A dynamic approach for planning preventive railway maintenance activities
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1 A dynamic approach for planning preventive railway maintenance activities G. Budai 1 & R. Dekker 2 1 Erasmus University Rotterdam, Tinbergen Institute, The Netherlands 2 Erasmus University Rotterdam, The Netherlands Abstract In this paper some useful methods for finding optimal track possession intervals for carrying out preventive maintenance works are provided. The objective is to minimise the inconvenience for the train operators and the infrastructure possession time. In these models the train free periods are mostly used for this purpose, namely the hours between two consecutive train operations. This approach can be useful for some European railway companies for carrying out preventive maintenance works. Keywords: railways, preventive maintenance, work scheduling. 1 Introduction Statistics have shown that the demand for railway transport has increased considerably in the last few years as a result of overcrowded roads, parking problems, environmental pollution, etc. In order to satisfy the demand, there is a need for a high quality and modern railway infrastructure, for reliable service, for more trains per hour, for railway safety and improved punctuality. However, increasing the number of trains (and their speed) leads to an increase of deterioration of infrastructure. Hence, more intensive maintenance and renewal works are needed. This means that the infrastructure possession time for these maintenance activities, i.e. the time when the track is blocked from train traffic and it is handed over by the train operators to the maintenance engineers for maintenance, will increase as well. Therefore, it is more and more difficult to find a timetable for those possession intervals in such of way that railway traffic is not severely disrupted.
2 324 Computers in Railways IX The purpose of this paper is to provide useful methods for finding optimal track possession intervals for carrying out preventive maintenance works and inspections. The schedules are constructed in such a way that the inconvenience for the train operators, the disruption to and from the scheduled trains and the infrastructure possession time for maintenance is minimized. A literature review (Budai and Dekker [1]) shows that in some articles the track possession is modelled in between operations (Higgins [4] and Cheung et al. [2]). This can be done for occasionally used track, which is the case in Australia and some European countries. If tracks are used frequently, one has to go over to night maintenance, when the train traffic is almost absent. In that case one can either make a cyclic static schedule, which is made by den Hertog et al. [3] and van Zante-de Fokkert et al. [5] for the Dutch situation or a dynamic schedule with a rolling horizon, which is presented in Cheung et al. [2]. Here a more general planning method is given, which results in a dynamic timetable for preventive maintenance activities. This timetable is made such that jobs are performed as much as possible in train free periods or in hours with less impact to the operators and the number of hours required for these works is minimized, by clustering as much as possible the preventive maintenance activities. By dynamic timetable we mean that tracks are handed over by the train operators to maintenance engineers only in cases if maintenance has to be carried out on those track segments and as long as the work duration requires. Here it is also taken into consideration the situation when these train free periods are not long enough for carrying out the maintenance works, e.g. long projects. Since it is not always possible to interrupt the maintenance work by letting some trains to pass by, train cancellation is needed or one has to arrange alternative transport, e.g. buses. This paper is focusing on the infrastructure maintenance, mainly on rail, ballast, sleepers, switches and fasteners, excluding the rolling stock. 2 Problem description In some countries or regions the railway network is not densely used and on some sections only few trains run per day. This also means that between two consecutive train services there might be enough time to carry out inspections or small maintenance works. Hence one part of the maintenance work can be done not only during nights, when there are even less trains, but also in daytime in these train free periods and only big projects need to be done during nights, weekends or other low-traffic times. This is quite often the cheapest way of executing preventive maintenance. Moreover the working conditions on daytime are better than during the night in the sense of having natural light; some governments have strict rules in order to balance the working time of the maintenance crew between day and night. Since the main lines of the railway network are densely used in the Netherlands as well as in some other countries, especially during the daytime, the daily train free periods are quite short for maintenance and longer track possession time would cause severe disturbances. The trains timetable uses a repetitive basic hour pattern in which no time for maintenance possession is
