Minimising costs in scheduling railway track maintenance

Transcription

1 WIT Press, ISBN Minimising costs in scheduling railway track maintenance M. Lake, L. Ferreira and M. Murray School of Civil Engineering, Queensland University of Technology, Australia Abstract In Australian freight operations, 5-35 percent of total train operating expenses are track maintenance related. Therefore significant savings in expenditure can be achieved if track maintenance is conducted in the most cost effective manner. Railways, however, operate under the conflicting objectives of minimising the infrastructure expenses while continuing to provide adequate service. The conflict between maintenance and train operations has intensified over recent years due to a number of factors including: increased traffic on railways; the reduction of route and track kilometres and an increasing move towards the separation of the track ownership and the track infrastructure management. This paper reports on the development of a model for the short-term scheduling of track maintenance activities, after the train schedule and maintenance activities have been planned. The model schedules the track maintenance activities, including assigning the maintenance crews to the activities, with the objective of minimising the total maintenance costs. The formulation allows different crews to be assigned to the same activity at different times and incorporates the individual set-up and take-down times required each instance an activity is conducted. This maintenance scheduling model has been solved using a two stage heuristic technique, with the first stage generating a feasible solution and the second stage implementing simulated annealing. The paper presents the results of applying the model to a problem with twenty track segments and a seven-day scheduling period.

2 WIT Press, ISBN Introduction Computers in Railways VII The maintenance of a rail network significantly contributes to the total cost of operating the network. It has been estimated that for freight operations in Australia, 5-35 percent of total train operating expenses are related to track maintenance []. The maintenance of existing networks therefore needs to be undertaken according to a plan that maximises the overall net benefit to the rail operator. Although Australian rail systems have achieved considerable productivity gains in recent times, unit operating costs are still well below world's best practice. Australian track maintenance productivity lagged behind the world's best practice by an estimated $A8 million in 993/ []. Significant savings in expenditure can therefore be achieved if track maintenance is conducted in the most cost effective manner. Railways operate under the conflicting objectives of minimising the infrastructure expenses while continuing to provide adequate service. This conflict between maintenance and train operations has intensified over recent years due to a number of factors. Increased traffic on railways and the reduction of route and track kilometres have raised traffic densities, reducing the time available to conduct maintenance, while also increasing track maintenance requirements. In addition, the railway industry in Australia is undergoing very significant changes with respect to ownership and management models, as well as operational practices. There is an increasing move towards the separation of the track ownership and the track infrastructure management, making the need to schedule track maintenance activities extremely important. In an attempt to coordinate maintenance and train operations, maintenance has been scheduled at night, outside peak train times or on the weekends [3]. This is not always feasible, however, due to other considerations in the scheduling of maintenance, such as noise restrictions, safety aspects or personnel rostering. Burlington Northern and Santa Fe have conducted maintenance by having a day shutdown of a 5 mile section of railway track to complete one years worth of maintenance []. The majority of railways would be unlikely to be able to conduct this sort of total track closure for maintenance, however, due to the lack of available personnel, equipment, detour routes or accommodating customers. Thus the need exists for a method of scheduling track maintenance in the work windows between trains. Track maintenance scheduling The majority of the research into track maintenance has focused on the planning of the maintenance, that is, determining what maintenance should be conducted. A relatively small amount of research has been carried out on reducing the conflict between the trains and track maintenance by the short term scheduling of

