Analysis of Hump Operation at a Railroad Classification Yard

Analysis of Hump Operation at a Railroad Classiﬁcation Yard

Maria Gisela Bardossy Information Systems and Decision Science, University of Baltimore, 1420 N. Charles Street, Baltimore, U.S.A.

Keywords: Simulation, Hump Sequencing, Priority Rules, Classiﬁcation Yard, Discrete-event Simulation.

Abstract: Railroad classification yards play a significant role in freight transportation: shipments are consolidated to benefit from economies of scales. However, the disassembling of inbound trains, the classification of railcars and reassembling of outbound trains add significant time to the overall transportation. Determining the operational schedule of a railroad classification yard to ensure that railcars pass as quickly as possible through the yard to continue with their journey to their final destination is a challenging problem. In this paper, we create a simulation model to mimic the dynamics of a classification yard and investigate the effect of two simple but practical priority rules (train length and arrival time) for the sequencing of inbound trains through the humping operation. We monitor the effect of these rules on performance measures such as average wait time (dwell time) at the yard and daily throughput as the complexity and frequency of the trains vary. We run the simulation on four data sets with low and high complexity of trains and low and high frequency of trains.

1 INTRODUCTION

Classification yards take the role of hub in railroad networks. Shipments are consolidated to benefit from economies of scales and full journeys are fragmented in shorter journeys, which might include one or more Figure 1: Layout of a typical classification yard. classification yards. Classification yards add time to the total length of the journey, in many cases idle classification yards have three major sections, shown time. Bontekoning and Priemus (2004) state that in in Figure 1, that make up its structure: the receiving Europe, classification yard operations may take 10- area, the classification area, and the departure area. 50% of trains total transit time.Dirnberger and Barkan Each region of the yard plays a role in moving the (2007) pointed classification yard as an area of high cars to its respective terminal. Once an inbound train potential for total transit time improvement. However, is received, the train is directed to an available receiv- there are a number of working components in the op- ing track for inspection. During this time, the loco- eration of a classification yard that can lead to chal- motive is removed from the train and the railcars are lenges in its potential optimization. In particular, the processed in the receiving area. humping sequence as it is most crucial and directly After inspection is complete, the cars are approved influences the outbound trains departure times, Jaehn for transfer into the classification area. In order to et al. (2015). Eggermont et al. (2009) noted the hard- reach the classification tracks, an engine is used to ness of train rearrangement even in the most simple propel the railcars from the selected receiving track layouts. There are two types of classification yards: over the hump towards the classification area. Cars flat and hump. On hump yards there is track on a that are enroute to the same destination are grouped small hill over which a hump engine pushes the cars, together to create a block. A number of switches are which are then directed using switches to the appro- used to move blocks from the hump to the appropriate priate classification track. Our study concentrates on classification track. An ideal situation would be for hump classification yards. Armstrong (1990) provide each block to have its own classification track. How- a throughout description of railroad operations. ever, due to capacity limitations of the yard, multiple For the purpose of analysis, following we provide blocks may be required to use the same classification a concise description of a hump classification yard track. and its most salient operational characteristics. Most The classification area stores the inventory of

Bardossy M.. Analysis of Hump Operation at a Railroad Classiﬁcation Yard. 493 DOI: 10.5220/0005546704930500 In Proceedings of the 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH-2015), pages 493-500 ISBN: 978-989-758-120-5 Copyright c 2015 SCITEPRESS (Science and Technology Publications, Lda.) SIMULTECH2015-5thInternationalConferenceonSimulationandModelingMethodologies,Technologiesand Applications