3 Computers in Railways IX 325 incorporated. Thus renewal and preventive maintenance activities (even small routine maintenance works) are carried out mostly during the nights or weekends when the passenger traffic is low. During the nights some five hours are available per link for preventive maintenance and renewal work, since almost no passenger trains (sometimes some cargo trains) are operating at that time. All along this article the terms track corridors and segments or links are used. In Figure 1 A, F, I, L and N indicates major cities and B, C, D, E, G, etc. the intermediate places or stations. The track connecting cities A B-C-D-E-F is called track corridor. The track segments or links connect two consecutive intermediate places/stations, for instance A-B, B-C, C-D, etc. A track link contains single or double/triple tracks. If a link contains double/triple tracks then in the maintenance of each track will be separately planned. Thus, from now on it is assumed that track segments have only single tracks. Furthermore, if there is a junction on a link (e.g. between stations J and K), then the place where the junction starts can be defined as a dummy station or place (e.g. station J in Figure 1). If a maintenance work is carried out in one part of the link, then the whole link is out of service. It is also assumed that these track segments are approximately 5-10 km long and they have more or less same length. Figure 1: Track corridors and track segments. In this paper preventive maintenance works consists of routine (spot) maintenance activities, viz. small repairs that do not take much time and are done frequently (e.g. revision of track and switch, inspection of rail, switch, signalling system, switch lubrication) and projects, viz. larger works that take much time to be done and are carried out once/twice in few years (e.g. ballast cleaning, rail grinding, tamping) Table 1 presents different types of works, focusing on when the activities are performed and what the consequences of their possession times are. It is assumed that some of the preventive maintenance works (cases 1 and 2) on some links can be combined. Combination of projects is left out of consideration. However, a number of routine maintenance works can be combined with some projects or with some other routine works as well. Having given information about the frequency of the routine maintenance works or/and the type of projects that have to be scheduled in a given year and their duration, in Step 1 a plan is defined that gives which work will be performed on which segment in which time period (month/week/hours). The
4 326 Computers in Railways IX routine works have different frequencies and some projects are carried out on parts of the network once/twice in 1-7 years; in the beginning of each year it is identified which projects will be carried out in that actual year. If the duration of a project lasts few weeks/months, then they are scheduled for consecutive weeks/months. The possible earliest and latest starting times for each project are known beforehand. Table 1: Classification of the maintenance works. case Type of work When is the work performed? Works which do not take much Daytime, during time and works which are not train services 1 done on the track, only next to a used railway track, doesn t affect the track or the catenary system; e.g. visual inspections Works with short duration and During train free done on the track, affecting the periods within track. Furthermore works can operation if risk is 2 be split up, i.e. works which acceptable, or can be interrupted by passing nights in train trains; e.g. changing clips free period if risks are not acceptable Projects which take longer time Daytime or nights and cannot be split up and with blocking these major works done on the train services 3 track; e.g. tamping, switch renewal Possession consequences Work does not require separate possession It might be unsafe for the maintenance crew. Train service is interrupted: cargo trains are rerouted, passenger trains cancelled. Better utilization of the resources. Here are mentioned three ways for executing projects. In the first two cases it is assumed that the projects can be interrupted and in the third case not. In the first case the projects are performed only in the maximum length train free periods (once per day) on a number of consecutive days. In this way there is no disturbance for the train operators and there is no need for train cancellation. However projects take more time, thus the so-called cost associated for not using efficiently the resources (machines and human resources) is much higher, since moving the equipments only for few hours per day to the place where maintenance should be carried out is not very effective. Therefore, in the second case it is assumed that projects are carried out on weekends, blocking the track segments for 48 hours. The penalty cost for blocking the train operation will be quite high, but on the other hand the machines and the equipments will be used better. Moreover three shifts of maintenance crew can work continuously in two consecutive days. The third option results in the best utilization of the resources, since the execution of the projects is scheduled for a number of consecutive
5 Computers in Railways IX 327 weekdays and weekends respectively, blocking the train operation for a couple of days or weeks, for 24 hours per day. This means also that the amount that is given out for cancelling trains for these days will be high. From these three cases the one with the lowest penalty cost and the highest utilization factor (i.e. the lowest penalty cost for not using efficiently the resources) will be selected. The costs for cancelling trains and the penalty costs assigned for the utilization of the resources are set by the model users, actually by the maintenance planners. The calculation of these costs is a very tough work, because cancelling a train for even few hours on a given segment would cause big disturbances in the whole network, so it is difficult to evaluate what the real losses are and how much money it would cost to the railway company. There is an extra cost, called possession cost, that is paid each time period when a track is handed over by the train operators to the maintenance engineers for maintenance. The objective is first to minimize the infrastructure possession time and consequently the cost of possession by clustering as much as possible the preventive maintenance works, but still balancing the workload for the maintenance crew. Secondly, the projects are planned such that cancellation cost plus the penalty cost assigned to inefficient utilization of the resources is minimized. In Step 2 a detailed planning is made for those time periods (e.g. weeks, months) for which at least one preventive maintenance work (cases 2 and 3 from Table 1) has been planned. This approach is subject of a next article. The resulting model is an integer-programming problem, with constraints on track availability, work continuity and work deadline. 