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Optimal track utilization in electric multiple unit maintenance depots
Accepted Manuscript Optimal Track Utilization in Electric Multiple Unit Maintenance Depots Haodong Li, Mingzhou Jin, Shiwei He, Zhirui Ye, Jinglu Song PII: DOI: Reference:
S0360-8352(17)30127-4 http://dx.doi.org/10.1016/j.cie.2017.03.031 CAIE 4683
To appear in:
Computers & Industrial Engineering
Received Date: Revised Date: Accepted Date:
14 March 2016 3 January 2017 28 March 2017
Please cite this article as: Li, H., Jin, M., He, S., Ye, Z., Song, J., Optimal Track Utilization in Electric Multiple Unit Maintenance Depots, Computers & Industrial Engineering (2017), doi: http://dx.doi.org/10.1016/j.cie. 2017.03.031
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Optimal Track Utilization in Electric Multiple Unit Maintenance Depots Haodong Li School of Traffic and Transportation Beijing Jiaotong University, Beijing, PR China 100044. E-mail: [email protected], Phone: 86-010-51688442 Mingzhou Jin (Corresponding Author) Industrial and Systems Engineering The University of Tennessee, Knoxville, TN, USA. E-mail: [email protected], Phone: (865)974-9992, Fax: (865)974-0588
Shiwei He School of Traffic and Transportation Beijing Jiaotong University, Beijing, PR China 100044. E-mail: [email protected] Phone: 86-10-51687135, Fax: 86-10-51687135 Zhirui Ye Jiangsu Key Laboratory of Urban ITS Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies Southeast University E-mail: [email protected], Phone: 86-025-83790533 Jinglu Song Industrial and Systems Engineering The University of Tennessee, Knoxville, TN, USA. E-mail: [email protected]
1
Optimal Track Utilization in Electric Multiple Unit Maintenance Depots ABSTRACT The Chinese high-speed rail network has a fast-growing number of electric multiple units (EMU) in service and is facing increasing pressure of maintaining all EMUs on-time. The capacity at an EMU maintenance depot is relevant to its track utilization rate, which can be improved by a better EMU-to-track assignment in various areas, such as the maintenance yard, temporary storage yard, and washing yard. Most tracks at EMU depots have two sections that can accommodate one long EMU of sixteen railcars or two short EMUs of eight railcars. The two yard types, stub-end and through, further add complexity to the assignment problem, which is currently handled manually. To make the assignment process more efficient, this paper proposes a simple optimization model for yards with either type and with any combination of long and short EMUs. The numerical results based on a real-world case show that the proposed solution method can yield an assignment plan with the optimal track utilization in a small amount of computational time and can be implemented in a computer-aided planning system easily. The case also discusses potential changes in practice to improve the track utilization rate, such as changing the maintenance schedule and connecting two short EMUs into a long EMU. After comparing the track utilization rates between the two yard types, the paper suggests that the through type is more appropriate for the current schedule at EMU depots, especially for the maintenance yard.
Keywords: High-speed Railroad; EMU Maintenance Depot; Track Utilization; EMU-to-Track Assignment, Yard Layout 1. INTRODUCTION By the end of 2015, there were more than 19,000 km of high-speed rail in China (1) and 2,395 electric multiple units (EMUs) provide more than 2,000 couples of passenger services everyday by July 2016. EMUs are regularly maintained to ensure their safety following the schedule listed 2
in Table 1. Different types of EMUs (e.g., CRH1, CRH2, CRH3 and CRH5) have different cycles for maintenance with levels ranging from 1 to 5. CRH2 EMUs, for example, require a maintenance service at Level 1 after running 4,000 km or 48 hours. It takes 110 minutes, 8 hours, 15 days, 20 days and 30 days to conduct a maintenance service at Leve 1 through 5, respectively. There are currently 61 EMU depots in China that provide maintenance services to EMUs, including 11 Class I depots and 50 Class II depots. Class I depots can fulfill all five levels of maintenance while class II depots can only conduct the first two levels of maintenance. TABLE 1 Maintenance Regulation of EMUs in China[1] EMU Types Maintenance Levels
Maintenance Cycle CRH1
CRH2
CRH3
CRH5
Level 1
4,000km or 48h
4,000km or 48h
4,000km or 48h
5,000km or 48h
Level 2
12,500km
30,000km
20,000km
60,000km
Level 3
1,200,000km
600,000km
1,200,000km
1,200,000km
Level 4
2,400,000km
1,200,000km
2,400,000km
2,400,000km
Level 5
4,800,000km
2,400,000km
4,800,000km
4,800,00km
An EMU depot has multiple functions such as inspection, maintenance, washing, temporary storage, and emergency response. At an EMU depot, EMUs (also called trains in this paper) are inspected, washed, and put through various maintenance tasks at different yards (also called areas in this paper). Each yard is formed by a set of tracks that are equipped with certain facilities for its specific task. After arriving at a depot, an EMU may enter the temporary storage yard waiting for maintenance, be pushed into the maintenance yard directly, or go to the washing yard. A major daily dispatching decision at an EMU depot is to allocate tracks in different yards to EMUs. The decision includes two steps, process sequencing and EMU-to-track assignment. The work sequence of each EMU is decided first. A possible sequence of an EMU could be 1) [1] China Railway. Procedures and Standards of EMUs Maintenance in China[M]. China Railway Publishing House, Beijing, 2013. 3
maintenance → washing → temporary storage, 2) temporary storage → maintenance → washing → temporary storage, 3) temporary storage → maintenance → temporary storage → washing → temporary storage, or others. The EMU-to-track assignment in each area then decides the track for each EMU based on all EMUs’ arrival and departure times, which are determined by the process sequencing step. Almost all track assignment problems in traditional train maintenance depots follow one general rule that one track can only be occupied by one train at any time, regardless of train’s makeup/formation. At EMU depots, most tracks are designed for accommodating 16 railcars. Each track can be occupied by a long EMU, a reconnected EMU that are formed by two short EMUs, or two separate short EMUs. This flexibility provides an opportunity to improve the EMU-to-track assignment. Currently, the daily dispatching at EMU depots is manually made following the two steps of process sequencing and EMU-to-track assignment. As maintenance demand in EMU depots approaches their depot capacity, manual planning becomes very challenging and often results in infeasible operational plans, which cause delayed departures. If an EMU misses the scheduled departure time, daily train services may be influenced or even canceled. The capacity utilization also influences the assignment of EMUs to different depots for maintenance in short-term and influences the depot investment decision in long-term. Therefore, there is a need to develop a computer-driven planning tool for operations at EMU depots. This paper develops an optimization tool for the second step of the EMU-to-track assignment to maximize track utilization in two types of yards, through yard and stub-end yard, reports its applicability with a real case, and studies the impact of the yard type on the overall yard capacity. The EMU-to-Track assignment problem was part of our project for computerizing daily dispatching at EMU depots for China Railway Corporation to improve their productivity. The interface of the computerized system is shown in Appendix A. We also worked with Shanghai Railway and Guangzhou Railway, owned by China Railway Corporation, to validate the method proposed by this paper. The remainder of the paper is structured as follows. Section 2 reviews the relevant literature. Section 3 introduces the EMU-to-track assignment problem. An optimization model is 4