rail cars available for assembly into outbound trains. questions in railroad operations. Railroad yard oper- Once the predetermined amount of railcars needed for ation in particular was their 2013 challenge problem. an outbound train become available, an engine will Earlier works on this problem had mostly focused on move into the classification area. The engine will then high-level analytical models; these initiatives in con- take the necessary blocks from one or more tracks trast seek to drill down to the specifics and provide and arrange them in a distinct order. After the cars detailed solutions to these operational decisions. are lined up in the appropriate order, the newly as- Boysen et al. (2012) provides a thorough review of sembled outbound train is pulled into an available de- the literature in the last 40 years. The focus is on sort- parture track. It is at this point that the locomotive is ing strategies and identifying research opportunities reattached and a final inspection of the railcars is com- in the field. The work presented in this paper closely pleted before the outbound train leaves the departure relates to Kraft (2002), He et al. (2003), Hansmann area. and Zimmermann (2008), Marton´ et al. (2009), and Railroad yard operations are focused on making Jaehn et al. (2015) as it concentrates in the detailed connections between inbound trains and outbound scheduling decisions for disassembling and reassem- trains. The yardmaster is responsible for generating bling of trains. He et al. (2003) propose a mixed 0- a plan that manages these movements while ensuring 1 programming formulation and a decomposition op- that all operational constraints are met. Our goal is timization solution method to determine the optimal to characterize the effect of simple but practical pri- decisions. They consider a model with a single hump ority rules such as FIFO (first in first out) and total engine and with set outbound train schedules. Their hump time on yard performance measures such as av- model objective is to minimize train delays and depar- erage wait time and daily throughput as the complex- tures from the outbound train schedule. While Marton´ ity and frequency of the train vary. The sequence in et al. (2009) combine an integer programming ap- which trains are hump has a downstream effect on the proach and a computer simulation tool to successfully outbound trains. That effect can be soothed or am- develop and verify an improved classification sched- plified by characteristics of the flow of inbound trains ule for a real-world train classification instance. They as well as operational constraints of the yard such as derive the scheduling program from a bitstring repre- the number of classification tracks. The rest of this sentation which it includes all the restrictions from a paper is organized as follows. In 2 we review prior Swiss classification yard. Jaehn et al. (2015) inves- optimization work on railroad operations and on se- tigates also the optimal humping sequence in order quencing at the hump in particular. In 3 we survey the to minimize a weighted tardiness of outbound trains. classification yard operations and present a discrete- They show that the problem is NP-hard and present a event simulation model. In 4 we describe four data mix integer programming formulation. sets of inbound trains with distinct characteristics in Describing earlier work, Cordeau et al. (1998) terms of the complexity of the inbound trains and in- presents a survey of optimization models for the most terarrival rate. In 5 we characterize the effect of the commonly studied rail transportation problems. A priority rules on yard performance measures such as whole section is dedicated to analytical yards models average wait time (or dwell time) and daily through- highlighting the importance of the problem in railroad put. In addition, we discuss how these insights can operation. In the majority of the papers reviewed by modeled operational decisions in train sequencing. 6 the authors, the model of choice is a queuing model provides concluding remarks and directions for future and the main objective is to understand the impact research. of different strategies on the transit times at a policy level. Keaton (1989) explains that car time in interme- 2 LITERATURE REVIEW diate terminals occurs in classification and assembly operations and while waiting for the departure of an Optimization of railroad operations has received re- outbound train, but also as a result of yard congestion. vived attention in the last years. The Railway Ap- Earlier, Crane et al. (1955) presents an analysis of a plication Section (RAS) from the Institute for Op- particular hump yard and discussed the queuing pro- erations Research/Management Science (INFORMS) cesses identified in inspection and classification oper- has contributed to direct operation research (OR) ations. A model for the location of a classification academics and practitioners’ attention to challeng- yard was proposed by Mansfield and Wein (1958). ing problems in the field (INFORMS, 2015). Since Petersen (1977a,b) develops queuing models to rep- 2010 each year RAS has partnered with leaders in the resent the classification of incoming traffic and the field to sponsor research competitions on challenging assembly of outbound trains. In these queuing mod-

