Approaches for train vehicle maintenance

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Delft University of Technology

FACULTY MECHANICAL, MARITIME AND MATERIALS ENGINEERING

Department Maritime and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl

This report consists of 8 pages. It may only be reproduced literally and as a whole. For commercial purposes only with written authorization of Delft University of Technology. Requests for consult are only taken into consideration under the condition that the applicant denies all legal rights on liabilities concerning the contents of the advice.

Specialization: Transport Engineering and Logistics

Report number: 2013.TEL.7810

Title:

Approaches for train vehicle

maintenance

Author:

C.J. Berenbak

Title (in Dutch) Benaderwijze voor het onderhoud van trein voertuigen

Assignment: literature Confidential: no

Initiator (university): Prof. dr. ir. Gabriel Lodewijks

Initiator (company): -

Supervisor: Dr. Francesco Gorman

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Delft University of Technology

FACULTY OF MECHANICAL, MARITIME AND MATERIALS ENGINEERING

Department of Marine and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl

Student: C.J. Berenbak Assignment type: Literature

Supervisor (TUD): Dr. Francesco Gorman Creditpoints (EC): 10 Specialization: TEL

Report number:

2013.TEL.7810

Confidential: No

Subject: Approaches for train vehicle maintenance

Railway traffic is operated following the combination of physical equipment (vehicles and infrastructure), managerial processes (the published timetable), and human resources (crew and control room personnel). Disruptions of the process are very common, on average more than 15 per days, partly relating to the unavailability or problems with train vehicles or rolling material. In fact, trains are very costly assets that require preventive maintenance to match safety regulation and achieve a high level of reliability during operations. Strive for efficient operations and reduction of fixed costs (purchase) and operating costs (i.e. old inefficient vehicles are dismissed or used as least as required) make fewer trains run more, at the cost of increased maintenance and risk of failures. This literature assignment is to study and make an overview of the approaches and technologies used for train vehicle maintenance. In particular,

• Identify preventive maintenance regulations and requirements (e.g. periodic on operating hours; periodic on operating km)

• classify different preventive vehicle maintenance strategies

• review models and approaches for integrating preventive train vehicle maintenance management into operations, such as making rolling stock rosters with bundled maintenance periods

• Corrective maintenance and extent of the most common problems

• analyze effect of train maintenance on operations, from the point of view of time required; and of disruptions caused.

This report should be arranged in such a way that all data is structurally presented in graphs, tables, and lists with belonging descriptions and explanations in text.

The report should comply with the guidelines of the section. Details can be found on the website. The mentor,

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3

Summary

In the Netherlands the total amount of rolling stock in operation is around 3000 carriages. These carriages are maintained by NedTrain at approximately 40 locations spread over the Netherlands. These locations can be split between locations for daily checks at railway stations, maintenance depots and refurbishing and overhaul workshops. Maintenance depots are generally visited by rolling stock once every three months or after traveling 30.000 km, the refurbishing and overhaul workshop is visited once every five to fifteen years. The distance travelled by trains in the Netherlands in 2011 was 161 million km of which 147 million km was travelled by passenger trains.

The maintenance of rolling stock is of vital importance for smooth and safe operation of railroad operations. Since most rolling stock will be used by passengers, safety and comfort are of great concern, the tolerance for disturbances is because of the great visibility extremely low. The government has a lot of influence on the public transport companies and demand high levels of safety and reliability with the use of legislation and performance agreements.

To reach the required level of safety and reliability needed of rolling stock, preventive maintenance is required. Maintenance in general can be accomplished using a number of different approaches. The three most relevant approaches to maintenance of rolling stock are corrective maintenance, preventive maintenance and condition based maintenance. Corrective maintenance is using a machine or in this case rolling stock till it breaks. After a part breaks, the broken part is fixed and the rolling stock is used again till the next part breaks. This leads to unreliable and unsafe operations of rolling stock. Preventive maintenance is maintaining the parts of rolling stock after a certain amount of time or usage. If preventive maintenance is carried out correctly, parts are maintained before they would break down, making the rolling stock much more reliable. For condition based maintenance, individual parts are monitored with for example the use of sensors, parts get maintenance once the sensors notices that maintenance is required. Condition based maintenance can lower the amount of maintenance required but also requires more effort to collect the data from the sensors.

