Larsen, Allan

Madsen, Oli B.G.

Petersen, Hanne Løhmann

Røpke, Stefan

Passengers using public transport systems often experience waiting times when transferring between two scheduled services. We propose a planning approach which seeks to obtain a favorable trade-off between the conflicting objectives passenger service and operating cost, by allowing some moderate modifications of the timetable during the vehicle scheduling phase. This planning approach is referred to as the Simultaneous Vehicle Scheduling and Passenger Service Problem (SVSPSP). The SVSPSP is solved using a large neighbourhood search metaheuristic. The proposed framework is tested on data inspired by the express-bus network in the Greater Copenhagen Area. The results are encouraging and indicate a potential decrease of passenger waiting times in the network of 10-20%, with the vehicle scheduling costs remaining largely unaffected

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Downloaded from orbit.dtu.dk on: Dec 17, 2017The Simultaneous Vehicle Scheduling and Passenger Service ProblemPetersen, Hanne Løhmann; Larsen, Allan; Madsen, Oli B.G. ; Røpke, StefanPublication date:2010Link back to DTU OrbitCitation (APA):Petersen, H. L., Larsen, A., Madsen, O. B. G., & Røpke, S. (2010). The Simultaneous Vehicle Scheduling andPassenger Service Problem. Abstract from Tristan VII : Triennial Symposium on Transportation Analysis,Tromsø, Norway, .The Simultaneous Vehicle Scheduling andPassenger Service ProblemHanne L. Petersen1, Allan Larsen, Oli B.G. Madsen, Stefan RøpkeDepartment of TransportTechnical University of Denmark, Kgs. Lyngby, Denmark1 Email: hlp@transport.dtu.dk1 Problem descriptionPassengers using public transport systems often experience waiting times when transferring be-tween two scheduled services. We propose a planning approach which seeks to obtain a favourabletrade-off between the conflicting objectives of operating cost and quality of passenger service aspart of the vehicle scheduling process for such systems.The well-known Vehicle Scheduling Problem (VSP) is concerned with determining a set ofvehicle schedules to operate a given timetable at the lowest possible cost. This problem is oftenencountered within bus operation in public transport.The Simultaneous Vehicle Scheduling and Passenger Service Problem is based on the VSP, withtwo significant modifications: First, the trips of the timetable are allowed to be shifted by a fewminutes to an earlier or later departure time, in the hope that this increased flexibility can leadto a lower operating cost, without introducing significant changes to the timetable. Secondly, ameasure of passenger service is introduced for the evaluation of solutions, in order to control theeffects of this timeshifting.The measure of passenger service used in the calculations is based on the passenger waitingtimes at transfers between different lines. These transfers can take place between two lines thatare both under the control of the model (and thereby have varying departure times), or to/froma line that is external to the model (and thereby has a fixed timetable). It should also be notedthat passenger waiting times considered in this work, are only waiting times at transfers and notthose experienced by passengers entering the system.An application from the Greater Copenhagen Area is studied, dealing with the network of localexpress buses, which is build up around the local train network. A schematic overview of thisnetwork can be seen in Figure 1, where the dashed lines represent train lines (roughly with theform of a fan), and the solid lines (all shades) show the available bus lines, of which most areperpendicular to the train lines.Figure 1: The structure ofthe overall public transportationnetwork in the Greater Copen-hagen AreaThe SVSPSP takes as input existing timetables and dataregarding passenger flow at transfer points. For the SVSPSPthese passenger flows are assumed to be fixed and independentof the operated timetables. The set of input timetables dictatesthe required level of service, and the number of departures isunchanged by the solution. Additionally, each departure canonly be timeshifted by a limited number of minutes, meaningthat the overall distribution of departures over the span of theday is not changed significantly.To the authors’ knowledge, no existing literature deals witha problem identical to the SVSPSP, and few similar prob-lems have been treated, integrating vehicle scheduling andtimetabling problems. The integration of timetabling andmulti-depot vehicle scheduling is studied in [2] with the aim ofreducing costs (reducing the number of vehicles) while ignoringpassenger waiting times. The approach allows the trip startingtimes for each line to be timeshifted to allow greater flexibilityin the vehicle scheduling part. The paper presents integer pro-gramming models as well as a local search algorithm that solvesa network flow problem in each local search iteration. [1] alsointegrates vehicle scheduling and timetable synchronisation inan optimisation problem. The authors consider several termsin the objective function: number of vehicles required, numberand quality of transfer possibilities and the so-called headway evenness. The second term aims atminimising passenger inconvenience, while the last term attempts to make regular arrivals on eachline. These three terms are weighted together.2 Data issuesThe problem has been solved on a dataset derived from real-life data from the Greater CopenhagenArea, providing