formulated in Section 4 for the EMU-to-track assignment problem at both through and stub-end yards. The computational analysis and a case study, based on data from an EMU depot in China, are presented and discussed in Section 5. Finally, Section 6 concludes the paper with major findings and future research directions. 2. LITERATURE REVIEW In the last two decades, very few studies have been reported on the track utilization issue in high-speed rail EMU depots. Wang et al. (2) studied shunting planning at EMU depots without considering track utilization. Zhang et al (3) proposed a track assignment model for EMU depots, which is nonlinear as it covers two yard types at the same time. The model proposed in this paper is linear by a set definition representing relationship among EMUs for either yard type. Similar studies on track utilization have been conducted for hump yards, freight yards or passenger stations. He et al. (4) presented an integrated dispatching model for classification yards, considering track assignment in the receiving area and the departure area. A similar problem was studied with a different solution method in his previous paper (5). Lin and Cheng simulated the track assignment of the receiving area, forwarding area and departure area in a hump yard (6)(7). The track allocation problem at hump yards is an integral component at the tactical level with regards to the problems of timetabling and train routing (8)(9). For more details about the track assignment problem, we recommend the review by Richard and Jesper (10). Different from track assignment in rail yards, the purpose of the track allocation problem is to route trains through complex junctions/stations of a railway network over time when a timetable is provided, though some principles of the two problems are the same. For example, one track/section can only be occupied by one train; and one train can use only one track/section at any moment. The track allocation problem is further related to the train platforming problem, which is focused on routing conflicts in rail stations. Cornelsen and Stefano (11) studied the track assignment and platform assignment problem, in which a set of trains may enter and depart a station from the left or right side. Each train has to use a track or platform without being blocked by any other trains. This problem was solved as a graph coloring problem based on the 5
assumption that each track and platform has infinite length. Blasum et al. (12) designed a dynamic program for train assignment to the tracks of a storage yard. Winter and Zimmermann (13) studied real-time dispatching of trains by assigning trains to proper positions at different stacks to achieve a departure order satisfying a given schedule. Several research studies also focused on the platform assignment in rail stations with multiple platforms and multiple conflicting lines to ensure that there are no conflictions between any two trains (14). Zwaneveld et al. (15) and Kroon et al. (16) considered the train routing problem to find a feasible routing plan to satisfy basic headway and train connection constraints. Classification track allocation (also called block-to-track assignment) in a hump yard is another intriguing research stream. A block is a set of shipments with the same destination in a hump yard. Kraft (17) and Wang (18) proposed various mixed integer models to optimize the block-to-track assignment, which decides on how to build each outbound train on different classification tracks. One classification track may have railcars of the same block or those of different blocks. Those blocks are pulled out and assembled to form outbound trains through the trim end where humped railcars are assembled at departure tracks, or pulled back to the hump for reclassification. Bohlin et al. (19, 20) focused on the classification track allocation with mixed tracks for temporary railcar storage. 3. EMU-TO-TRACK ASSIGNMENT PROBLEM Similar to the train-to-track assignment at freight yards, the EMU-to-track assignment problem is to assign each EMU to a track to implement maintenance or other tasks and to make sure that there is no routing conflict among EMUs. This paper assumes that the processing sequence of EMUs and all arrival and departure times are given. Most tracks at EMU depots have two sections. Each section can accommodate one short train, which typically has eight railcars. The two sections may also be used together to have one long train, which typically has sixteen railcars, or a reconnection train. If two separate short trains stop on one track, the routing conflict may be different depending on the yard type. There are two typical yards at EMU depots, through yard and stub-end yard, as shown in Figure 1. In a through yard, an EMU enters a track and leaves a track following the same 6
direction. In other words, when two short EMUs utilize the same track at the same time, the EMU that arrives earlier must also leave the track earlier than the other EMU. Both EMUs move in the same direction. For example, EMUs 1 and 2 both use track 2 in the through yard illustrated in Figure 1.a. EMU 1 should arrive and depart before EMU 2. Train 3 is a long train that occupies both sections of track 1. In a stub-end yard, the EMU that arrives earlier must depart later than the other EMU that shares the same track. EMUs 4 and 5 both use track 1 in the stub-end yard in Figure 1.b. EMU 5 arrives at track 1 later but leaves track 1 earlier than EMU 4. Please note that two short EMUs that occupy the same track at any time always move with the same direction in a through yard. Bi-directional movements of two short EMUs are not allowed in practice because they may cause complex shunting operations and therefore waste capacity.
Flow Direction
Flow Direction
FIGURE 1: Typical Yards in EMU Depots
Let W denote a set of tracks in an EMU yard and let w be its index. Define I as the set of EMUs considered in a daily plan, and i as its index. The set of short EMUs and long EMUs are denoted by and , respectively, so we have = ∪ . EMU , if assigned to track , stays at track from time point to . is the time when EMU enters the track while is the time when it departs the track. Each track has two sections that can accommodate up to two short EMUs or just one long EMU. The challenge of the EMU-to-track assignment at an EMU depot is to avoid the time confliction of any two EMUs that occupy the same track. There are six 7
possibilities of time confliction for two EMUs using the same track, as shown in Figure 2. There is no time conflict for EMUs and in (a) and (b) so they can use the same track no matter whether they are short or long. For (c) through (f), two long EMUs cannot share the same track in any type of yard, while two short EMUs may or may not occupy the same track, depending on the yard type. Short EMUs and in (c) and (d) can be assigned to the same track at a through yard but not at a stub-type yard. Furthermore, Short EMUs and in (e) and (f) can be assigned to the same track at a stub-type yard but not at a through yard.