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els, the author observed that the delay between end 3 HUMP OPERATION AND of classification to start of assembly is a minor source SIMULATION MODEL of yard congestion in comparison with classification and assembly operations. A thorough description of The operations of a classification yards is modeled us- railyards is presented in the first paper. ing a discrete-event simulation model. Given a flow Turnquist and Daskin (1982) models yard opera- of inbound trains, the model determines when incom- tions from the perspective of freight cars and devel- ing trains are humped and moved through the yard to oped queuing models for classification and connec- outbound trains. There is no outbound train schedule tion delays that consider individual cars as the basic pre-defined, the outbound train schedule is defined by units of arrival. Martland (1982) described a method- the model and the decisions made in the process. ology for estimating the total connection time of cars The model is based on the following assumptions: passing through a classification yard. The model is • The classification sequence of the inbound trains. based on a function, fitted using actual data from the When the number of inspected trains in the re- railroad, that relates the probability of making a par- ceiving yard exceeds one, the model determines ticular train connection to the time available to make which train should be humped next. This is es- that connection and other variables such as traffic pri- pecially important to ensure that incoming trains ority and volume. find an open receiving track while grouping the In terms of sorting strategies and block-to- necessary blocks for the outbound trains. Shortest classification track assignment, Siddiqee (1971) com- trains require less time to hump which frees up re- pares four sorting and train formation schemes in a ceiving tracks quicker but limits the construction railroad hump yard. Yagar et al. (1983) proposes of outbound trains. a screening technique and a dynamic programming approach to optimize humping and assembly opera- • The assembly sequence of the outbound trains. tions. They propose an algorithm consisting of two When the number of cars to form a unit or com- main components: a screening technique and a de- bination train in the classification area exceeds a tailed cost minimization procedure for the humping certain number (minimum number of cars deter- and assembly phases. Daganzo et al. (1983) inves- mined by the operational constraints), the pull- tigated the relative performance of different multi- back engine can assemble the string of cars into stage sorting strategies. In multistage sorting, several an outbound train. When there are multiple po- blocks are assigned to each classification track, and tential outbound trains, the model has to deter- cars must be resorted during train formation. More mine which train to pullback. In the given speci- recently, in multistage sorting Jacob et al. (2011) de- fications there are two identical pullback engines, velops a novel encoding of classification schedules, so while the model determines which engine pulls which allows characterizing train classification meth- the train it is not critical for the operational plan. ods simply as classes of schedules. Avramovic´ (1995) In our model, there are additional operating char- models the physical process of cars moving down the acteristics that were established beforehand: hump of a yard. This process is represented by a sys- • Scheduling is non preemptive. Once a humping tem of differential equations that incorporate several job is started it cannot be interrupted until all the factors, such as hump profile and rolling resistance, railcars in the train have been completely humped. affecting the movement of a car. Similarly, the assembling of outbound trains can- The simulation model presented here draws from not be interrupted; all tracks that will form the out- some of the findings presented in these earlier papers. bound train must be pulled sequentially and with- Yagar et al. (1983) also considers a FIFO strategy for out delay between pullbacks. the humping; however, it does not investigate how the • Block-to-track assignment is dynamic. Blocks are performance of each strategy is correlated to the flow assigned to tracks as they are necessary. Empty of the inbound trains. The purpose of the analysis tracks become available immediately to whatever here goes beyond proposing priority rules to under- block requires them. stand the dynamics of the flow of trains jointly with the priority rules. In order to concentrate our atten- • Block-to-track assignment follows a decreasing tion, we have decided to relegate for now aspects such order. When multiple classification tracks store as sorting decisions (Daganzo et al., 1983) and distri- the same block type, new cars are first assigned bution of times (Martland, 1982). to the track with the highest inventory up to reach capacity. Similarly, when a track of a block type needs to be pulled, the track with the most railcars is pulled first.

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Table 1: Operational Constraints. Receiving tracks (capacity) 10 (185) Classiﬁcation tracks (capacity) 42 (60) Departure tracks (capacity) 7 (207) Inspection time 45 min Hump rate 2.2 cars/min Interval between humping jobs 10 min Hump engines 1 Pullback engines 2