One of the most important aspects of preventive maintenance is planning. Maintenance workshops have a certain capacity, increasing this capacity for peak loads can be very expensive. Maintenance has to be planned in such a way that the demand for maintenance is constant and peak loads are limited, but the rolling stock also have to be maintained close to the required date. Doing maintenance too early will increase the cost since more maintenance actions will be done over the lifetime of the rolling stock. Doing the maintenance too late will lead to lower reliability and safety. Another important aspect related to maintenance is how to get the rolling stock to the required location. Preventive maintenance happens at a limited number of workshops located through the country. Driving rolling stock specifically for maintenance across country is very costly and would also impact the planning of the normal train service. The best option would be to take the need for maintenance of rolling stock into account while making the planning for the normal train service and move the train during normal operations towards the workshop. This can be mainly done during shuttling operations on train stations where trains can be assigned a certain route.

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Table of content

1. Introduction 2. Real life situation 3. Maintenance types 4. Preventive maintenance 5. Scheduling 6. Maintenance routing 7. Conclusion 8. Bibliography

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LITERATUUR ASSIGNMENT , DELFT UNIVERSITY OF TECHNOLOGY, NOVEMBER 11, 2013 1

Approaches for train vehicle maintenance

Coen Berenbak

Abstract—Rolling stock require preventive maintenance to satisfy the safety regulations and operate at a required customer service level. Since rolling stock is capital intensive with a long lifetime, schedules have to be made to minimize the cost of maintenance. Getting the rolling stock to the workshop where the maintenance will be done, is another challenge. This process has to be done with the least amount of disturbances to the regular roster and for low cost. In this paper an overview is given of a number of models concern with the discussed challenges.

Index Terms—Preventive Maintenance, Rolling Stock

I. INTRODUCTION

T

HE MAINTENANCE of rolling stock is of vital impor-tance for smooth and safe operation of railroad opera-tions. Since most rolling stock will be used by passengers, safety and comfort are of great concern, the tolerance for disturbances is because of the great visibility extremely low. The government has a lot of influence on the public transport companies and demand high levels of safety and reliability with the use of legislation and performance agreements. This paper gives an overview of models available that are relevant for preventive maintenance of rolling stock. In the first chapter an overview will be given of the situation in the Netherlands. The second chapter will give an overview of three different approaches to maintenance and provide more information on preventive maintenance. The third chapter will focus on planning preventive maintenance. Finally, routing rolling stock towards a workshop will be discussed.

November 11, 2013 II. REAL LIFE SITUATION

The different maintenance approaches described in this paper are related to the train service in the Netherlands. The company that is responsible for the maintenance of the rolling stock in the Netherlands is NedTrain. According to ¨Ozkan (2008) [1] and Vernooij (2011) [2] the amount of rolling stock in service consists of about 3000 carriages and a single carriage costs about 2.500.000,-. On average a train consists of around 5 carriages so this means that there are approximately 600 trains that NedTrain maintenances. For the maintenance of the trains NedTrain has over 40 locations spread over the Netherlands. These locations can be split into three types: service depots, maintenance depots and a refurbishment and an overhaul workshop. At the service depots a train is being cleaned during the night, some small tests are done to check the systems and small repairs can be made if needed. The second type of maintenance locations are maintenance depots (MD), there are three reasons why a train has to go to a maintenance depot: 1. All rolling stock goes to the MD after a certain amount of time or kilometres driven (preventive maintenance). 2. If during one of the checks in the service

depot problems are detected which the service depot cannot repair themselves, the rolling stock is moved to the MD (corrective maintenance). 3. If the rolling stock breaks down in the field (corrective maintenance).