3 WIT Press, ISBN Computers in Railways VII oc\n the maintenance and the required resources. One such study [5], which schedules the maintenance by altering the train schedule, does not assign the maintenance crews to activities. When the number of crews for a maintenance scheduling region is small, however, the maintenance schedule should not necessarily be constructed with the assumption that enough crews are available to conduct the activities. The schedule may then need to be substantially altered to accommodate the availability of the crews. Research was also conducted by Higgins [6], with the weighted objective of minimising the maintenance activity finishing time and the expected interference delays due to delayed trains and maintenance. The objective of minimising the maintenance activity finishing times may not be the most appropriate, however, as work place agreements may not permit intensive work for a certain time, then no work for the remainder of the schedule. The train schedule treated as a fixed input, and assigns the maintenance crews to the activities, however, these crews are assigned to an activity permanently, so a different crew cannot conduct the maintenance activity at a later time. The finishing time of the maintenance activity was minimised in Higgins [6] without considering individual set-up and take-down times, only using one length of time if the work is conducted in one consecutive block or another if the maintenance is done in more than one block. The opportunity therefore exists to develop a model which optimises the short-term scheduling of track maintenance activities and the crews required, considering the factors discussed above.. Model formulation The problem of scheduling the short-term track maintenance from an existing maintenance plan and train timetable has been formulated as a mixed integer non-linear programming problem. Included in the formulation is the assignment of crews to maintenance activities and the activities, which may or may not require track closure, to track segments for given time periods. The track segment term used is a length of railway track in which only one train or activity that requires track closure may be at any one time. The objective is the minimisation of the cost of conducting the track maintenance. Aspects of the scheduling process that are considered in the formulation include: the times the various crews are permitted to work; and the set-up and take-down times required for the maintenance. The latter becomes particularly important when the maintenance is done discontinuously. Also incorporated are factors such as the restrictions on the times the maintenance activities are permitted, due to safety or other considerations; the limits on the track segments that maintenance crews are allowed to work on; and the activities that the different crews are permitted to conduct. The formulation allows different crews to be assigned to the same activity at different times or different track segments. The model therefore includes the following constraints:

4 OQO Computers in Railways VII, C.A. Brebbia J.Allan, R.J. Hill, G. Sciutto & S. Sone (Editors) WIT Press, ISBN Computers in Railways Vll. A track segment must be available, that is, it must not be occupied by a train for an activity to be scheduled on it (for the maintenance activities that require track closure).. The total number of time periods for an activity on a track segment is the production time required plus the number of time periods for the set-up and take-down. 3. A track maintenance crew must be available in a time period to be assigned to an activity.. An activity must be allowed to be conducted at a certain time period to be assigned to that time period. 5. A crew must be permitted to maintain a track segment to be assigned an activity on that track segment. 6. A crew must be allowed to conduct an activity to be assigned to that maintenance activity. 7. The appropriate ordering of the activities must be adhered to.. Solution method Due to the non-linearity and the large number of variables, applying optimisation techniques to create a solution for the formulation is difficult. The application of commercially available optimisation software was attempted, however, this meet with limited success. Some of the constraints were required to be removed, and still solutions for only certain extremely small problems could be obtained, for example 8- hours on less than 5 track segments. To achieve a good, but not necessarily an optimal solution in a limited time frame, a heuristic may be used. A heuristic method is a technique to solve a problem by trial and error when an algorithmic approach is impractical [7]. A heuristic technique consisting of two stages was applied to the formulation. The first stage generates a feasible solution, that is a solution that satisfies all the constraints but is unlikely to be the optimal solution. The second stage implements simulated annealing, which is an iterative technique that explores a set of problem solutions, moving from one solution to another in the same neighbourhood, to ultimately obtain an optimal or near optimal solution. To prevent convergence to a local optima, a non-improving solution can be accepted based on a probability which depends on the value of the objective function with the previous solution, the value with the new solution and a control parameter [8].3 Application The following situation is based on information for a section of railway track operated and maintained by Queensland Rail in Queensland, Australia. The track section in which the maintenance is being scheduled for has track segments or signalling blocks, with 5 different maintenance activities required for the scheduling period. Table gives the number of time periods of productive maintenance required for each track segment.

