routes to reduce travel time. 6. Concluding remarks In this paper, the problem of fleet management is explored in two parts: vehicle assignment and real-time route updating. The vehicle assignment is accomplished through a classical algorithm: the sweep method. The real-time route updating algorithm is developed through the tabu search algorithm to consider possible dynamic variations of link travel times, and these algorithms are then simulated in a realistic simulation environment. Through the experiments, the sweep method provides a basic ability to
cluster demand nodes, and initial routes are able to generate through the application of the sweep method. Furthermore, the tabu search approach solves DVRP efficiently. The core of the framework, DynaTAIWAN, provides traffic simulation and assignment capabilities under mixed traffic flow conditions; however, only real-time current traffic condition is obtained. Possible predicted traffic conditions could enhance the benefits from real-time route updating. The framework provides a practical tool for the evaluation of vehicle routing strategies under real-time information. This capability is necessary to evaluate phenomena where time-variation is essential, including dynamic fleet management and real-time information systems. The numerical results indicate that real-time information could provide positive benefit only under careful consideration and design; however, interval of updating routes might lead to worse results due to overheads in route changing. The results provide useful insights into actual traffic systems, and the impact of realtime information on commercial vehicle operations. Acknowledgements This paper is based on work partially supported by National Science Council, Taiwan, ROC. Of course, the authors are solely responsible for the contents of this paper. References Bodin, L., Golden, B., Assad, A., & Ball, M. (1983). Routing and scheduling of vehicles and crews: The state of the art. Computers & Operations Research, 10, 63–211. Booch, G., Rumbaugh, J., & Jacobson, I. (1999). The unified modeling language: User guide. Reading, MA: Addison-Wesley. Bramel, J., & Simchi-Levi, D. (1997). The logic of logistics. Springer (p. 281). Brown, G., & Graves, G. (1981). Real-time dispatch of petroleum tank trucks. Management Science, 27, 19–32. Chopra, S., & Meindl, P. (2001). Supply chain management. Prentice-Hall (p. 457). Fleischmann, B., Gnutzmann, S., & Sandvob, E. (2004). Dynamic vehicle routing based on on-line traffic information. Transportation Science, 38(4), 420–433. Fowler, M., & Scott, K. (2000). UML distilled: A brief guide to the standard object modeling language. Addison Wesley Longman, Inc. Gavish, B. (1981). A decision support system for managing the transportation needs of a large corporation. AIIE Transactions, 61–85. Gendreau, M., Cuertin, F., Potvin, J. Y., & Tailiard, E. (1999). Parallel tabu search for real-time vehicle routing and dispatching. Transportation Science, 33(4), 381–390. Gendreau, M., Laporte, G., & Séguin, R. (1996). Invited review stochastic vehicle routing. European Journal of Operational Research, 88, 3–12. Ghiani, G., Guerriero, F., Laporte, G., & Musmanno, R. (2003). Real-time vehicle routing: Solution concepts, algorithms and parallel computing strategies. European Journal of Operational Research, 151, 1–11. Gillett, B., & Miller, L. (1974). A heuristic algorithm for the vehicle dispatch problem. Operations Research, 22, 340–349. Hu, T. Y. (2001). Evaluation of dynamic vehicle routing strategies under real-time information. Transportation Research Record, 1774, 115–122. Hu, T. Y., Liao, T. Y., Chen, L. W., Huang, Y. K., & Chiang, M. L. (2007). Dynamic simulation-assignment model (DynaTAIWAN) under mixed traffic flows for ITS applications. In The proceedings of 86th transportation research board annual meeting, Washington, DC. Hu, T. Y., Liao, T. Y., & Lu, Y. C. (2003). Study on solution approach for dynamic vehicle routing problems under real-time information. Transportation Research Record, 1857. Ichoua, S., Gendreau, M., & Potvin, J. Y. (2003). Vehicle dispatching with timedependent travel times. European Journal of Operational research, 144, 379–396. Laporte, G., Gendreu, M., Potvin, J. Y., & Semet, F. (2000). Classical and modern heuristics for the vehicle routing problem. International Transactions in Operational Research, 7, 285–300. Laporte, G., Louveaux, F., & Mercure, H. (1992). The vehicle routing problem with stochastic travel times. Transportation Science, 26(3), 161–170. Liao, T. Y. (2004). A tabu search algorithm for dynamic vehicle routing problems under real-time information. Transportation Research Board, 1882, 140–149. Malandraki, C., & Daskin, M. (1992). Time dependent vehicle routing problems: formulations, properties and heuristic algorithms. Transportation Science, 26, 185–200. Powell, W. B., & Spivey, M. Z. (2004). The dynamic assignment problem. Transportation Science, 38(4), 399–419. Psaraftis, H. N. (1995). Dynamic vehicle routing: Status and prospect. Annals of Operations Research, 61, 143–164.