FIGURE 2: Time Conflictions of Two EMUs
To capture all six possibilities illustrated in Figure 2, we define as the set of EMUs that cannot be assigned to the same track with EMU i. For a long EMU , we have
= < < or < < , ∀ ∈ , ∀ ∈ .
(1)
Here, only EMUs that satisfy relationships (a) and (b) in Figure 2 can be assigned to the same track with long EMU , (i.e., not belonging to ). For a short EMU , the definition of depends on the yard type. For a through yard, we have
= < < < or < < < , ∀ ∈ , ∀ ∈ .
(2)
Please note that defined by (2) only includes EMUs that have the relationships (e) 8
and (f). Of course, a long EMU also cannot be assigned together with a short EMU if they follow relationships (c) and (d). However, that case will be avoided by for ∀ ∈ in the following optimization model called ETT. For a stub-end yard, similarly, we have
= < < < or < < < , ∀ ∈ , ∀ ∈ .
(3)
In other words, defined by (3) for a short EMU in a stub-end yard include all other EMUs that have relationships (c) and (d). The EMU-to-track assignment problem can be formulated by the following model called ETT with binary variable = 1 if EMU is assigned to track w; and = 0 otherwise. ETT
max = ∑ ∈ ∑∈ s.t.
(4)
∑∈ ≤ 1
∀ ∈ ;
(5)
+ ≤ 1
∀ ∈ , ∈ , ∈ " ;
(6)
∈ #0,1%.
The objective function (4) of the ETT model maximizes the total number of EMUs that can be arranged on any track to finish the specific tasks. Under ideal conditions, the value of the objective function is equal to the number of all EMUs under consideration. Constraint set (5) ensures that each EMU can only be assigned to one track. Constraint set (6) means that EMU cannot be assigned to the same track with EMU if ∈ , which is defined by Equations (1) through (3) based on the EMU type and yard type. Because the model is unimodular, it can be solved to its optimality by its linear relaxation. Any optimization solvers can be used to obtain the optimal solution in a small amount of time. The planning horizon at EMU depots is usually no more than one day (24 hours). We tested the model by using IBM ILOG CPLEX Studio under different scenarios on a PC with an I5 CPU and 4 GB RAM. For all of those scenarios, CPLEX can yield an optimal schedule within 0.1 second. 4. CASE STUDY We further conducted a case study with the real-world data from an EMU depot of China Railway Corporation to validate the proposed ETT model and to gain managerial insights for 9
practitioners. This is a class II EMU depot of the stub-end type, which has a temporary storage yard, maintenance yard and washing yard, as shown in Figure 3. The depot has 20 tracks in total, 10 tracks for temporary storage, 8 tracks for maintenance and 2 tracks for washing. The trim end of the yard layout is simplified by eliminating most of the switches. Each track has two sections that can accommodate either one long EMU or two short EMUs. In this case study, we only consider the track utilization in the maintenance area and temporary storage area. The washing area is not the bottleneck of the depot though the method is applicable to the washing area as well. All EMUs can be washed within 30 minutes as the washing yard is equipped with automatic facilities together with a large number of workers for peak hours.
FIGURE 3: Layout of the EMU Depot in the Case Study
The case study considered a shift plan with about 12 hours and 14 EMUs. Table 2 lists the arrival time, starting time and ending time of maintenance, and departure time of each EMU. In the “makeup” column, “L” refers to a 16-railcar long EMU or a reconnected EMU of two 8-railcar short EMUs while “S” represents an 8-railcar short EMU. After arriving at the depot, each EMU stops in the temporary storage yard waiting for maintenance. After being maintained, 10
each EMU is pulled out to the temporary storage yard again waiting for departure. Therefore, each EMU stays twice in the temporary storage area. For example, EMU 3533L needs to stay in the temporary storage area from 18:24 to 19:12 and from 22:44 to 8:38 on the next day. We can treat two stays as two different EMUs, one from its arrival time to its maintenance starting time and the other from its maintenance ending time to its departure time. The transfer time between different yards has been included in the track utilization time. We do not consider the routing confliction at the trim end of the yard. TABLE 2: Information of EMUs Maintenance Makeup Arrival Time Starting Time Ending Time
Departure Time (Second Day)
Index
EMU ID
1
3533L
L
18:24
19:12
22:44
8:38
2
3027C
S
18:54
19:42
23:14
7:18
3
3026C
S
19:04
19:52
23:24
5:18
4
3534L
L
19:56
20:44
23:16
9:43
5
3022C
S
20:25
21:13
0:45
6:53
6
2564L
L
20:50
21:38
1:10
9:28
7
3033C
S
21:09
21:57
1:29
8:18
8
3051C
S
21:09
21:57
1:29
9:48
9
3041C
S
22:00
22:48
2:20
12:53
10
3075C
S
22:09
22:57
2:29
7:38
11
2566L
L
22:50
23:38
3:10
11:55
12
2559L
L
23:10
23:58
3:30
9:04
13
3043C
S
23:22
0:10
3:42
7:03
14
3038C
S
0:04
0:52
5:24
11:12
4.1 Results of the Case Study We still used IBM ILOG CPLEX 12.2 to solve the ETT model for the case. The run times for the ETT in the maintenance area and temporary storage area were 0.01s and 0.03s respectively. The results are listed in Tables 3 and 4 and show that all of the EMUs can follow the schedule in Table 2 when we have 8 tracks for maintenance and 10 tracks for temporary storage, as illustrated in Figure 3. 11