During normal operations (no corrective maintenance needed) rolling stock goes to the maintenance depot about once every three months. The last location is the refurbishment and overhaul workshop, every five to fifteen years all the main parts of the rolling stock are replaced by refurbished ones. NedTrain uses three different types of parts in their operations: consumables, repairables and main parts. Consumables are the parts that are discarded after being used for a certain amount of time or distance, these parts are generally the cheapest. The repairables can be repaired after they have been used. The main parts will also be repaired but differ from repairables in terms of cost, technical importance and uniqueness. The details of every individual main part is stored in a database. An example of a main part is given in figure 1. The website rijdendetreinen [3] keeps track of the number of disturbances on the Dutch railroads, the total amount of disturbances where 2.074 over 2012 of which 261 were caused by defect trains. The total amount of distance travelled by trains in the Netherlands according to the Intermediate report on the development of railway safety in the European Union (2013) [4] in 2011 where 161 million km of which 147 million km where passenger trains.

In a phone conversation with Manager Maintenance De-velopment of NedTrain, Bob Huisman [5] stated that the time at which preventive maintenance is required is mainly planed by distance travelled followed by time. Some of the more common parts that require corrective maintenance are automated connections and the doors of rolling stock. These corrective maintenance actions are mainly done by service crews located at a number of stations. If the service crew cannot repair the broken part, the rolling stock has to be taken to a maintenance depot. If a rolling stock visits a maintenance depot between scheduled maintenance sessions, only the broken part is fixed after which the rolling stock is returned to the roster.

Compared to the viewpoint of Özkan (2008) and Vernooij (2011), Maróti and Kroon (2004, 2005) [6] [7] looked at the Dutch train system from the view point of the Dutch train operator NS Reiziger instead of NedTrain. NS Reiziger is responsible for the transportation of passengers and daily planning of the routes the trains will take. According to them the rolling stock needs preventive maintenance every 30.000 km or roughly once every month depending on the train type. This time estimate is different than the one stated by Özkan and Vernooij, an explanation can be that Marti and Kroon look from the viewpoint of NS Reiziger instead of NedTrain.

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Fig. 1. Example of a Bogie.

III. MAINTENANCE TYPES

According to Smith (1993) preventive maintenance can be split in four different approaches of which one is an approach that is purely based on the decision making. The main goal of this approach is to determine if it is necessary to maintain that particular part. As example the spare tire of a car is given. Is it really necessary to maintain that spare tire in a country like the Netherlands, car service is one call away so the part does not have to be reliable. Since this approach is not extremely relevant for train maintenance, the paper will focus on the other three approaches. The first approach is corrective maintenance which is in fact run till it breaks. When the corrective maintenance strategy is used, the machine or in this chase, rolling stock is used till a part breaks down. Once a part breaks down, the part will be replaced and the rolling stock will be used again till the next part breaks down. The main advantage of this approaches is that the parts are being used till the end of their lifetime, disadvantages are the very low reliability of the rolling stock and lack of safety. Depending on which part breaks, getting the rolling stock to a workshop can be extremely expensive. The second maintenance strategy is preventive maintenance. When preventive maintenance is used, parts are replaced after a certain amount of time or amount of uses. In the case of rolling stock this can be distance travelled. The main advantage of preventive maintenance is the increase of reliability since parts are already changed for new ones before they break down. The main disadvantage is the fact that the parts are replaced before their entire lifetime has been used, increasing operation cost. The last maintenance strategy is condition based maintenance. In the case of condition based maintenance parts are being monitored, once their lifetime is nearly over, they are replaced with new parts. The parts can for example be monitored with the use of vibrations or the composition of the lubrication. Once the number of certain particles reaches a level in the lubrication, the part has to be changed. The main advantage is that a high reliability can be reached but parts still can be used to near the end of their life time, the disadvantage is the extra cost and effort involved with the monitoring of the parts.