Contents lists available at ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
An object-oriented evaluation framework for dynamic vehicle routing problems under real-time information Tsai-Yun Liao a,⇑, Ta-Yin Hu b a b
Graduate Institute of Marketing and Logistics/Transportation, National Chiayi University, No. 580, Sinmin Rd, Chiayi City 60054, Taiwan, ROC Department of Transportation and Communication Management Science, National Cheng Kung University, Taiwan, ROC
a r t i c l e
i n f o
Keywords: Logistics management Vehicle routing problem Vehicle assignment Real-time information Sweep method Tabu search
a b s t r a c t The dynamic vehicle routing problems (DVRP) is an extension of vehicle routing problems (VRP) in order to consider possible variations of travel times in the network. In this research, a two-stage framework for solving dynamic vehicle routing problem is proposed. In the first stage, the sweep method is adopted in vehicle assignment. In the second stage, a tabu search algorithm is implemented to improve routes under real-time information. The framework is implemented in an object-oriented approach and possible benefit from real-time information is illustrated through numerical simulation. The simulation-assignment model, DynaTAIWAN is applied in numerical simulation to evaluate real-time routing strategies in a traffic network. Numerical experiments are conducted in a 50 Nodes Network and a Taichung City. The results show that positive benefits could be achieved through utilization of real-time information with careful design. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction As the advancement of information technology (IT), the competition of businesses has been changed from single entity to a whole supply chain. Logistics management has been one of the most important parts in the supply chain management (Chopra & Meindl, 2001). More and more distribution centers (DC) have been established to provide the flexibility of sales and supply. Major daily operation issues in distribution centers are routes and schedules of trucks. The IT applications in commercial vehicle operations (CVO), especially in communication and information technologies, allow the study of dynamic vehicle routing problems under new and updated information, such as real-time traffic conditions, vehicle status, and new coming demands (Gendreau, Cuertin, Potvin, & Tailiard, 1999; Ghiani, Guerriero, Laporte, & Musmanno, 2003; Hu, Liao, & Lu, 2003; Psaraftis, 1995). Two major operational benefits of CVO include: (1) dynamically assign vehicles to time-sensitive demands, and (2) efficiently reroute vehicle according to current traffic conditions. However, critical problems, involved in obtaining these benefits, include vehicle assignment and vehicle routing problem (VRP) in real time. Vehicle assignment and routing problems have been studied for several decades (Bodin, Golden, Assad, & Ball, 1983; Powell & Spivey, 2004). Although most real-world vehicle routing problems
⇑ Corresponding author. Tel.: +886 5 2732935; fax: +886 5 2732932. E-mail address: [email protected] (T.-Y. Liao). 0957-4174/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2011.04.041
are dynamic, and the traditional methodologies for this class of problems has been based on adaptations of static algorithms. These static routing strategies are developed under static travel time, but they do not consider real-time traffic flow conditions. Dynamic vehicle routing problems (DVRP) need to consider real-time information as well as demands, and thus information attributes are important to the DVRP. DVRP is an extension of VRP in order to consider possible variations of travel times in the network. A vehicle fleet of fixed capacities has to serve customers of fixed demand from a central depot. Customers must be assigned to vehicles and the vehicles are routed so that the total time spent on the routes is minimized. The travel time between two customers or between a customer and the depot depends on the traffic network characteristics as well as traffic conditions. In this research, a two-stage framework for solving DVRP is proposed. In this framework, DVRP is divided into vehicle assignment and real-time route improvement. In both stages, simple algorithms are integrated in a complicated environment. In the first stage, the sweep method is adopted in vehicle assignment process. In the second stage, a tabu search algorithm is implemented to improve routes under real-time information. The advantages of the proposed framework are (1) each stage is modularized, (2) these simple algorithms provide positive benefits and (3) the framework is easy to be implemented. The contributions of this research include the integration of two existing algorithms, the implementation in an object-oriented approach, and the illustration of possible benefits of real-time information.
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The solution approach is experimented through numerical experiments in an evaluation framework in which assigning and routing operations could be simulated in a realistic traffic environment. The simulation-assignment model, DynaTAIWAN (Hu, Liao, Chen, Huang, & Chiang, 2007), is applied to evaluate assigning and routing strategies in a traffic network. Numerical experiments are conducted in a 50 Nodes Network and a Taichung City Network to explore the simulation framework for dynamic fleet management problem under real-time information supply strategies. This paper is organized as follows: the next section briefly describes some related research. The research framework and solution algorithms are discussed in the third section. The simulation model, DynaTAIWAN, is discussed in the fourth section, followed by numerical experiments and analysis. Concluding comments are given in the last section.