3 Model description The purpose of the authors through this paper is to give an optimal dynamic schedule for carrying out preventive maintenance works. This is done in two steps. In the first step maintenance works are assigned to different time periods (months/weeks) and to different track segments and in the second step the previously defined jobs per time periods are assigned to train free periods or extensions of them. The latter case happens if delays or trains cancellation are needed in order to have long enough time windows for maintenance. In the optimisation activities are combined in a given link for a given time interval. Next the mathematical formulation of Step 1 is presented; Step 2 is treated later. STEP 1 Let PA and RA be sets of projects and routine works respectively, which have to be done within the planning horizon T. By A = PA RA the set of all activities is denoted. Let L be a set of track links in a given corridor. The planning horizon T (e.g. years) is split up into discrete time periods (e.g. months, weeks). Let K={1,2,3} be a set of options regarding the execution time of the projects. Parameter max l denotes the maximum length of the train free period on link l L. The combinable works are given in the set Comb= {( m, n, l) works m and
6 328 Computers in Railways IX n can be combined on link l, m, n A, l L}. Parameter G al denotes the frequencies per planning horizon T of activities a RA on link l L; =0, if activity a RA is not relevant for link l L. TW denotes the total workload (in hours) for project p PA on link l L. Furthermore, the binary parameter I pl denotes whether in planning horizon T a project p PA has to be performed on link l L, or not. Let the duration of project p PA on link l L using option k K be D = ceil /(7 max )) if k=1 or ceil( TW / 48) if k=2 ( TW pl l or ceil( TW pl /(7 24) ), where ceil denotes the ceiling function. Let LST pl and UST pl be the earliest/latest possible starting time of project p PA on link l L and F = ceil T / G ) denotes the planning cycle for each routine work a RA al ( al on different links l L. Let Clt be the cost for possession of link l L at time t T, CCostkl is the cancellation cost on link l L using option k K and MCost is the penalty cost for resource utilization if option k K is chosen for performing project p PA on link l L. The decision variable X alt indicates whether activity a A on link l L is assigned to time period t T, or not. Furthermore M denotes whether period t T is used for preventive maintenance lt work, or not, while Y t indicates whether the execution of project p PA starts at time t T on link l L if option k K is chosen, or not. Variable B indicates whether the execution of project p PA on link l L is done according to option k K, or not. The track possession problem can now be formulated as follows. Min C M + B D CCost + MCost ) lt lt ( kl l L t T k K p PAl L X alt = G al a RA l L t T pl pl G al s.t. (1), (2) X = I D B p PA, l L (3) plt pl t T k K mlt + nlt s+ Fal 1 s+ Fal 1 T alt + X alt t= s t= 1 T + 1 X X 1 t T, ( m, n, l) Comb (4) X 1 a RA, l L, s T (5) D Y = p PA, l L, t (LST,UST ) t B t= 1 t + D 1 s= t k K X pls D * Y t pl pl k K (6) p PA, l L, t T, t T D +1, I = 1, k K (7) B = 1 p PA, l L (8) pl
7 Computers in Railways IX 329 M a A, l L, t T (9) X lt X alt alt { 0,1 }, M { 0,1 }, Y { 0,1 }, B {0,1 } lt t a A, t T, l L, k K (10) The objective minimizes on one hand the number of time periods for which maintenance work is planned per planning horizon T and consequently the possession cost and on the other hand the cost for carrying out the scheduled projects. Actually there are three possibilities for performing the projects. That option is chosen which gives us the lowest combination of the penalty cost for cancelling trains and inefficiently used resources. Constraints (2) and (3) ensure that all routine maintenance activities and projects respectively are assigned to the right number of time periods for each link. On the same link and at the same time only combinable activities can be carried out. This is ensured by Constraint (4). These combinable jobs can be either routine works or projects. Constraint (5) forbids the routine maintenance works to be carried out on time intervals close to each other. It has to be F al time periods between two subsequent occurrences of the same job on the same link. Constraint (6) warrants that the starting time for performing the projects is in the interval (earliest possible starting time, latest possible starting time). If the starting execution time for each project has been chosen, then the projects are assigned to subsequent intervals. This is ensured by Constraint (7). Constraint (8) warrants that one of the three execution options is chosen for performing the identified projects. Constraint (9) ensures that time period t T will be used for preventive maintenance work if and only if for that time period on one of the segments at least one work is planned. Constraint (10) ensures that the decision variables of the model are binary. In Step 1 a maintenance plan is presented per planning horizon T. This plan gives us which maintenance work will be carried out on which segment in which time period. This schedule is used in Step 2 as input information. Therefore, a detailed hour based planning is made for each of the time periods for which in Step 1 at least one maintenance work has been scheduled. 4 Numerical example The maintenance scheduling problem can be modelled in GAMS as an integer programming problem and solved using state-of-the art MIP solvers, like CPLEX 7.1. The following hypothetical example is meant for testing the model presented above. Five different types of maintenance works are considered, three routine maintenance works and two projects. RA={r1, r2, r3}, PA={p1, p2} and T=1 year. A time plan in weeks is made. Furthermore, it is assumed that each routine maintenance work has different frequencies and they can be combined on some links with other routine works or projects. We assume that the corridor is not densely used; approx trains are operating per day and each track link has a length of 8-10 km. L={L1, L2, L3, L4, L5} is the set of links, e.g. in Figure 1 the upper corridor: A-B-C-D-E-F. The track possession cost is assumed to be constant over time and over links and it is 100 per link. Table 2 summarizes the