IV. PREVENTIVE MAINTENANCE

Preventive maintenance can be accomplished using a num-ber of different approaches. The first approach is the use

of time-based preventive maintenance. The original equip-ment manufacturer (OEM) almost always provides some sort of maintenance and operations manual with the delivered equipment. The documentation can be used to determine after how many uses or time the equipment needs preventive maintenance. According to Smith (1993) [8] the maintenance manual provided has not necessary been thought trough for a comprehensive and cost-effective fashion and is mainly fo-cused on protecting the manufacturer for equipment warranty. This is the origin of many conservative preventive maintenance tasks.

Another approach which originally originate from the aircraft industry is Reliability-Centred maintenance (RCM). RCM was created as response to rapidly increasing main-tenance cost, poor availability and concerns about the ef-fectiveness of time-based preventive maintenance. Kister and Hawkins (2006) [9] state that the general used definition of RCM is that it is a process used to determine the maintenance requirements of any physical asset in its operating context. Perhaps a more complete, or accurate, definition is that RCM consists of processes used to determine what must be done to ensure that any physical asset continues to do whatever its user wants it to do in its present operating context. Preventive maintenance is based on the assumption that the age-reliability pattern of parts have a bathtub curve, meaning most parts fail at the beginning or at the end of their lifetime. At the beginning of the lifetime of parts, more failures are expected because of production or material errors, at the end of the lifetime because of fatigue and wear. In figure 1 a summary of an extensive investigation in the late 1960s by United Airlines is shown [10] A number of interesting conclusion can be drawn from the figure. Only four percent of the components follow the traditional bathtub curve concept. More importantly, only six percent of the components experienced a distinctive aging region during the components lifetime. 89 percent of the parts never saw any aging or wear out mechanisms develop over the components lifetime. The most interesting conclusion is that in 68 percent of the components, the overall reliability is actually lowered when the components are replaced. The conclusion drawn from this research is that one must be very carefully what component get replaced and what not. This means that RCM is mainly useful for preventive maintenance of series of equipment like aircrafts or rolling stock since a lot of data is needed to determine the correct strategy.

V. SCHEDULING

The first set of models that will be discussed in the paper are about scheduling maintenance. The time between preventive maintenance cannot be too long since reliability will become lower. This in turn influences the customer service and the safety requirements. If preventive maintenance is done too soon, cost will rise since more manpower is required. The availability of space in the workshop and the availability of the rolling stock itself also have to be taken into account. The different models will be discussed in the following order. First the problem will be discussed and after that the scope of the model will be given. Next the approach will be discussed followed by the conclusion and findings they proposed.

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Fig. 2. Age-reliability patterns for non-structural aircraft equipment (United Airlines).

Helm, Painter and Oakes (2002) [11] give a comparison between three different methods for scheduling preventive maintenance for high cost, long-lived capital assets. This is valid for rolling stock since they are high cost, earlier is stated that a single carriage cost about 2.5 million euro. The planed lifetime of rolling stock is according to NS [12] 30 years but the oldest current operational rolling stock by the NS is 47 years old. Examples of other high cost, long-lived capital assets are airplanes and boats. The main topic discussed in this paper is a comparison of the three different methods. The scope is high cost capital assets with an assumed lifetime of 50 years. The approach of this paper is to measure the difference between the three different methods using the height of the peaks when maximum maintenance is required. The maintenance capacity required for a workshop is the height of such peaks, so the lower the peaks the better. In the case of this comparison a constant maintenance requirement is the best possible result. The three method classes are quasi-manual using standard spreadsheet technology, a Constraint Programming-based software package and a genetic program written specifically for this application. The conclusion drawn from their comparison is that the spreadsheet approach has the least amount of maintenance hours but the highest peaks. The constraint programming based approach has the most maintenance hours but the peak is lower than the spreadsheet approach. The genetic program approach has the lowest peak but more maintenance hours are required then the spreadsheet approach.