2. Literature review The fleet management problem includes two types of subproblems: fleet assignment problem and routing problem (Bramel & Simchi-Levi, 1997). Assume a dispatcher uses a fleet of vehicles of limited capacity to serve a set of demands. First, the dispatcher must decide how to partition the demands into groups that can be served by a vehicle. Second, the dispatcher must decide what sequence to use so as to minimize cost. VRP is the problem of constructing vehicles routes of minimum total cost starting and ending at a depot, such that each node is visited by one vehicle, and satisfying some constraints, such as capacity, duration, and time windows. Since VRP problem is NP-Hard, different solution techniques, including heuristics, mathematical programming based heuristics, meta-heuristics, and polyhedral combinatorics based optimization algorithms, are applied to obtain acceptable solutions within a reasonable time frame. For dynamic assignment problem, Powell and Spivey (2004) described a set of network assignment models, from deterministic to stochastic models, and also presented a hybrid model. Brown and Graves (1981) presented an integer linear programming formulation of a real-time routing and scheduling problem for petroleum tank trucks. The model developed truck tours for known (deterministic) customer demands. Gavish (1981) described an optimization-based, hierarchical model for real-time routing scheduling. All of these papers presented optimal algorithms or near optimal heuristics for use in a real-time environment. The underlying models do not incorporate forecasted demands and/or real travel time. With the advancement of communication and information technologies, real-time traffic conditions as well as dynamic demands are possible to obtain during the vehicle’s journey, thus a realistic vehicle routing problem is defined as DVRP. Psaraftis (1995) addressed some basic characteristics of DVRP, and pointed out that computer and communication technologies, such as electronic data interchange (EDI), geographic information systems (GIS), global positioning systems (GPS), and Intelligent Transportation Systems (ITS), have significantly enhanced the possibilities for efficient dynamic routing. Possible information attributes might include evolution of information (static/dynamic), quality of information (known-deterministic/forecast/probabilistic/unknown), availability of information (local/global), and processing of information (centralized/decentralized) (Psaraftis, 1995). These information attributes might have great impact on how to develop and design an efficient and good dynamic vehicle routing algorithms. Under on-line VRP consideration, Ghiani et al. (2003) listed several possible applications for this type of problems: dynamic fleet management, couriers, rescue and repair service companies, dial-a-ride system, taxi cab service, emergency services. Possible DVRP can be classified as follows (Hu et al., 2003):
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1. On-line VRP Demand information is not known when vehicles are assigned, and demand information is revealed on-line. Thus, the problem focuses on how to incorporate new demands into existing and/ or new vehicle routes in order to minimize total travel cost. 2. DVRP under real-time information Another category of DVRP is vehicle routing under real-time traffic conditions, such that vehicles could be efficiently rerouted according to current traffic conditions. 3. On-line VRP under real-time information In order to corporate possible coming demands and current traffic conditions, on-line VRP problems can also developed with consideration of real-time information. In order to consider travel time variations, different approaches have been developed. Malandraki and Daskin (1992) used a step function to represent time-dependent issue and develop a heuristic approach. Stochastic VRP (SVRP) has been proposed to consider such travel time variations (Gendreau, Laporte, & Séguin, 1996; Laporte, Louveaux, & Mercure, 1992). Due to the difficulties of capturing the variation of travel time in a traffic network, simulation models have been used to generate realistic travel time and applied in different routing strategies. Hu (2001) provided an evaluation framework under the consideration of real-time information, and the vehicle routing strategies are solved through a heuristic approach. Hu et al. (2003) applied a SVRP approach in a chance-constrained formulation (Laporte et al., 1992) and the SVRP solution formulation is solved through branch-and-bound technique by CPLEX. Ichoua, Gendreau, and Potvin (2003) proposed time-dependent vehicle speed model to consider possible travel time variation for different time intervals and links, and the approach is solved through a parallel tabu search heuristic. Fleischmann, Gnutzmann, and Sandvob (2004) used dynamic information and dynamic path calculation, and propose three different heuristics to solve DVRP. According to Laporte, Gendreu, Potvin, and Semet (2000), the tabu search heuristics have proved to be the most successful meta-heuristic approach. The tabu search algorithm, a memorybased search strategy, attempts to guide the local search method to continue its search beyond a local optimum. The algorithm keeps a tabu list of moves or solutions that have been made or visited in the past. The purpose of the tabu list is to record a number of most recent moves and prohibit any repetition or cycling. A number of researchers have applied the tabu search algorithm on VRP. Gendreau et al. (1999) proposed a tabu search heuristic approach to the dynamic VRP and implemented on a parallel computer platform to increase the computational effort. Liao (2004) addressed the DVRP problem and implemented a tabu search heuristic algorithm. 3. Framework for DVRP under real-time information A two-stage framework for solving DVRP is proposed in this research, namely, vehicle assignment and real-time vehicle route improvement. Several key issues and algorithms are discussed in detail in this section. These issues include the solution algorithm, the sweep method for vehicle assignment, and the tabu search algorithm for real-time route updating process. 3.1. Solution framework for DVRP under real-time information According to the basic formulation, the research aims at developing a solution approach for the DVRP under real-time information, and the solution strategy is then evaluated in a realistic traffic simulation framework. Basic inputs of the framework include vehicles with associated attributes, traffic network descriptions, and other data, such as