TABLE: 3 EMU-to-track Assignment of the Maintenance Area Track No. 1 2 3 4 5 6 7 8
Makeup S L S L S L S L S L S L S L S L
Section I
Section II 2564L
3041C 3027C 2566L 3026C, 3043C 3022C, 3038C
3533L, 2559L 3075C 3534L 3051C
In Table 3, the maintenance yard, including all 8 tracks, uses 49.467 track-hours for all EMUSs. The maintenance plan in this case spans 10.2 hours (i.e., from 19:12 to 5:24 on the next day) so the overall utilization rate of tracks in the maintenance area is 49.467 ÷ 10.2 ÷ 8 = 60.62%, which is very low. However, if we reduce the number of maintenance tracks to 7, the optimal objective function value of the ETT will become 13. In other words, only 13 EMUs can be maintained at most. The reason for such a low utilization rate is that the given arrival and departure times are not suitable for a stub-end type yard. EMUs that arrive earlier often depart earlier, while the stub-end type yard follows the first-in last-out fashion when two short EMUs share a track. In this case study, the temporary storage area with 10 tracks can accommodate all 14 EMUs, each staying in the area twice. If we reduce the yard size to 9 tracks, the optimal objective function value of the ETT is less than 28. The utilization rate of the temporary storage area with 10 tracks is 61.84%. In practice, the maintenance yard is usually considered the bottleneck of this EMU depot and its utilization rate needs to be improved. 12
TABLE 4: EMU-to-track Assignment of the Temporary Storage Area Track No. 1 2 3 4 5 6 7 8 9 10
Makeup S L S L S L S L S L S L S L S L S L S L
Section I
Section II
3533L, 3534L, 2564L, 2566L 3027C, 3022C 3533L 3026C, 3033C, 3041C, 3075C 3051C, 3041C 3034C
3075C, 3033C
3038C 2564L, 2566L 2559L 3027C
3034C, 3022C 3051C 2559L 3534L
3038C
3026C
The number of daily services of high-speed rail in China is expected to increase and the number of EMUs that require maintenance will increase even more because older ones need more maintenance. There is therefore an urgent to improve the utilization of tracks in the maintenance area to meet the expected higher demand. As shown in Table 2, the starting and ending times of each EMU at the maintenance area are given based on a master shift plan, in which most of EMUs that arrive at the maintenance yard earlier also depart the yard earlier. For this situation, there are two ways to increase the service capacity of a maintenance yard with the stub-end type as follows. (1) Reconnect two short EMUs as one long EMU and keep them together. For example, the EMUs of 3033C and 3051C are reconnected together and treated as a long EMU. The same reconnection is applied to 3041C and 3075C. The maintenance starting time and ending time of 13
the new 3033C+3051C are 21:57 and 1:44 (15 min of shunting time is added) respectively. Similarly, the maintenance starting time and ending time of the new 3041C+3075C are 22:57 and 2:29 respectively. After these two reconnections, we need only 7 tracks in the maintenance yard for the resulting 12 EMUs. After being reconnected, EMU 3041C is pulled out to the temporary storage yard at 2:29, which is 9 minutes later compared to the schedule in Table 2 but can still depart on time for daily service. This method is applicable if there are some short EMUs that arrive at the maintenance yard with a short time interval. Since this method will increase shunting work, the trim end of the depot may become a bottleneck. (2) Reschedule the maintenance starting and ending times of some EMUs. If the arrival and departure times of two short EMUs follow the policy of arrival earlier and departure later as shown in scenario (e) and (f) in Figure 2, those two short EMUs can share the same track. For example, if we change the departure time of EMUs 3027C and 3041C to 23:25 and 2:30 and change the arrival time and departure time of 3033C to 21:56 and 1:30, one track will be saved for all 14 EMUs. In other words, we can use 7 tracks to accommodate all maintenance tasks. Three pairs of short EMUs can share the same track, such as 3027C and 3026C, 3033C and 3051C, and 3041C and 3075C. However, this method may lead to longer dwell time on the maintenance track for some short EMUs. 4.2 Capacity of Stub-end Yard vs. Through Yard The service capacity of different yard types in an EMU depot depends on the maintenance schedule. If most of the short EMUs follow the first-in first-out rule at a yard, it is more suitable to design this yard with the through type. Otherwise, it may be more suitable to design it with the stub-end yard type. For this case study, short EMUs in general follow the first-in first-out rule so the service capacity of a through yard is larger than a stub-end yard. If the maintenance yard is turned into the through type so that EMUs moves from left to right, the computational time for CPLEX to solve the ETT with the same data in Table 2 is the same as that for the stub-end yard. The results show that only 6 tracks are needed in the maintenance yard for accommodating all 14 EMUs, as shown in Table 5. Compared to the 14
stub-end yard, 2 tracks are saved for serving the same number of EMUs. The track utilization rate is improved to 80.83%, much higher than the rate of 60.62% with the stub-end type.