In the model proposed by Vernooij (2011) the main focus is how to plan the preventive maintenance and revisions in such a way that peak loads are minimized. The problem described by Vernooij is that the capacity of the workshop is limited so during peak loads problems can arise. To avoid problems the workload has to be spread over time. The peak loads originate from the fact that bogies of a certain type come in the field at approximately the same time, so the revisions are also at the same time. The scope of the model is focusing on the

bogies of the rolling stock that is maintained by NedTrain. These main parts are chosen since they are in this case the most interesting part and the model can easily be translated to the other main parts of the rolling stock. The approach to the problem compared with most other models is a bit more extensive. This model also takes the finite lifetime of the rolling stock into account and tries to plan the maintenance in such a way that the time between the last maintenance and the end of the equipment lifetime is as large as possible. The model is based on information obtained from NedTrain making it very useful for modeling the current situation of maintenance in the Netherlands, but the model does not take the availability of trains into account. The assumption is that trains are always available for maintenance while in reality a train is only available for maintenance once every three months. The conclusion drawn by the author is that if the model is used, it is possible to flatten the peaks in maintenance requirement. The real problem described before, that some periods the capacity is fully used and other time noting happened, can only be solved by spreading the revision deadlines over time. The planning of the maintenance by NedTrain is currently short term, according to the author, long based planning could reduce the maintenance capacity needed and reduce costs.

In the model proposed by Sriskandarajah, Jardine and Chan (1998) [13] a Genetic algorithm was developed to optimize the maintenance overhaul scheduling of rolling stock. The model is developed for the Mass Transit Railway Corporation in Hong Kong to plan the overhaul maintenance for an annual planning. The scope of the model is about 95 trains that are used for the three metro lines in Hong Kong. For modeling the problem a genetic algorithm (GA) is used, it is implemented in the following way: GAs view sequences (of train) as individuals (the candidate schedules or solutions), which in turn are members of a population. Each individual (a schedule) is characterized (merited) by its fitness (for example, the total penalty for not satisfying the due dates). Therefore the fitness of an individual is measured by the associated value of the objective function (here the total penalty for not satisfying the due dates, the smaller the better). The GA procedure works iteratively (emulating an algorithm) with the members of the population and each new iteration in the GA terminology being referred to as a generation. In GA the individuals that have the highest fitness are being used for the next generation, this is repeated until the desired number of generations is created. By recording the best population a maintenance schedule can be created. The approach to the problem had to take a number of challenges into account. The first challenges for the model is the fact that the maintenance of the rolling stock changes from single unit to train based. A train consists of three different types of units which have their own maintenance requirements. The new planning has to schedule the maintenance of the trains in such a way that the date of maintenance does not deviate too much from the required maintenance date of the individual units the train consists of. The model also takes the limited space for maintenance, workdays and holidays into account. To minimize the maintenance cost, no idle time in the workshop is allowed. Maintaining a train too soon may be costly since extra manpower is required while maintaining a train too late will

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decrease reliability which in turn affects customer service. By assigning penalties too maintaining a train too late or too early and minimizing the overall penalty, the overall schedule will be optimized. The conclusion drawn from the model is that computed results with the Genetic algorithm is highly efficient and gave near optimal results. A total cost reduction of 25 percent for the two years where the planning is determined by the model can be reached. The new schedule however could not be used in practice because of the large number of switches of units between trains, the recommendation from the authors is to use the model over a longer time period to optimize the amount of switches.