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Step 2: Vehicle assignment Vehicle assignment is implemented through the sweep method. The demand nodes are clustered into several groups according to sweep angles and the sweep is performed for each node. After the sweep method, vehicles are assigned to serve these groups one by one. The number of vehicles is equal to the number of groups. Step 3: Traffic simulation In DynaTAIWAN, vehicles are generated according to the timedependent origin-destination (OD) demands, and the current best paths are assigned to these vehicles. General vehicles and commercial vehicles are loaded into the network according to their departure times. The routes for commercial vehicles are the output from the sweep method. The vehicles are moved in the network, and thus detailed vehicle movements can be simulated and real-time information can be generated and provided to distribution centers. Step 4: Real-time information generation In DynaTAIWAN, travel time on links as well as at junctions is calculated based on simulated traffic flow distributions. An all-pair shortest path algorithm, the Floyd–Warshall Algorithm,
traffic control. Within this framework, vehicles, including commercial or other special vehicles, could be sent out by dispatchers to handle specific demands. The simulation-assignment model, DynaTAIWAN (Hu et al., 2007), is used to simulate mixed traffic flow patterns, and real-time information is processed to design dynamic dispatching strategies, and the results are assigned back to commercial vehicles. The solution approaches for the DVRP are implemented in two phases: pre-trip route assignment and real-time route updating. The initial route is generated according to the sweep method. Then, the dynamic route information is provided to commercial vehicles to achieve real-time route updating. The overall research structure is depicted in Fig. 1. The algorithmic steps are further described as follows: Step 1: Initialization Prepare input data for vehicle route assignment and simulation. The input data include network data, demand data, vehicle capacity, and time-dependent origin-destination (OD) trip tables.
Time Dependent OD Trip
Network Geometric Data
VRP Data
Vehicle Assignment : The Sweep method
Vehicle Assignment
Initial Route Generation
Commercial Vehicles
DynaTAIWAN
Floyd-Warshall Algorithm Real-Time Route Updating : Tabu Search
New Routing
Real-Time Roue Update
Yes
No No
Stop Yes End
Fig. 1. Research framework for DVRP under real-time information.
On-line Route Improvement
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is applied to calculate travel time from node to node in order for paths and/or routes updating process. In practice, flow movements and possible travel time information could be gathered through vehicle detectors (VD) and other possible surveillance measures. Step 5: Commercial vehicle route updating process Upon receiving real-time information, distribution centers update routes based on current traffic conditions. The route updating is implemented based on the tabu search algorithm. Step 6: Updating If new routes for commercial vehicles are determined, the commercial vehicles are assigned to new routes according the received information. If no new route is generated, then go to step 7. Step 7: Stop rule If the simulation is terminated, travel statistics are summarized. Otherwise, go to step 3 and continue the simulation process.
Initialization
Select the Reference Point
Calculate theAngle
Sorting by Angle Value
3.2. Vehicle assignment: the sweep method Vehicle dispatching center usually arrange one commercial vehicle for one specific zone; therefore, demand nodes in neighborhood are clustered together. Although several approaches have been developed to efficiently solve the problem, the sweep method is chosen due to the capability to group neighboring nodes. The sweep method (Gillett & Miller, 1974) constructs a solution in two stages. First, it assigns nodes to vehicles and then it sequences the order in which each vehicle visits the nodes assigned to it. It is assumed that the problem is Euclidean, an ordering can easily be obtained by numbering the vertices in increasing order of the angle between the line linking the vertex to a reference point (e.g. the depot) and an arbitrary axis passing through the chosen reference point. Demand nodes are added to a route as they are swept. Our implementation uses two reference points: the depot location and the customer location. Every demand nodes are set to be one of the reference points, thus n possible solutions are obtained. Among all possible route combinations, the strategy with the minimum cost is selected as an initial solution for real-time updating. The algorithmic steps, as shown in Fig. 2, are described. Step 1: Initialization Obtain input data, such as demand nodes and associated coordinates, vehicle capacity, and travel times from nodes to nodes. Step 2: Selection of the reference point Select a reference point from N, the set of demand nodes. Step 3: Angle calculation Calculate the polar coordinates, from the two reference points, the depot and the selected reference point. Step 4: Sorting Obtain an ordering in increasing order of the angle. Step 5: Vehicle assignment and routing Select demand nodes in sequence, and check the loads and vehicle capacity. If the load is less than the remaining capacity, assign the demand node to the vehicle. Step 6: Check If all the demand nodes have been scanned, then stop. If the demand load exceeds the remaining vehicle capacity, dispatch another vehicle and go to step 5. Step 7: Reference point reselection Select the next node as the reference point and repeat the process from step 3 to step 6. 3.3. Real-time route updating: the tabu search algorithm The tabu search algorithm is applied in the real-time route updating process. The process considers unvisited demand nodes
Route Generation
Choose Next Demand Node
Less than Vehicle Capacity
Yes
No No
Have all Nodes been served?