• Hump and pullback engines cannot be idle while trains wait. While theoretically engines could await for better trains to hump or pull back, in our model that is not allowed. If the hump engine becomes available and there are trains waiting in the receiving area, the engine must immediately start humping the next train. Similarly, if a pullback engine becomes available and there are enough railcars to form an outbound train, the engine will commence to pullback the available unit or block combination. Other operating constraints such as the number of receiving, classification, and departure tracks, inspection time, and interval between humping jobs are shown in Table 1. In the next section, we briefly describe some characteristics of the inbound trains in Figure 2: Simulation Pseudocode. each dataset. Figure 2 highlights the core of the simulation model where a Schedule list keeps track of each ferred as the fairest as it achieves the lowest variance of the events that take place and a Clock subsequently in waiting times. On the other hand the hump time advances as the simulation progresses. can be used for a shortest train first criterion or longest There are train arrivals, humping, pulling and de- first criterion. The rationale for Shortest Train First is partures that interact through state variables such as that an inbound train in the receiving area, regardless the state of tracks, engine and location of railcars. In of the length, occupies the entire receiving track, and this simulation model, there is one spot time when a under certain circumstances humping shorter trains decision -select a train- with consequences that will first to quickly free up a track for incoming trains cascade through the system take place. For those de- might yield a decreased chance of rescheduling in- cisive moments, we identify some decision rules. We bound trains and improving performance measures. develop rules for prioritizing the humping of trains in A disadvantage to humping the shortest train is its the receiving area and the construction of outbound eventual limitations to generate outbound trains due trains. These guidelines determine the order that in- to a lack of acceptable block combinations. Similarly, bound trains should be humped when more than one the rationale for Longest Train First is longer trains train is present in the receiving area, the classifica- increase the number of potential outbound train com- tion tracks required to pull the selected block combi- binations that will be available in the next stage of the nation, and secures the necessary inventory for out- rail yard. bound train departure. At the time of humping all ready to hump trains Humping Rules: are given a score, s, that depends on the amount of We concentrate in two simple but practical crite- time that the trains has been in the receiving area, w, ria: the idle time in the receiving area and the hump- and the amount of time that it would take to complete ing time required by the train. The idle time in the the hump job for the train, l. Both times are mea- receiving area represents the amount of time that the sured in minutes. The total score is the sum of both train has been ready (after inspection) and waiting for time multiplied respectively by an importance weight. humping while the humping time is a function of the Then, the train with the highest score is humped (dis- train length. The idle time can be used as a first in first carding any train that would not fit in the classification out (FIFO) criterion. This queue discipline is often re- tracks.)

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Table 2: Summary Train Information. Table 3: Summary Results 1. Feature Dataset 2 Dataset 3 Dataset 4 Dataset 5 Data set 2 Data set 3 Blocks 13 13 33 33 Measure min max min max Inbound Trains 339 491 339 491 Dwell Time 1.137 1.200 0.889 0.965 Trains per Day 19 27 19 27 Delayed Trains 0 0 8 16 Train Length 70 72 70 72 Daily Throughput 1344.69 1345.85 1818.71 1845.16 Total Railcars 24330 34130 24330 34130 Hump Utilization 55% 56% 76% 77% Cars per Day 1352 1896 1352 1896 Pullback Utilization 47% 51% 65% 69% Interarrival Time 1:16 0:52 1:16 0:52 Hump Cycle 0:42 0:43 0:42 0:43 Common Block AH AH AH AH Table 4: Summary Results 2. Rare Block BG BG AO AO Data set 4 Data set 5 Measure min max min max s = α ∗ w + β ∗ l (1) Dwell Time 2.688 2.785 2.434 2.541 where α and β are the respective weights. Delayed Trains 0 0 8 16 Daily Throughput 1343.24 1346.07 1820.15 1848.93 Pullback Rules: Hump Utilization 55% 56% 76% 77% For pullback operations, we select the longest pos- Pullback Utilization 71% 75% 87% 89% sible outbound train regardless the amount of time that it requires to assemble. This might be suboptimal longer times to consolidate the minimum number of since unit trains are faster to assemble and pull than railcar to assemble an outbound train. In other words, combination trains and the gain in a longer train might based on this information we expect the cycle time to be lost when the time factor is considered. Anyway, assemble trains in data set 3 and 5 to be considerably we choose this strategy since its simplicity allows to longer than in data set 2 and 4. Our model will assist observe more clearly the effect of humping rules. to deﬁne whether more emphasis should be given to wait time or the length of the train in either case.