In the model proposed by Cheng, Yang and Tsao (2010) [14] the rolling stock maintenance strategy is determined through multiple criteria decision-making by expert choice. The prob-lem discussed in the paper is how to balance preventive and corrective maintenance while also taking safety and comfort into account. The model focuses on general mathematical results, but is checked with the use of data of 321 metro rolling current collecting shoes. The model is based on a staged approach. First the Analytic Network Process (ANP) method is used to obtain the appropriate maintenance strategy and to decide the evaluation factors. ANP is a type of Hierarchical models, the building of an ANP model requires the definition of elements and their assignment to clusters. ANP is founded on ratio scale measurements and pair-wise comparisons of elements to derive priorities of selected alternatives. To provide the data for the ANP model a two phase questionnaire is used to determine the weight factors and sub-factors. The second phase of the model is to decide the possible ratio between preventive maintenance and corrective maintenance with the use of the data collected with the ANP method. The final phase is to determine the optimum number of spare parts in storage that is needed when the earlier calculated balance between preventive and corrective maintenance is used. An interesting conclusion from the weight factors in this model is that safety is far more important for the maintenance strategy then cost and reliability or quality and efficiency. To use this model in a real life situation, planning also has to influence the model. The model only determines the optimal replacement interval of the parts and does not take availability or lifetime of the rolling stock into account.

VI. MAINTENANCE ROUTING

The second set of models that will be discussed in this paper is about how to get the rolling stock at the correct location. As stated before, only at a certain number of locations through the Netherlands preventive maintenance on rolling stock can be undertaken. The rolling stock that needs maintenance must be directed to the correct location with the least amount of disturbances to normal operations and with as little extra cost as possible.

The first two models that will be discussed are proposed by Mar´oti and Kroon (2004, 2005). The problem definition in both models is the same but the method is different in each model. NS Reiziger makes a rolling stock schedule with a fixed planned horizon of three days. This rolling stock schedule

Fig. 3. Directing a single urgent rolling stock unit towards maintenance..

contains all rolling stock movements between different stations but not the movement of rolling stock inside the stations themselves. The movement inside a station is described as shunting plans created by the local shunting crew. If a rolling stock requires preventive maintenance, the rolling stock has to be directed towards a certain location. This is mainly done by switching two or more trains inside a station so the train that needs preventive maintenance goes towards the required station. Maintenance planners try to make a planning that will lead the rolling stock that needs maintenance towards the correct station within the deadline. In figure 2 an example of a maintenance planning is presented. The thick lines represent tasks, the dashed lines indicate the regular transitions and the arrows the new transitions that lead the urgent rolling stock that requires maintenance towards the maintenance location.

For the transitions shunting plans are required. Creating shunting plans for a single middle sized station is a difficult problem so maintenance route planners themself cannot decide the practical feasibility of a modified plan. Therefore they must contact the local shunting crew to check if the proposed scenario can be carried out. The communications between the local shunting crew and the maintenance route planners takes time therefore they are usually satisfied with the first available solution. In the two models, changes to the original planning get a cost value. The higher the impact of the change, the higher the cost. The measure of how hard the new scenario is compared to the original scenario is basically the sum of all the costs. The goal of the two models is to develop an interactive decision support system that proposes a scenario to the maintenance planner who in turn can contact the local shuttling crews to check the feasibility. If the solution provided by the model is not feasible, the model can be run again with modified specifications.

The first proposed model is the interchange model. The formulation of the interchange models is as follows: Select a collection of pair wise independent changes such that, when executing these changes, the urgent units are routed to a node representing an appropriate maintenance task. Minimise the total cost of the solution, defined as the sum of the individual cost of those arcs that are used by the urgent train units until they reach a maintenance task. A transition is defined as an arc. The model looks if a transition of two trains is feasible by checking if the two trains share a certain buffer time at the same station. If an action is feasible the cost of that action is calculated, the model also checks if the shunting operations not interfere with each other. Because of this, the model requires a lot of details of the shunting operations, more than generally is available in practice. Collecting and maintaining the data

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required for the model will be time-consuming therefore another model based on the same principal has been proposed that require less details.