Yes Finished Reference Point Selection?
No
Select the Next Reference Point
Yes Select the Route with Minimum Cost
Stop Fig. 2. The sweep algorithm.
and generates possible solutions through the 2-opt exchange method. These possible solutions are evaluated through tabu lists and aspiration criteria. The detailed flowchart is illustrated in Fig. 3, and the steps are summarized as follows: Step 1: Initialization Input demand nodes, associated demands, and initial routes. Step 2: Travel time matrix updating Update the travel time matrixes generated from DynaTAIWAN.
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Step 10: If there are remaining demand nodes, go to step 2. Otherwise, stop the algorithm. In order to operate the tabu search algorithms, several parameters are determined numerically (Liao, 2004). The parameters include number of iterations, and the size of tabu list.
Step 3: Route improvement Routes (candidate lists) are generated through 2-opt exchange method. Step 4: Route selection Select the best routes from possible candidates. Step 5: Tabu list check If the link used in the selected route is in the tabu list, check the aspiration level. If yes, go to step 6. If not, the candidate route is not considered, go to step 4. Step 6: Update information Update route information, current solution, and tabu list. Step 7: Stop criteria If the solutions satisfy the stop criteria, stop. Otherwise, go back to step 3. Step 8: Route conversion Update the vehicle’s routes.
3.4. DynaTAIWAN DynaTAIWAN (Hu et al., 2007) is an integrated dynamic simulation-assignment model for ITS applications in Taiwan. DynaTAIWAN is structured based on the concept of simulationassignment method. The DynaTAIWAN is composed of two layers, namely simulation-layer and real-time control layer. The simulation layer is designed to simulate traffic flow patterns according to assumed tripmaker characteristics and/or under a set of given conditions; the real-time control layer receives real-time vehicle
Start
Determine the demand node Real-time travel time matrix
Initial Routes Generate all move from the candidate list Determine the best move
Spatial tabu list Yes
No
Does the move be tabu
No
Yes Satisfy with aspiration level
Reject the move
Update
Satisfy with stopping criterion Yes
No
Route switch
Yes
Does it have demand node No Stop
Fig. 3. The tabu search algorithm with real-time information.
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compiler C++ is chosen for the simulation core due to its efficiency; the object-oriented language Java is chosen for the GUI due to its capability of cross-platform capabilities. The sequence diagram defines message passing and interrelationship of objects and classes. In Fig. 4, the sequence diagram for simulation process is illustrated. Classes involved in this process include CTimer (simulation timer class), CNet (network class), CVehicle (vehcile class), CPath (path class), CQueue (queue class) and CLink (link class). According to the sequence diagram, the simulation process is summarized as follows:
information and forecast short-term traffic flow patterns. One of the key features of DynaTAIWAN is its ability to model mixed traffic flows in both urban streets and freeways. 4. Program implementation 4.1. Object-oriented system analysis The framework is analyzed and designed through objectoriented approach via UML (Unified Modeling Language) (Booch, Rumbaugh, & Jacobson, 1999; Fowler & Scott, 2000), and the model is implemented in C++ to inherit object-oriented characteristics. The object-oriented approach provides the capabilities to enhance the correspondence between objects and their semantic representation and to allow the user to control the levels of detail and summarize and aggregate data during decision-making. UML is a visual modeling language adopted as a standard for object-oriented modeling and design in software development by the Object Management Group (OMG). UML consists of a set of diagrams that are used to represent models of a system in diagrammatic notation through stages of development. The latest release is UML 1.3 which this paper refers to (UML 2.0 has been official announced in March, 2005). The implementation of DynaTAIWAN includes two parts: simulation core and graphic user interface (GUI). The object-oriented
:CTimer
:CNet
TempEntry:CQueue
:CVehicle
1. CTimer initiates the simulation process. 2. CNet calculates number of vehicles at this time interval, denoted as C. 3. TempEntry: generates and stores these new vehicles. 4. Setup vehicle and behavior attributes for new vehicles. 5. Calculate the capacity for LinkEntry, and move generated vehicle entities to LinkEntry. 6. Calculate the capacity for Link i, and load the vehicles onto the network. 7. Calculate the average speed for Link i. 8. Move the car and motorcycle according the average speed and adjusted speed. 9. Obtain path information from CPath, and determine the entering Link j.