8 330 Computers in Railways IX data for the routine works per year and per link. The identified projects, their duration and the possible starting times are given in Table 3. The cost structure for performing the identified projects is plotted in Table 4. The result for one scenario after running Step 1 is shown in Table 5 and in Figure 2 the annual maintenance planning is shown. Table 2: Routine maintenance works frequencies per year. Routine work Frequency T=52 weeks L1 L2 L3 L4 L5 R R R Table 3: Identified projects; their duration and earliest/latest starting time. Projects Identification Project Total workload (hours) T=52 weeks L1 L2 L3 L4 L5 L1 L2 L3 L4 L5 P P Earliest starting time (weeks) Latest starting time (weeks) P P The optimal objective value for scenario 1 shows that the total number of links on which at least one maintenance work has been scheduled is 57 (33% lower than not applying this method and planning separately each maintenance work, which is 85 links), resulting in a 5700 possession cost. Table 4: The cost structure for different projects under different scenarios. Options Cancellation cost Penalty cost for inefficient resource utilization L1 L2 L4 L1 L2 L Furthermore, carrying out three type of routine works on five links and two projects on three links leads to a cost of 5865, which is actually a combination of costs for cancelling trains in order to carry out long projects and of a penalty
9 Computers in Railways IX 331 cost which is paid if the resources (equipment, machines and the human resources) are not used efficiently. In the annual planning from Figure 2 one can see, that combination of multiple works on the same link has an effect on minimizing the track possession times. On some weeks no work has been scheduled, which means that the maintenance crew can work on another part of the railway network, carrying out maintenance on other segments belonging to other corridors. At this moment the cheapest option for carrying out the two projects in three links is to perform each of them on consecutive days, nights and weekends, so this results in a combination of penalty cost for inefficient usage of the resources and train cancellation costs of 165. Table 5: Combination of works T=52 week (r1,r2),(r1,r3),(r2,r3) l L (r1,p1- L1),(r3,p2-L2), (r2,p2- L4) Val.Opt Solut. Results for different scenarios. Nr. used links/yr. Val. LP relaxat. Sol. time (sec) Statist var constr. Link Work Type L1 L2 L3 L4 L5 R1 R2 R3 P1 R1 R2 R3 P2 R1 R2 R3 R1 R2 R3 P2 R1 R2 R3 Annual Maintenance Planning 1 st quarter 2 nd quarter Figure 2: Annual maintenance planning.
10 332 Computers in Railways IX The running time of the program can be reduced if a separate model calculates the best execution option for each project. The chosen option for each project can then be used in the rough maintenance planning model. 5 Conclusion In this paper an optimization model is presented, which aims to improve rail maintenance decisions by creating a dynamic schedule for carrying out preventive maintenance activities. The approach presented here has two steps, while here only the first step has been elaborated. In the first step maintenance works are assigned to different time periods (months/weeks) and to different track segments and in the second step previously defined jobs per time periods are assigned to train free periods or extensions of them. Routine maintenance works and projects are planned together. The example shows that combining some routine works with projects or with other routine works results in a 33% reduction in the track possession time and cost. This planning approach has some weaknesses, namely it can be only used for planning the maintenance works of tracks between two cities or stations and not including the maintenance work of the infrastructure in the stations. Secondly, the maintenance crew allocation is also not included in the present model. These issues need further research. Acknowledgement We would like to thank the experts from the Strukton Railinfra, the Netherlands, for providing us information about planning railway maintenance activities. References [1] Budai, G. and Dekker R., An overview of techniques used in planning railway infrastructure maintenance and its effect on capacity, Report, Reprints Series Econometric Institute EI-1230, Erasmus University Rotterdam, [2] Cheung, B.S.N., Chow, K.P., Hui, L.C.K. and Yong, A.M.K., Railway track possession assignment using constraint satisfaction, Engineering Applications of Artificial Intelligence, vol. 12, p ,1999. [3] Den Hertog, D., Van Zante-de Fokkert, J.I. and Sjamaar, S.A., Beusmans, R., Safe Track Maintenance for the Dutch Railways, Part I: Optimal working zone division, Report, University of Tilburg, [4] Higgins, A., Scheduling of railway maintenance activities and crews, Journal of the Operational Research Society (49), p , [5] Van Zante-de Fokkert, J.I., Den Hertog, D., Van den Berg, F.J. and Verhoeven J.H.M., Safe Track Maintenance for the Dutch Railways, Part II: Maintenance schedule, Report, University of Tilburg, 2001.
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