TABLE 5: EMU-to-track Assignment of the Maintenance Area of Through Type Track No. 1 2 3 4 5 6
Makeup S L S L S L S L S L S L
Section I 3075C
Section II 3022C, 3038C
3051C
3033C
3043C
3041C 3533L
3026C
3027C 2564L 2566L 3534L, 2559L
TABLE 6: EMU-to-track Assignment of the Temporary Storage Area of Through Type Track No. 1 2 3 4 5 6 7 8 9
Makeup S L S L S L S L S L S L S L S L S L
Section I
Section II
3534L, 2564L, 3534L 3033C 3051C, 3043C 2559L 3041C 3022C, 3075C, 3027C 3533L 3026C, 3041C, 3038C, 3075C 3051C 2566L 3033C 3043C 2559L 3027C, 2566L 3022C 3026C, 3038C
2564L 3533L 15
Similarly, the number of tracks at the temporary storage yard could be reduced by one (i.e., we need only 9 tracks to accommodate all 14 EMUs twice) if we convert it into the through type, as shown in Table 6. In other words, the track utilization rate could be improved from 61.84% to 68.71% through the conversion. However, compared to the maintenance yard, the utilization improvement is smaller for the temporary storage yard in this case study. A possible reason for the smaller improvement is that the storage tasks span 16 hours and 48 minutes. 5. CONCLUSIONS This paper proposes an optimization model called ETT for the EMU-to-track assignment problem at high-speed rail EMU depots. This simple model, whose computational burden is very trivial, can be used for both stub-end yards and through yards and for any combinations of long and short EMUs. The time conflict constraints for stub-end yards and through yards are formulated through defining a set of EMUs that cannot share the same track with any given EMU. The set definition depends on the EMU type (long or short) and yard type (stub-end or through). A case study based on data from a Chinese Class-II EMU depot was conducted. The results show that the proposed method can help to generate an optimal EMU-to-track assignment with the highest track utilization. Furthermore, we found that the maintenance area is more suitable to be designed as through type with the maintenance times fixed for most of the EMUs, which in general follow the first-in first-out rule currently. Reconnecting two short EMUs to be maintained together as one long EMU or postponing the departure time of some short EMUs can help to improve the track utilization rate for a maintenance yard with the stub-end type. A possible future research direction is to schedule the dispatching plan of an EMU depot, which includes track assignment of different yards as well as detailed arrival and departure times of each EMU in each area based on the maintenance schedule of all EMUs. When we consider all areas in an integrated way and adjust the number of tracks assigned to each area, computational complexity is expected to be a challenge. Furthermore, the proposed ETT does not consider the time conflict at the trim end. It may be worthwhile to incorporate switch time conflicts to make the dispatching plan more executable. 16
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Approaches for Transportation Modeling, Optimization and System, 2004. [12] Blasum, U., Bussieck, M. R., Hochstattler, W., Scheel H. H., and Winter, T. Scheduling Trains in the Morning. Mathematical Methods of Operation Research, Vol. 49, No. 1, 1999, pp. 137-148. [13] Winter, T. and Zimmermann, U. T. Real-time Dispatch of Trains in Storage Yards. Annals of Operations and Research, Vol. 90, 2000, pp. 287-315. [14] Carey, M. and Carville, S. Scheduling and Platforming Trains at Busy Complex Stations. Transportation Research Part A, Vol. 37, No. 3, 2003, pp. 195-224. [15] Zwaneveld, P., Kroon L. J., Romeijn, H. E., Salomon, M., Dauzereperes, S., Hoesel, S. V., and Ambergen, H. W. Routing Trains through Railway Stations: Model Formulation and Algorithms. Transportation Science, Vol. 30, No. 3, 1996, pp. 181-194. [16] Kroon L. J., Romeijn, H. E., and Zwaneveld, P. J. Routing Trains through Railway Stations: Complexity Issues. European Journal of Operational Research, Vol. 98, No. 3, 1997, pp. 458-498. [17] Kraft, C. A. Mixed-integer Optimization Model to Improve Freight Car Classification in Railroad Yards. TIMS/ORSA 1993 Joint National Meeting, 1993, Arizona. [18] Wang, X. Improving Planning for Railroad Yard, Forestry and Distribution. PH.D. Dissertation, Department of Operations and Information Management, Wharton School, University of Pennsylvania, Philadelphia, PA, 1997. [19] Bohlin, M., Flier, H., Maue, J., and Mihalak, M. Hump Yard Track Allocation with Temporary Car Storage. In The 4th International Seminar on Railway Operations Modelling and Analysis (RailRome), 2011. Available on http://soda.swedish-ict.se/5089/. [20] Bohlin, M., Flier, H., Maue, J., and Mihalak, M. Track Allocation in Freight-Train Classification with Mixed Tracks. In 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization and Systems, Vol.20, Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, Germany, pp.38–51.
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APPENDIX
Appendix A. Interface of the Daily Dispatching Application for Class II EMUs Depot
19
Optimal Track Utilization in Electric Multiple Unit Maintenance Depots Highlights
•
Build a simple model for improving the maintenance efficiency of electric multiple units in Chinese high-speed rails.
•
The solution method yields the optimal track utilization in a small amount of computational time.
•
A case is presented to show the real application of the method and discuss the difference caused by the track layout.
20
S0360-8352(17)30127-4 http://dx.doi.org/10.1016/j.cie.2017.03.031 CAIE 4683
To appear in:
Computers & Industrial Engineering
Received Date: Revised Date: Accepted Date:
14 March 2016 3 January 2017 28 March 2017
Please cite this article as: Li, H., Jin, M., He, S., Ye, Z., Song, J., Optimal Track Utilization in Electric Multiple Unit Maintenance Depots, Computers & Industrial Engineering (2017), doi: http://dx.doi.org/10.1016/j.cie. 2017.03.031
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Optimal Track Utilization in Electric Multiple Unit Maintenance Depots Haodong Li School of Traffic and Transportation Beijing Jiaotong University, Beijing, PR China 100044. E-mail: [email protected], Phone: 86-010-51688442 Mingzhou Jin (Corresponding Author) Industrial and Systems Engineering The University of Tennessee, Knoxville, TN, USA. E-mail: [email protected], Phone: (865)974-9992, Fax: (865)974-0588
Shiwei He School of Traffic and Transportation Beijing Jiaotong University, Beijing, PR China 100044. E-mail: [email protected] Phone: 86-10-51687135, Fax: 86-10-51687135 Zhirui Ye Jiangsu Key Laboratory of Urban ITS Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies Southeast University E-mail: [email protected], Phone: 86-025-83790533 Jinglu Song Industrial and Systems Engineering The University of Tennessee, Knoxville, TN, USA. E-mail: [email protected]
1
Optimal Track Utilization in Electric Multiple Unit Maintenance Depots ABSTRACT The Chinese high-speed rail network has a fast-growing number of electric multiple units (EMU) in service and is facing increasing pressure of maintaining all EMUs on-time. The capacity at an EMU maintenance depot is relevant to its track utilization rate, which can be improved by a better EMU-to-track assignment in various areas, such as the maintenance yard, temporary storage yard, and washing yard. Most tracks at EMU depots have two sections that can accommodate one long EMU of sixteen railcars or two short EMUs of eight railcars. The two yard types, stub-end and through, further add complexity to the assignment problem, which is currently handled manually. To make the assignment process more efficient, this paper proposes a simple optimization model for yards with either type and with any combination of long and short EMUs. The numerical results based on a real-world case show that the proposed solution method can yield an assignment plan with the optimal track utilization in a small amount of computational time and can be implemented in a computer-aided planning system easily. The case also discusses potential changes in practice to improve the track utilization rate, such as changing the maintenance schedule and connecting two short EMUs into a long EMU. After comparing the track utilization rates between the two yard types, the paper suggests that the through type is more appropriate for the current schedule at EMU depots, especially for the maintenance yard.