The second proposed model is the transition model. The main difference between the interchange model and the tran-sition model is that the trantran-sition model requires far less information on the shunting process and this information is easier to obtain. The sole criterion of the transition model if a shunting move is allowed is if there is sufficient time available to complete the shunting operations without causing any delays. After that a cost function is assigned to every feasible transition. The transition model may produce less acceptable solutions then the interchange model but is easier to use in practice.

The model proposed by Feo and Bard (1989) [15] is developed for airlines but is also relevant for rolling stock. The goal of the model is to minimize the number of maintenance locations at airports by scheduling the flights in such a way that airplanes that require maintenance overnight at an airport with the correct facilities. At the time of creating the model a large number of maintenance stations where opened on airports each with inventory carrying costs that may exceed 215,000 dollar per year. The model focuses on the so called A check, at the time of creation of this model this check had to be completed every 65 flight hours or once a week according to the federal regulations. Some companies adopted a maintenance policy that the A check had to been done at least once every four days, for a check the airplane had to stay at an airport overnight. Since the maintenance can only happen overnight, the model only looks at the starting and ending airports of a work day. The scope of the model are over 300 aircrafts operated by American Airlines that flew to 150 cities. The model used for solving this problem is a closed-loop network. The networks are modelled with Eulerian properties. Because of the Eulerian properties the schedule had to consist of seven days or a multitude of this. In practice, a four week scheduling period is the optimum. The conclusion drawn by the authors is that with the use of the model five of the 22 maintenance bases could be closed with negligible loss of flexibility. The model does not take the cost of closing a maintenance station into account also, no limit of the amount of planes a maintenance station can service at the same time has been used. Another factor not taken into account is that airplanes might have to fly a certain route for marketing considerations.

VII. CONCLUSION

Preventive maintenance of rolling stock is in the Nether-lands mainly done by experience and manufactures speci-fications. The time between preventive maintenance differs between papers but it is clear that it is based on a certain amount of distance or time. The parts of the rolling stock get inspected and if needed changed. According to Vernooij (2011), Nedtrain is working on incoperation of the measure-ment of the condition of parts in the field in the planning for maintenance.

VIII. BIBLIOGRAPHY

REFERENCES

[1] E. ¨Ozkan. New control mechanisms for the repairables in nedtrain. Master thesiss, 2010.

[2] K. Vernooij. An aggregate planning for preventive maintenance of bogies by nedtrain, master thesis. 2011.

[3] http://www.rijdendetreinen.nl/statistieken/2012, accessed 16-07-2013. [4] Intermediate report on the development of railway safety in the european

union. european railway agency. 2013.

[5] B. Huisman. Interview by telephone. 2013, Aug 19.

[6] G. Mar´oti and L. Kroon. Maintenance routing for train units: The transition model. Transportation science, 2005.

[7] G. Mar´oti and L. Kroon. Maintenance routing for train units: The interchange model. Computers and Operations Research, 2007. [8] A. M. Smith. Reliability-centered maintenance. 1993.

[9] T. C. Kister and B. Hawking. Maintenance planning and scheduling handbook. 2006.

[10] F. S. Nowlan and Howard F. H. Reliability-centered maintenance. 1978. [11] Oakes W. R. Helm, T. M. and S. W. Painter. A comparison of three optimization methods for scheduling maintenance of high cost, long-lived capital assets. Simulation Conference, Proceedings of the Winter, 2002.

[12] http://www.ns.nl/over-ns/wat-doen-wij/ontdek-ns/wetenswaardigheden, accessed 10-11-2013.

[13] Jardine A. K. S. Sriskandarajah, C. and C. K. Chan. Maintenance scheduling of rolling stock using a genetic algorithm. The Journal of the Operational Research Society, 1998.

[14] Yang A. Y. Cheng, Y. H. and H. L. Tsao. Study on rolling stock maintenance strategy and spares parts management. International Journal of Production Economics, 2010.

[15] T. A. Feo and J. F. Bard. Flight scheduling and maintenance base planning. Management Science, 1989.