LinkEntry:CQueue
i:CLink
Waiting:CQueue
INTOO:CQueue
:CPath
j:CLink
Count Vehicle-Entry() Vehicle Generated() Set Tripmakers' Attributes() Calculate Revenue Capacity()
Vehicle Added() Calculate Revenue Capacity()
Vehicle Generated()
Compute Vehicle Average Speed() move() check path()
Arrive Stop Line() Calculate Outflow()
Vehicle Added() Vehicle Added() Calculate Revenue Capacity() Repeat Until Arrive the Destination()
Arrive Destintion()
Fig. 4. Sequence diagram of simulation process.
Vehicle Generated()
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Fig. 5. The overall program structure.
Fig. 6. 50-node test network.
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N15-NR
N15-R3
N15-R5
Fig. 7. Routes for 15 demand nodes in peak loading pattern.
10. When vehicles reach the stop line, Link i calculates outflow capacity and stores the possible leaving vehicles into waiting queues. 11. Vehicles in Link i waiting queue is assigned to each downstream Link j INTOO queue. 12. Calculate possible capacity for Link j and move vehicles from INTOO queue to Link j. 4.2. Program structure The evaluation framework is implemented in object-oriented approach, and five major modules are developed. The overall program structure is shown in Fig. 5. These modules are described hereafter: 1. Input module In the evaluation framework, required data sets include timedependent O–D trip tables, VRP data, and network data. The VRP data include number of commercial vehicles, number of demand nodes to be served, and the location of the depot. The time-dependent O–D trip tables and network data are primarily used in the simulation to reflect realistic traffic environment. 2. Vehicle assignment module The vehicle assignment module processes the sweep algorithm to calculate initial routes for commercial vehicles, and these initial routes are assigned to commercial vehicles. 3. Traffic simulation module The main purpose of the module is to simulate vehicle’s movements in realistic traffic conditions. Simulated vehicles include passenger cars, motorcycles, and commercial vehicles. Passenger cars and motorcycles are generated though O–D tables and commercial vehicles are generated according to the VRP data. During the simulation, link travel costs are estimated for every simulation interval and a travel time matrix from node to node is calculated based on the Floyd–Warshall algorithm, the all pair shortest path algorithm. The travel time matrix is used in the route updating module to calculate new routes for commercial vehicles. 4. Route updating module The module uses the tabu search algorithm to re-calculate optimal routes for commercial vehicles based on real-time travel costs. The algorithm updates service sequence and paths between each pair of demand nodes. 5. Output module The module keeps track updated routes and travel time information for each vehicle.
Data and message are passed among these modules through several functions, and the message passing functions are described as follows: 1. Vehicle assignment module The module obtains commercial vehicles information through VRPdata() function, and generates initial routes for each vehicle. The initial route information is passed to DynaTAIWAN to simulate vehicle’s movements and to route updating module through AssignResult() function. 2. Traffic simulation module Traffic simulation module is constructed based on DynaTAIWAN. DynaTAIWAN obtains basic input data through Demand() function, and commercial vehicles from AssignResult() function. Real-time link travel cost and travel time matrix are stored in CostResult() function. The route updating module can retrieve cost values through CostResult() function. 3. Route updating module Based on the data from AssignResult() and CostResult() functions, the route updating module re-calculates optimal routes for commercial vehicles, and new routes are updated through RouteResultUpdate() function. 5. Numerical experiments Two networks, a 50-node test network and a real Taichung City Network, with different factors are experimented to illustrate the proposed approach and to investigate possible benefits from realtime route updating strategies. General assumptions for both networks are summarized as follows:
Table 1 The results for 15 demand nodes in peak loading pattern. Experiment
Vehicle
Number of links in the route
Travel time (min)
Improvement (%)
N15-NR
1 2 3
11 12 16
11.10 12.34 14.10
– – –
N15-R3
1 2 3
11 12 16
11.34 12.34 14.10
2.16 0 0
N15-R5
1 2 3
11 12 16
11.10 12.34 14.10
0 0 0
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Fig. 8. The Taichung City Network in DynaTAIWAN.
III-N10 -NR
I II -N10-R5
III-N10-R10
III-N10-R15
Fig. 9. Routing strategies for 10 demand nodes in the Taichung City Network.