Keywords: High-speed Railroad; EMU Maintenance Depot; Track Utilization; EMU-to-Track Assignment, Yard Layout 1. INTRODUCTION By the end of 2015, there were more than 19,000 km of high-speed rail in China (1) and 2,395 electric multiple units (EMUs) provide more than 2,000 couples of passenger services everyday by July 2016. EMUs are regularly maintained to ensure their safety following the schedule listed 2
in Table 1. Different types of EMUs (e.g., CRH1, CRH2, CRH3 and CRH5) have different cycles for maintenance with levels ranging from 1 to 5. CRH2 EMUs, for example, require a maintenance service at Level 1 after running 4,000 km or 48 hours. It takes 110 minutes, 8 hours, 15 days, 20 days and 30 days to conduct a maintenance service at Leve 1 through 5, respectively. There are currently 61 EMU depots in China that provide maintenance services to EMUs, including 11 Class I depots and 50 Class II depots. Class I depots can fulfill all five levels of maintenance while class II depots can only conduct the first two levels of maintenance. TABLE 1 Maintenance Regulation of EMUs in China[1] EMU Types Maintenance Levels
Maintenance Cycle CRH1
CRH2
CRH3
CRH5
Level 1
4,000km or 48h
4,000km or 48h
4,000km or 48h
5,000km or 48h
Level 2
12,500km
30,000km
20,000km
60,000km
Level 3
1,200,000km
600,000km
1,200,000km
1,200,000km
Level 4
2,400,000km
1,200,000km
2,400,000km
2,400,000km
Level 5
4,800,000km
2,400,000km
4,800,000km
4,800,00km
An EMU depot has multiple functions such as inspection, maintenance, washing, temporary storage, and emergency response. At an EMU depot, EMUs (also called trains in this paper) are inspected, washed, and put through various maintenance tasks at different yards (also called areas in this paper). Each yard is formed by a set of tracks that are equipped with certain facilities for its specific task. After arriving at a depot, an EMU may enter the temporary storage yard waiting for maintenance, be pushed into the maintenance yard directly, or go to the washing yard. A major daily dispatching decision at an EMU depot is to allocate tracks in different yards to EMUs. The decision includes two steps, process sequencing and EMU-to-track assignment. The work sequence of each EMU is decided first. A possible sequence of an EMU could be 1) [1] China Railway. Procedures and Standards of EMUs Maintenance in China[M]. China Railway Publishing House, Beijing, 2013. 3
maintenance → washing → temporary storage, 2) temporary storage → maintenance → washing → temporary storage, 3) temporary storage → maintenance → temporary storage → washing → temporary storage, or others. The EMU-to-track assignment in each area then decides the track for each EMU based on all EMUs’ arrival and departure times, which are determined by the process sequencing step. Almost all track assignment problems in traditional train maintenance depots follow one general rule that one track can only be occupied by one train at any time, regardless of train’s makeup/formation. At EMU depots, most tracks are designed for accommodating 16 railcars. Each track can be occupied by a long EMU, a reconnected EMU that are formed by two short EMUs, or two separate short EMUs. This flexibility provides an opportunity to improve the EMU-to-track assignment. Currently, the daily dispatching at EMU depots is manually made following the two steps of process sequencing and EMU-to-track assignment. As maintenance demand in EMU depots approaches their depot capacity, manual planning becomes very challenging and often results in infeasible operational plans, which cause delayed departures. If an EMU misses the scheduled departure time, daily train services may be influenced or even canceled. The capacity utilization also influences the assignment of EMUs to different depots for maintenance in short-term and influences the depot investment decision in long-term. Therefore, there is a need to develop a computer-driven planning tool for operations at EMU depots. This paper develops an optimization tool for the second step of the EMU-to-track assignment to maximize track utilization in two types of yards, through yard and stub-end yard, reports its applicability with a real case, and studies the impact of the yard type on the overall yard capacity. The EMU-to-Track assignment problem was part of our project for computerizing daily dispatching at EMU depots for China Railway Corporation to improve their productivity. The interface of the computerized system is shown in Appendix A. We also worked with Shanghai Railway and Guangzhou Railway, owned by China Railway Corporation, to validate the method proposed by this paper. The remainder of the paper is structured as follows. Section 2 reviews the relevant literature. Section 3 introduces the EMU-to-track assignment problem. An optimization model is 4
formulated in Section 4 for the EMU-to-track assignment problem at both through and stub-end yards. The computational analysis and a case study, based on data from an EMU depot in China, are presented and discussed in Section 5. Finally, Section 6 concludes the paper with major findings and future research directions. 2. LITERATURE REVIEW In the last two decades, very few studies have been reported on the track utilization issue in high-speed rail EMU depots. Wang et al. (2) studied shunting planning at EMU depots without considering track utilization. Zhang et al (3) proposed a track assignment model for EMU depots, which is nonlinear as it covers two yard types at the same time. The model proposed in this paper is linear by a set definition representing relationship among EMUs for either yard type. Similar studies on track utilization have been conducted for hump yards, freight yards or passenger stations. He et al. (4) presented an integrated dispatching model for classification yards, considering track assignment in the receiving area and the departure area. A similar problem was studied with a different solution method in his previous paper (5). Lin and Cheng simulated the track assignment of the receiving area, forwarding area and departure area in a hump yard (6)(7). The track allocation problem at hump yards is an integral component at the tactical level with regards to the problems of timetabling and train routing (8)(9). For more details about the track assignment problem, we recommend the review by Richard and Jesper (10). Different from track assignment in rail yards, the purpose of the track allocation problem is to route trains through complex junctions/stations of a railway network over time when a timetable is provided, though some principles of the two problems are the same. For example, one track/section can only be occupied by one train; and one train can use only one track/section at any moment. The track allocation problem is further related to the train platforming problem, which is focused on routing conflicts in rail stations. Cornelsen and Stefano (11) studied the track assignment and platform assignment problem, in which a set of trains may enter and depart a station from the left or right side. Each train has to use a track or platform without being blocked by any other trains. This problem was solved as a graph coloring problem based on the 5