4 DESCRIPTION OF INBOUND TRAINS 5 COMPUTATIONAL EXPERIMENT AND Five distinct data sets of inbound trains where ana- CHARACTERIZATION OF lyzed. Data set 1 was used to test the functionality of the simulation model. Data sets 2 and 3 have a lim- RESULTS ited number of incoming blocks (13 blocks) and block combinations (5 combinations), fewer trains per day We are going to report on a set of performance mea- and fewer railcars per day; whereas data sets 4 and 5 sures to compare the different priority rules. We vary are more comprehensive with 33 blocks, more com- the weight for wait time and hump time between - binations (13 combinations) and more daily trains. 2 to 2 in steps of 0.2. A negative weight indicates While the data sets had their own randomly gen- that such dimension is given an inverse importance; erated inbound train combinations, there were sev- for example, instead of longest train first, the shortest eral similarities between them. On average, the train train goes first. The performance measures consid- length for each data set was approximately the same ered are the following: at 70 cars per train. In addition, the interarrival times Arrivals: On time arrivals of inbound trains are of the trains were relatively consistent in its sequence. essential in order to ensure that a continuous flow of Each data set consists of 18 days of inbound trains. railcars is available for departure. The rescheduling of As shown in Table 2, the data sets presented sim- an inbound train for a later time prevents the contents ilar patterns within its measurements. The major dif- of that train from being available as expected which ferences between the data sets comes from the in- ultimately affects other events occurring within the creased variety of blocks applicable to the full data system. Delays evaluate how closely the simulation sets. The modification in the assortment of blocks meets the given inbound train schedule. At the end of spread across the same amount of railcars in each data the simulation, the model compares the time stamps set causes a smaller volume of each block to be avail- of the inbound trains to their expected arrival times. able for outbound trains. There are not notable dif- It then calculates the total number of trains that were ferences between incoming trains in terms of their processed and if the output matches the pre-scheduled constitution. Most trains have at least one railcar of times. This information is useful in determining how each block type; consequently, more blocks translate often the receiving area is occupied versus available. to diversified trains with few blocks of each type and Hump Engine: The hump engine plays a vital role

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Average Dwell Time for Dataset 2 Average Dwell Time for Dataset 3 2 2

1.5 1.5

1 1

0.5 0.5

0 0

-0.5 -0.5 Weight for Hump Time Weight for Hump Time

-1 -1

-1.5 -1.5

-2 -2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Weight for Wait Time Weight for Wait Time Figure 3: Dwell time Data set 2. Figure 4: Dwell time Data set 3. in limiting arrival time delays by ensuring the receiv- for pullback jobs, which yield considerably good re- ing tracks are available for future incoming trains. sults for the four data sets in terms of average dwell To accomplish this task, the hump engine should be time. In the data sets analyzed, the classification area working to eliminate the pending workload in the re- has ample capacity; consequently, the main link be- ceiving area. By studying the waiting times of in- tween the humping engine and the pullback engine bound trains housed in the available receiving tracks, is through the flow of railcars that the hump engine we are about to evaluate how effectively the hump en- produces in a purely downward direction. The de- gine is working. Our objective is to maximize the uti- cisions at pullback engine are not transmitted to the lization rate of the hump engine while minimizing the hump engine in an upward direction; the hump engine time a railcar must occupy the receiving area. is safeguarded of the actions of the pullback engine Classification Tracks: Proportion of classification thanks to the extra capacity available in the classifica- tracks that are used at its peak; that is, the maximum tion area. proportion of the current tracks that are ever used. Tables 3 and 4 summarize the results for the four Overall average proportion of time that classification data sets. When FIFO in used for humping, for Data tracks are in use; that is time that used tracks are used Set 2 and 4 there are no delay arrivals and the ar- divided by the total available time. This is only for rival, hump engine and classification track perfor- the percentage of tracks that are ever occupied. mance measures are identical independently of the Pullback Engines: Expediting the removal of rail- priority rule implemented by the pullback engines. In cars from the classification area adds more space for Data Set 3 and 5, about 17% of the arriving trains are incoming rail cars. The examination of the actions of delayed depending on the weights given to wait time the pullback engine monitors the process of eliminat- and hump time, but again the performance measures ing rail cars within the system. In reviewing how the for the arrival and classification areas are the same pullback engines are managed, we should have more across the different pullback criteria. Figure 3-6 show data to evaluate the strength of corresponding strat- how dwell time varies for the different weight values. egy. The dark areas indicate the most salient performance Departure: Once an outbound train has been either with lowest average dwell time or highest aver- pulled into the departure area, statistical data is gen- age dwell times. In Figure 3 and 4 we can observe erated in reference to its contents. Details such as the some tendency and localize areas. In Figure 3 the number of railcars, the block combination, and classi- lowest dwell time are concentrated in the vertical cen- fication tracks pulled are used to gauge the character- tered area while the highest dwell times are in the istics of the outbound trains. upper left corner. In other words, best dwell times Dwell Time: Dwell time is time difference be- are observed toward relative positive weight for wait tween when a rail car enters the classification track time and negative weight for hump time. Negative until it departs to the departure area. Satisfying our weight for the hump time indicates that shortest trains objective requires reducing the amount of time a rail are given priority over longer trains. In Figure 4, the car spends within the classification yard. When re- lowest dwell times are also observed in the center area viewing each simulation, the average dwell time is but only on the lower part. On the lower left corner utilized to measure the potential benefits of the strat- and center upper are dwell times are at their highest. egy in question. We started with a base case defined Figure 5 also shows some distinctive areas. Here as FIFO priority for humping and longest train first there is no central dominating area. The lowest dwell