T.-Y. Liao, T.-Y. Hu / Expert Systems with Applications 38 (2011) 12548–12558 Table 2 Summary statistics for 10 demand nodes in the Taichung City Network. Experiment
Vehicle
Number of links in the route
Travel time (min)
Improvement (%)
III-N10-NR
1 2
23 19
31.20 25.30
– –
III-N10-R5
1 2
23 19
31.10 25.30
0.32 0
III-N10-R10
1 2
23 19
31.20 25.30
0 0
III-N10-R15
1 2
23 19
31.10 25.30
0.32 0
12557
from numerical experiments. The size of the tabu list is set to 2.375 N. The maximum iteration is set to 2000. 3. The results are evaluated in an improvement index, written as follows:
Improvement Percentage ¼ ðNRITT RITTÞ=NRITT 100% ð1Þ NRITT: Travel time of commercial vehicles without real-time information. RITT: Travel time of commercial vehicles with real-time information. 5.1. Experiments and results for the 50-node test network
Table 3 Summary statistics for the Taichung City Network. Experiment
Vehicle
Number of links in the route
Travel time (min)
Improvement (%)
III-N20-NR
1 2
31 29
46.84 69.76
– –
III-N20-R5
1 2
30 29
37.70 29.77
19.51 57.33
III-N20-R10
1 2
30 31
27.80 71.80
40.65 2.92
III-N20-R15
1 2
31 31
46.84 67.92
0 2.64
1. Commercial vehicles follow the new routes assigned by the dispatching center. 2. Since no experience has been made for the tabu search algorithm on the DVRP, several important parameters are selected
Fig. 6 depicts the test network used in the current study. The network, which consists of a freeway surrounded by a street network, includes 50 nodes and 172 links. Consequently, the network has 32 origin nodes and 10 destination nodes. All arcs are one-directional and have two lanes in each direction except the entrance and exit ramps that connect the street network to the freeway, these are directed arcs with one lane as shown in the figure. Each link is 500 m long. The freeway links have a free speed of 100 kph and all other links have a 50 kph free speed. The maximum bumper-to-bumper and jam densities are assumed to be 167 vehicles/km and 120 vehicles/km respectively for all links of the network. Different car and motorcycle OD trip matrices are applied in these experiments. In these experiments, 15 demand nodes with a fixed depot are considered, and a peak loading pattern is assumed. The peak loading pattern is generated to capture possible dynamic traffic peak pattern. There are 10 time intervals within 50 min, the total
III-N20-NR
III-N20-R5
III-N20-R10
III-N20-R15
Fig. 10. Routing strategies for the Taichung City Network.
12558
T.-Y. Liao, T.-Y. Hu / Expert Systems with Applications 38 (2011) 12548–12558
number of vehicles is about 31,800, the average travel time is about 14.57 min, and the average travel distance is about 2.42 km. In these experiments, real-time travel time information is provided for a certain intervals, including 3 and 5 min, in order to reflect the journey time for commercial vehicles. N15-NR, N15-R3, and N15-R5 represent 15 demands nodes without real-time information, with 3-min and 5-min real-time information updating intervals, respectively. The results are shown in Fig. 7 and Table 1. Under this scenario, the travel times of commercial vehicles remain about the same. The routes in most of the experiments remain the same and the improvement is not significant. 5.2. Numerical experiments and results for the Taichung City Network Numerical experiments are conducted in a Taichung City Network, as shown in Fig. 8, which includes 122 demand zones, 707 nodes and 2309 links. There are two sets of experiments: 10 and 20 demand nodes with a fixed depot. All these demand nodes are randomly picked up from CBD of the Taichung Network. The initial solution, as shown in Fig. 9, is generated from the sweep method. A peak traffic loading pattern is assumed, the total number of vehicles is about 73,140, the average travel time is about 32.31 min, and the average travel distance is about 5.70 km. In these experiments, real-time travel time information is provided for a certain intervals, including 5, 10 and 15 min. The notations of N10-NR, N10-R5, N10-R10 and N10-R15, N20-NR, N20-R5, N20-R10 and N20-R15 represent 10 and 20 demands nodes without real-time information, with 5-min and 10-min and 15-min real-time information updating intervals, respectively. 1. 10 Demand nodes The results for 10 demand nodes are summarized in Table 2 and Fig. 9. The improvement of real-time information is insignificant for different real-time information updating intervals. It indicates that traffic situation might not be congested. 2. 20 Demand nodes The results are summarized in Table 3 and Fig. 10. Through the real-time route updating, travel time could be greatly reduced in most of the cases. If the updating interval is 5 min, the percentages of saving for both vehicles are 19.51% and 57.33%, respectively. If the updating interval is 10 min, the percentages of saving for both vehicles are 40.65% and 2.92%, respectively. The results show that the best updating interval is about 5 min and it provides flexibility to switch to better routes. In Fig. 10, the final routes are slightly varied from one case to another, and this might indicate that links with high congestion are avoided during the real-time route updating process. From a series of experiments, it seems that number of demand nodes might be an important factor for real-time route updating process. When the number of demand nodes increases, the possible switching number also increases and it is more likely to obtain efficient routes to reduce travel time. 6. Concluding remarks In this paper, the problem of fleet management is explored in two parts: vehicle assignment and real-time route updating. The vehicle assignment is accomplished through a classical algorithm: the sweep method. The real-time route updating algorithm is developed through the tabu search algorithm to consider possible dynamic variations of link travel times, and these algorithms are then simulated in a realistic simulation environment. Through the experiments, the sweep method provides a basic ability to