5 Computers in Railways \ 7 Activity 3 5 Computers in Railways VII, C.A. Brebbia J.Allan, R.J. Hill, G. Sciutto & S. Sone (Editors) WIT Press, ISBN Table : Time Periods of Productive Maintenance Required Track Segment The set-up and take-down times and track closure details for the maintenance activities are given in Table. There are four crews available at certain times throughout the scheduling period of a week, which, with a time period of an hour, gives a total of 68 time periods. Table : Maintenance Activity Requirements Activity Set Up/Take Down Time Periods Track Closure Required Yes Yes Yes No Yes Ordering Requirements Prior activity Prior activity 5 Figure, which gives the best maintenance schedule found for the track section, is a time-distance graph, with the time period across the vertical axis and the track segment on the horizontal axis. The maintenance activities are shown in the colour and pattern given in Table, with the number of the crew assigned to the activity is shown on top. The trains are identified in a time period by a "T", which forms a line as the train moves through the track section. Only a small amount of maintenance is conducted within the last two days in the scheduling period, as these are the weekend days, which have higher crew costs. Scheduled for the weekend is one block of activity, which could not be accommodated in the less expensive days as only crews and were permitted to conducted this maintenance, and activity, which must be conducted after activity. The benefits of hiring additional crews or moving certain trains can be investigated by altering some of the inputs and solving the resulting problem. Employing another crew that can conduct activity, for example, may prove to be cost effective as more work windows during the weekdays may be able to be utilised. Removing or delaying a train may create a larger work window, permitting maintenance to be conducted in a larger block, therefore reducing the set-up and take-down time required.

6 WIT Press, ISBN «57 '"-glug^.gl.g-^^l * S3 Figure : The Maintenance Schedule

7 WIT Press, ISBN Computers in Railways VII 3 Conclusions A model has been developed for the short-term scheduling of track maintenance activities, after the train schedule and maintenance activities have been planned. The model schedules the track maintenance activities, including assigning the maintenance crews to the activities, with the objective of minimising the total maintenance costs. The formulation incorporates the individual set-up and takedown times required each time an activity is conducted and is solved using a two stage heuristic technique, with the first stage generating a feasible solution and the second stage implementing simulated annealing. The results of applying the model to a problem with twenty track segments and a seven-day scheduling period were presented in this paper. The maintenance scheduling model could be utilised as a decision support tool for infrastructure maintenance planners and train operators, especially for single track operations. The model would mainly be aimed at providing an 'off-line' planning function, however, it could be used in real-time to adjust a previously constructed timetable of maintenance after unplanned train services or train cancellations. A procedure for creating the train schedule could possibly be used iteratively with the developed maintenance scheduler to produce the optimal train and maintenance timetable. Acknowledgments The research presented here was funded by the Network Access Division of Queensland Rail. The authors would like to thank in particular Mr John Davey for his support in the continuing development of the model. The views expressed in this paper are solely those of the authors. References [] Ferreira, L. and Higgins, A. Scheduling Rail Track Maintenance. Proceedings of International Conference on Traffic and Transportation Studies, American Society of Engineers: Beijing, China, pp. 8-89, 998. [] Bureau of Industry Economics. Rail Freight 995: International Benchmarking. Report 95/, AGPS: Canberra, Australia, 995. [3] Aspebakken, J. I, Galen, G. L. and Stroot, R E. Service Maintenance Planning on High Density, Heavy Haul Traffic Routes. Preprints of the 99 International Heavy Haul Workshop, International Heavy Haul Association: Vancouver, Canada, pp. -6, 99. [] Vantuono, W Shutting down to build up - BNSF's Thayer Blitz. Railway Track and Structures,9(8), pp. 3-39, 998. [5] Ruffing, J. A. and Marvel, B. M. An Analysis of the Scheduling of Work Windows for Railway Track Maintenance Gangs. Proceedings of the 99 International Heavy Haul Conference, International Heavy Haul Association, pp. -, 99.

8 WIT Press, ISBN QQ9 Computers in Railways VII [6] Higgins, A. Scheduling of Railway Track Maintenance Activities and Crews. Journal of the Operational Research Society, 9(), pp. 6-33, 998. [7] Winston, W Operations Research: Applications and Algorithms. Duxbury Press: Belmont, California, 99. [8] Osman, I. Metastrategy Simulated Annealing and Tabu Search Algorithms for the Vehicle Routing Problem. Annals of Operations Research,, pp. -5, 993.