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Average Dwell Time for Dataset 4 2 6 CONCLUSIONS

1.5

1 We characterize the performance of two simple priority rules -FIFO and length of the train- and their 0.5 combination through a weighting function that com- 0 bines them into one simple score to deﬁne the hump- -0.5 ing sequence. We observe that neither purely FIFO Weight for Hump Time

-1 nor train length yield the shortest dwell times. In- stead, a combination of both yields the best perfor- -1.5 mance. The weights to obtain the optimal score de- -2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 pends on the characteristics of the ﬂow of incoming Weight for Wait Time trains. When the number of blocks is low, the optimal Figure 5: Dwell time Data set 4. score gives relative importance to the wait time and negative importance to the length of the train meaning Average Dwell Time for Dataset 5 2 that shorter trains are given priority. These observa-

1.5 tions become even stronger when the ﬂow of trains increases; that is, when the arrival rate of train in- 1 creases. On the other hand, the optimal score gives 0.5 priority to the length of the train and even a nega- 0 tive weight to the wait time in the receiving area when

-0.5 there is a larger number of blocks and a regular flow Weight for Hump Time of trains. Lastly, the performance for data set 5 is -1 very sensitive to the weights without a clear pattern -1.5 toward the wait time nor the length of the trains. This -2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 further shows the importance of devising optimized Weight for Wait Time priority rules for humping when the flow is high and Figure 6: Dwell time Data set 5. there is great variability of trains. In data set 5, we observe that small changes in the weights can change times are in the upper area (higher weight for hump radically whether the best or the worst dwell times time) and highest dwell time in the bottom area. Fig- can be attained. A model like the one described here ure 6 does not show such distinctive pattern which can assist in the process of discovering and adjusting indicates that as the complexity of the inbound trains the weights as the flow changes. The model present increases simple priority rules such as FIFO and train here can be enhanced to analyze other yards charac- length (or hump time) become more unpredictable. teristics. For example, it can assist to understand how Interestingly, we observe that complexity as the num- the number of classification tracks and their capacity ber of blocks has a more significant impact than the paces the flow of cars through the yard and the re- frequency of trains. From data set 2 to 3 as the flow lationship between the hump and pullback jobs. In of train increases but with similar complexity the pat- these data sets the main objective was to minimize tern intensifies. In Figure 6 some lowest dwell times the average dwell time while maximizing through- are observed in the upper center area while highest put; consequently, the highest achieving rules humped dwell times are observed in the center lower area. On trains immediately and pull back trains without de- the other hand, the priority rule used at the hump en- lay. The utilization rate of engines does not constitute gine determines the flow of railcars and practically a bottleneck in these problems and the engines can defines the outbound trains and the overall efficiency be freely assigned. Departure tracks are rarely full of the system. There are wide differences in the per- and trains spend minimum time in them. It would formance measures across priority rules. The shortest be interesting to analyze the upward effect of a con- train first yields consistently poor dwell time and high straining number of departure tracks. Our simulation delays. However, the longest train first depending on model provides a flexible framework to test and an- the data set yields ranging results: for Data Set 2 it alyze alternative priority rules for the operation of a yields competitive average dwell time and through- rail yard and yields valuable insight regarding the in- put performance and for Data Set 4 yields the highest tricate forces at play. throughput. A disadvantage of Longest First is the variability in dwell time.