cluster demand nodes, and initial routes are able to generate through the application of the sweep method. Furthermore, the tabu search approach solves DVRP efficiently. The core of the framework, DynaTAIWAN, provides traffic simulation and assignment capabilities under mixed traffic flow conditions; however, only real-time current traffic condition is obtained. Possible predicted traffic conditions could enhance the benefits from real-time route updating. The framework provides a practical tool for the evaluation of vehicle routing strategies under real-time information. This capability is necessary to evaluate phenomena where time-variation is essential, including dynamic fleet management and real-time information systems. The numerical results indicate that real-time information could provide positive benefit only under careful consideration and design; however, interval of updating routes might lead to worse results due to overheads in route changing. The results provide useful insights into actual traffic systems, and the impact of realtime information on commercial vehicle operations. Acknowledgements This paper is based on work partially supported by National Science Council, Taiwan, ROC. Of course, the authors are solely responsible for the contents of this paper. References Bodin, L., Golden, B., Assad, A., & Ball, M. (1983). Routing and scheduling of vehicles and crews: The state of the art. Computers & Operations Research, 10, 63–211. Booch, G., Rumbaugh, J., & Jacobson, I. (1999). The unified modeling language: User guide. Reading, MA: Addison-Wesley. Bramel, J., & Simchi-Levi, D. (1997). The logic of logistics. Springer (p. 281). Brown, G., & Graves, G. (1981). Real-time dispatch of petroleum tank trucks. Management Science, 27, 19–32. Chopra, S., & Meindl, P. (2001). Supply chain management. Prentice-Hall (p. 457). Fleischmann, B., Gnutzmann, S., & Sandvob, E. (2004). Dynamic vehicle routing based on on-line traffic information. Transportation Science, 38(4), 420–433. Fowler, M., & Scott, K. (2000). UML distilled: A brief guide to the standard object modeling language. Addison Wesley Longman, Inc. Gavish, B. (1981). A decision support system for managing the transportation needs of a large corporation. AIIE Transactions, 61–85. Gendreau, M., Cuertin, F., Potvin, J. Y., & Tailiard, E. (1999). Parallel tabu search for real-time vehicle routing and dispatching. Transportation Science, 33(4), 381–390. Gendreau, M., Laporte, G., & Séguin, R. (1996). Invited review stochastic vehicle routing. European Journal of Operational Research, 88, 3–12. Ghiani, G., Guerriero, F., Laporte, G., & Musmanno, R. (2003). Real-time vehicle routing: Solution concepts, algorithms and parallel computing strategies. European Journal of Operational Research, 151, 1–11. Gillett, B., & Miller, L. (1974). A heuristic algorithm for the vehicle dispatch problem. Operations Research, 22, 340–349. Hu, T. Y. (2001). Evaluation of dynamic vehicle routing strategies under real-time information. Transportation Research Record, 1774, 115–122. Hu, T. Y., Liao, T. Y., Chen, L. W., Huang, Y. K., & Chiang, M. L. (2007). Dynamic simulation-assignment model (DynaTAIWAN) under mixed traffic flows for ITS applications. In The proceedings of 86th transportation research board annual meeting, Washington, DC. Hu, T. Y., Liao, T. Y., & Lu, Y. C. (2003). Study on solution approach for dynamic vehicle routing problems under real-time information. Transportation Research Record, 1857. Ichoua, S., Gendreau, M., & Potvin, J. Y. (2003). Vehicle dispatching with timedependent travel times. European Journal of Operational research, 144, 379–396. Laporte, G., Gendreu, M., Potvin, J. Y., & Semet, F. (2000). Classical and modern heuristics for the vehicle routing problem. International Transactions in Operational Research, 7, 285–300. Laporte, G., Louveaux, F., & Mercure, H. (1992). The vehicle routing problem with stochastic travel times. Transportation Science, 26(3), 161–170. Liao, T. Y. (2004). A tabu search algorithm for dynamic vehicle routing problems under real-time information. Transportation Research Board, 1882, 140–149. Malandraki, C., & Daskin, M. (1992). Time dependent vehicle routing problems: formulations, properties and heuristic algorithms. Transportation Science, 26, 185–200. Powell, W. B., & Spivey, M. Z. (2004). The dynamic assignment problem. Transportation Science, 38(4), 399–419. Psaraftis, H. N. (1995). Dynamic vehicle routing: Status and prospect. Annals of Operations Research, 61, 143–164.