assumption that each track and platform has infinite length. Blasum et al. (12) designed a dynamic program for train assignment to the tracks of a storage yard. Winter and Zimmermann (13) studied real-time dispatching of trains by assigning trains to proper positions at different stacks to achieve a departure order satisfying a given schedule. Several research studies also focused on the platform assignment in rail stations with multiple platforms and multiple conflicting lines to ensure that there are no conflictions between any two trains (14). Zwaneveld et al. (15) and Kroon et al. (16) considered the train routing problem to find a feasible routing plan to satisfy basic headway and train connection constraints. Classification track allocation (also called block-to-track assignment) in a hump yard is another intriguing research stream. A block is a set of shipments with the same destination in a hump yard. Kraft (17) and Wang (18) proposed various mixed integer models to optimize the block-to-track assignment, which decides on how to build each outbound train on different classification tracks. One classification track may have railcars of the same block or those of different blocks. Those blocks are pulled out and assembled to form outbound trains through the trim end where humped railcars are assembled at departure tracks, or pulled back to the hump for reclassification. Bohlin et al. (19, 20) focused on the classification track allocation with mixed tracks for temporary railcar storage. 3. EMU-TO-TRACK ASSIGNMENT PROBLEM Similar to the train-to-track assignment at freight yards, the EMU-to-track assignment problem is to assign each EMU to a track to implement maintenance or other tasks and to make sure that there is no routing conflict among EMUs. This paper assumes that the processing sequence of EMUs and all arrival and departure times are given. Most tracks at EMU depots have two sections. Each section can accommodate one short train, which typically has eight railcars. The two sections may also be used together to have one long train, which typically has sixteen railcars, or a reconnection train. If two separate short trains stop on one track, the routing conflict may be different depending on the yard type. There are two typical yards at EMU depots, through yard and stub-end yard, as shown in Figure 1. In a through yard, an EMU enters a track and leaves a track following the same 6
direction. In other words, when two short EMUs utilize the same track at the same time, the EMU that arrives earlier must also leave the track earlier than the other EMU. Both EMUs move in the same direction. For example, EMUs 1 and 2 both use track 2 in the through yard illustrated in Figure 1.a. EMU 1 should arrive and depart before EMU 2. Train 3 is a long train that occupies both sections of track 1. In a stub-end yard, the EMU that arrives earlier must depart later than the other EMU that shares the same track. EMUs 4 and 5 both use track 1 in the stub-end yard in Figure 1.b. EMU 5 arrives at track 1 later but leaves track 1 earlier than EMU 4. Please note that two short EMUs that occupy the same track at any time always move with the same direction in a through yard. Bi-directional movements of two short EMUs are not allowed in practice because they may cause complex shunting operations and therefore waste capacity.
Flow Direction
Flow Direction
FIGURE 1: Typical Yards in EMU Depots
Let W denote a set of tracks in an EMU yard and let w be its index. Define I as the set of EMUs considered in a daily plan, and i as its index. The set of short EMUs and long EMUs are denoted by and , respectively, so we have = ∪ . EMU , if assigned to track , stays at track from time point to . is the time when EMU enters the track while is the time when it departs the track. Each track has two sections that can accommodate up to two short EMUs or just one long EMU. The challenge of the EMU-to-track assignment at an EMU depot is to avoid the time confliction of any two EMUs that occupy the same track. There are six 7
possibilities of time confliction for two EMUs using the same track, as shown in Figure 2. There is no time conflict for EMUs and in (a) and (b) so they can use the same track no matter whether they are short or long. For (c) through (f), two long EMUs cannot share the same track in any type of yard, while two short EMUs may or may not occupy the same track, depending on the yard type. Short EMUs and in (c) and (d) can be assigned to the same track at a through yard but not at a stub-type yard. Furthermore, Short EMUs and in (e) and (f) can be assigned to the same track at a stub-type yard but not at a through yard.
FIGURE 2: Time Conflictions of Two EMUs
To capture all six possibilities illustrated in Figure 2, we define as the set of EMUs that cannot be assigned to the same track with EMU i. For a long EMU , we have
= < < or < < , ∀ ∈ , ∀ ∈ .
(1)
Here, only EMUs that satisfy relationships (a) and (b) in Figure 2 can be assigned to the same track with long EMU , (i.e., not belonging to ). For a short EMU , the definition of depends on the yard type. For a through yard, we have
= < < < or < < < , ∀ ∈ , ∀ ∈ .
(2)
Please note that defined by (2) only includes EMUs that have the relationships (e) 8
and (f). Of course, a long EMU also cannot be assigned together with a short EMU if they follow relationships (c) and (d). However, that case will be avoided by for ∀ ∈ in the following optimization model called ETT. For a stub-end yard, similarly, we have
= < < < or < < < , ∀ ∈ , ∀ ∈ .
(3)
In other words, defined by (3) for a short EMU in a stub-end yard include all other EMUs that have relationships (c) and (d). The EMU-to-track assignment problem can be formulated by the following model called ETT with binary variable = 1 if EMU is assigned to track w; and = 0 otherwise. ETT
max = ∑ ∈ ∑∈ s.t.
(4)
∑∈ ≤ 1
∀ ∈ ;
(5)
+ ≤ 1
∀ ∈ , ∈ , ∈ " ;
(6)
∈ #0,1%.