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REFERENCES Marton,´ P., Maue, J., and Nunkesser, M. (2009). An improved train classification procedure for the hump Armstrong, J. H. (1990). The Railroad: What it is, What it yard lausanne triage. In ATMOS. Does. The Introduction to Railroading. Petersen, E. (1977a). Railyard modeling: Part i. predic- Avramovic,´ Z. Z.ˇ (1995). Method for evaluating the strength tion of put-through time. Transportation Science, of retarding steps on a marshalling yard hump. Euro- 11(1):37–49. pean journal of operational research, 85(3):504–514. Petersen, E. (1977b). Railyard modeling: Part ii. the ef- Bontekoning, Y. and Priemus, H. (2004). Breakthrough in- fect of yard facilities on congestion. Transportation novations in intermodal freight transport. Transporta- Science, 11(1):50–59. tion Planning and Technology, 27(5):335–345. Siddiqee, M. W. (1971). Investigation of sorting and train Boysen, N., Fliedner, M., Jaehn, F., and Pesch, E. (2012). formation schemes for a railroad hump yard. Techni- Shunting yard operations: Theoretical aspects and cal report. applications. European Journal of Operational Re- Turnquist, M. A. and Daskin, M. S. (1982). Queuing mod- search, 220(1):1–14. els of classification and connection delay in railyards. Cordeau, J.-F., Toth, P., and Vigo, D. (1998). A survey of Transportation Science, 16(2):207–230. optimization models for train routing and scheduling. Yagar, S., Saccomanno, F., and Shi, Q. (1983). An efficient Transportation science, 32(4):380–404. sequencing model for humping in a rail yard. Trans- Crane, R. R., Brown, F. B., and Blanchard, R. O. (1955). portation Research Part A: General, 17(4):251–262. An analysis of a railroad classification yard. Jour- nal of the Operations Research Society of America, 3(3):262–271. Daganzo, C. F., Dowling, R. G., and Hall, R. W. (1983). Railroad classification yard throughput: The case of multistage triangular sorting. Transportation Re- search Part A: General, 17(2):95–106. Dirnberger, J. R. and Barkan, C. P. (2007). Lean railroading for improving railroad classification terminal performance: bottleneck management methods. Transporta- tion Research Record: Journal of the Transportation Research Board, 1995(1):52–61. Eggermont, C., Hurkens, C. A., Modelski, M., and Woeg- inger, G. J. (2009). The hardness of train rearrange- ments. Operations Research Letters, 37(2):80–82. Hansmann, R. S. and Zimmermann, U. T. (2008). Optimal sorting of rolling stock at hump yards. Springer. He, S., Song, R., and Chaudhry, S. S. (2003). An integrated dispatching model for rail yards operations. Comput- ers & operations research, 30(7):939–966. INFORMS (2015). Railway Applications Section (RAS) problem solving competition. Jacob, R., Marton,´ P., Maue, J., and Nunkesser, M. (2011). Multistage methods for freight train classification. Networks, 57(1):87–105. Jaehn, F., Rieder, J., and Wiehl, A. (2015). Minimizing delays in a shunting yard. OR Spectrum, 37(2):407– 429. Keaton, M. H. (1989). Designing optimal railroad operating plans: Lagrangian relaxation and heuristic ap- proaches. Transportation Research Part B: Method- ological, 23(6):415–431. Kraft, E. R. (2002). Priority-based classification for improving connection reliability in railroad yards. In Journal of the Transportation Research Forum, volume 56. Mansfield, E. and Wein, H. H. (1958). A model for the location of a railroad classification yard. Management Science, 4(3):292–313. Martland, C. D. (1982). Pmake analysis: Predict- ing rail yard time distributions using probabilistic train connection standards. Transportation Science, 16(4):476–506.

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