the geographic information and route networks. The currently operated traintimetables have been used as fixed input, and the current bus timetables have been used as thestarting point for the solution.Real-life data regarding numbers of (dis)embarking passengers at each stop are unfortunatelynot available at present, and have instead been estimated depending on line, location, and timeof day. Furthermore, a percentage distribution of (dis)embarking passengers among lines availablefor transfer has been estimated. Finally, the combination of these numbers has led to the numberof transferring passengers at each existing connection.The units of the different objectives (operating cost and passenger waiting time) have beencombined by conversion to a common monetary unit, by using the value of travel time recommendedby the Danish Ministry of Transport.3 Solution and resultsThe SVSPSP has been solved using a Large Neighbourhood Search (LNS) approach [3], wherethe initial solution is constructed using a greedy VSP heuristic on the existing timetable. Thedestroy operator removes trips either at random, or based on similarity with previously removedtrips, where the measure of similarity is based on shared trip end points or proximity in time. Atinsertion each trip may be timeshifted with a certain percentage, and the procedure is then basedon a cheapest insertion principle. The acceptance criterion for a new solution is based on simulatedannealing.The solution algorithm has been tested on instances of 3 different sizes based on subsets ofincreasing size of the real-life data. First a “small” instance, containing 3 bus lines (black inFigure 1), which all have quite many (5–6) intersections with the train network, but few connectionsbetween buses. These lines have a rather high passenger intensity, and a total of 538 trips perday. The “medium” instance contains 5 bus lines and is a superset of the small instance (blackand dark grey in Figure 1), with on average slightly fewer intersections with the train network,and not quite as many passengers (792 trips per day). Finally, the “large” set contains all 8 buslines that are in current operation in the real-life dataset, with a mixture of transfers to trains andbuses and a total of 1400 trips per day.cost red. empty time shifts3 lines 3.3% −8.9% 18.1% 73.8%5 lines 3.2% −7.8% 22.5% 78.2%8 lines 2.0% −7.1% 16.4% 76.4%Table 1: Solution improvements for different problem sizesTable 1 summarises the results obtained by running the LNS heuristic for 24 hours, withreductions compared to a reference solution obtained using the same heuristic without allowingtimeshifting. The table shows the total cost reduction, the reduction in empty mileage (a negativereduction indicating that empty mileage has increased), the reduction in passenger waiting time,and the number of trips that have been timeshifted.The total cost that is considered in the table is a combination of operating cost and cost ofpassenger waiting time, and the results show that a certain reduction of this cost (2–3%) can beobtained by the suggested solution procedure. This happens at the expense of empty mileage(increasing by 7–9%), but leads to a considerable reduction of passenger waiting time at transfers.Finally, we can see that around 75% of all trips have been timeshifted in the final timetable,indicating that timeshifting certainly has an impact.Furthermore, we can consider the degree of “memorability” of the obtained solutions, which weuse to express that the timetable is easier for passengers to remember if buses depart at regularintervals. This is appreciated by operators, but has not been included in the optimisation. Forthe solutions reported above, the memorability is in the range 35–50%, which is a considerablereduction in comparison to the reference solution, where these values are in the range 72–84%.4 Further workSome suggestions for further work on the problem presented here would be twofold; first, it couldbe interesting to obtain better data for the passenger movements in the case study, and second,some improvements concerning the solution procedure are possible.In particular, the SVSPSP could be treated as a multiobjective problem, regarding the operatingcost and passenger waiting time as separate objectives, for example by considering the improvementof passenger waiting time, that can be obtained by limiting the allowed increase of total operatingcost (possibly to zero).Furthermore, the memorability of a solution could be considered an additional objective andadded to the solution procedure. The results so far indicate that this value does indeed deteriorateunder the current solution approach.References[1] V. Guihaire, J.-K. Hao, “Transit Network Re-Timetabling and Vehicle Scheduling”, Commu-nications in Computer and Information Science 14, 135-144 (2008).[2] A. van den Heuvel, J. van den Akker, M. van Koten Niekerk, “Integrating timetabling andvehicle scheduling in public bus transportation”, Technical Report, Department of Informationand Computing Sciences, Utrecht University, 2008.[3] P. Shaw, “Using constraint programming and local search methods to solve vehicle routingproblems”, CP-98 (Fourth International Conference on Principles and Practice of ConstraintProgramming) 1520, 417-431 (1998).

The Simultaneous Vehicle Scheduling and Passenger Service Problem

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The Simultaneous Vehicle Scheduling and Passenger Service Problem

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