The objective function (4) of the ETT model maximizes the total number of EMUs that can be arranged on any track to finish the specific tasks. Under ideal conditions, the value of the objective function is equal to the number of all EMUs under consideration. Constraint set (5) ensures that each EMU can only be assigned to one track. Constraint set (6) means that EMU cannot be assigned to the same track with EMU if ∈ , which is defined by Equations (1) through (3) based on the EMU type and yard type. Because the model is unimodular, it can be solved to its optimality by its linear relaxation. Any optimization solvers can be used to obtain the optimal solution in a small amount of time. The planning horizon at EMU depots is usually no more than one day (24 hours). We tested the model by using IBM ILOG CPLEX Studio under different scenarios on a PC with an I5 CPU and 4 GB RAM. For all of those scenarios, CPLEX can yield an optimal schedule within 0.1 second. 4. CASE STUDY We further conducted a case study with the real-world data from an EMU depot of China Railway Corporation to validate the proposed ETT model and to gain managerial insights for 9
practitioners. This is a class II EMU depot of the stub-end type, which has a temporary storage yard, maintenance yard and washing yard, as shown in Figure 3. The depot has 20 tracks in total, 10 tracks for temporary storage, 8 tracks for maintenance and 2 tracks for washing. The trim end of the yard layout is simplified by eliminating most of the switches. Each track has two sections that can accommodate either one long EMU or two short EMUs. In this case study, we only consider the track utilization in the maintenance area and temporary storage area. The washing area is not the bottleneck of the depot though the method is applicable to the washing area as well. All EMUs can be washed within 30 minutes as the washing yard is equipped with automatic facilities together with a large number of workers for peak hours.
FIGURE 3: Layout of the EMU Depot in the Case Study
The case study considered a shift plan with about 12 hours and 14 EMUs. Table 2 lists the arrival time, starting time and ending time of maintenance, and departure time of each EMU. In the “makeup” column, “L” refers to a 16-railcar long EMU or a reconnected EMU of two 8-railcar short EMUs while “S” represents an 8-railcar short EMU. After arriving at the depot, each EMU stops in the temporary storage yard waiting for maintenance. After being maintained, 10
each EMU is pulled out to the temporary storage yard again waiting for departure. Therefore, each EMU stays twice in the temporary storage area. For example, EMU 3533L needs to stay in the temporary storage area from 18:24 to 19:12 and from 22:44 to 8:38 on the next day. We can treat two stays as two different EMUs, one from its arrival time to its maintenance starting time and the other from its maintenance ending time to its departure time. The transfer time between different yards has been included in the track utilization time. We do not consider the routing confliction at the trim end of the yard. TABLE 2: Information of EMUs Maintenance Makeup Arrival Time Starting Time Ending Time
Departure Time (Second Day)
Index
EMU ID
1
3533L
L
18:24
19:12
22:44
8:38
2
3027C
S
18:54
19:42
23:14
7:18
3
3026C
S
19:04
19:52
23:24
5:18
4
3534L
L
19:56
20:44
23:16
9:43
5
3022C
S
20:25
21:13
0:45
6:53
6
2564L
L
20:50
21:38
1:10
9:28
7
3033C
S
21:09
21:57
1:29
8:18
8
3051C
S
21:09
21:57
1:29
9:48
9
3041C
S
22:00
22:48
2:20
12:53
10
3075C
S
22:09
22:57
2:29
7:38
11
2566L
L
22:50
23:38
3:10
11:55
12
2559L
L
23:10
23:58
3:30
9:04
13
3043C
S
23:22
0:10
3:42
7:03
14
3038C
S
0:04
0:52
5:24
11:12
4.1 Results of the Case Study We still used IBM ILOG CPLEX 12.2 to solve the ETT model for the case. The run times for the ETT in the maintenance area and temporary storage area were 0.01s and 0.03s respectively. The results are listed in Tables 3 and 4 and show that all of the EMUs can follow the schedule in Table 2 when we have 8 tracks for maintenance and 10 tracks for temporary storage, as illustrated in Figure 3. 11
TABLE: 3 EMU-to-track Assignment of the Maintenance Area Track No. 1 2 3 4 5 6 7 8
Makeup S L S L S L S L S L S L S L S L
Section I
Section II 2564L
3041C 3027C 2566L 3026C, 3043C 3022C, 3038C
3533L, 2559L 3075C 3534L 3051C
In Table 3, the maintenance yard, including all 8 tracks, uses 49.467 track-hours for all EMUSs. The maintenance plan in this case spans 10.2 hours (i.e., from 19:12 to 5:24 on the next day) so the overall utilization rate of tracks in the maintenance area is 49.467 ÷ 10.2 ÷ 8 = 60.62%, which is very low. However, if we reduce the number of maintenance tracks to 7, the optimal objective function value of the ETT will become 13. In other words, only 13 EMUs can be maintained at most. The reason for such a low utilization rate is that the given arrival and departure times are not suitable for a stub-end type yard. EMUs that arrive earlier often depart earlier, while the stub-end type yard follows the first-in last-out fashion when two short EMUs share a track. In this case study, the temporary storage area with 10 tracks can accommodate all 14 EMUs, each staying in the area twice. If we reduce the yard size to 9 tracks, the optimal objective function value of the ETT is less than 28. The utilization rate of the temporary storage area with 10 tracks is 61.84%. In practice, the maintenance yard is usually considered the bottleneck of this EMU depot and its utilization rate needs to be improved. 12
TABLE 4: EMU-to-track Assignment of the Temporary Storage Area Track No. 1 2 3 4 5 6 7 8 9 10
Makeup S L S L S L S L S L S L S L S L S L S L
Section I
Section II
3533L, 3534L, 2564L, 2566L 3027C, 3022C 3533L 3026C, 3033C, 3041C, 3075C 3051C, 3041C 3034C
3075C, 3033C
3038C 2564L, 2566L 2559L 3027C
3034C, 3022C 3051C 2559L 3534L
3038C
3026C
The number of daily services of high-speed rail in China is expected to increase and the number of EMUs that require maintenance will increase even more because older ones need more maintenance. There is therefore an urgent to improve the utilization of tracks in the maintenance area to meet the expected higher demand. As shown in Table 2, the starting and ending times of each EMU at the maintenance area are given based on a master shift plan, in which most of EMUs that arrive at the maintenance yard earlier also depart the yard earlier. For this situation, there are two ways to increase the service capacity of a maintenance yard with the stub-end type as follows. (1) Reconnect two short EMUs as one long EMU and keep them together. For example, the EMUs of 3033C and 3051C are reconnected together and treated as a long EMU. The same reconnection is applied to 3041C and 3075C. The maintenance starting time and ending time of 13
the new 3033C+3051C are 21:57 and 1:44 (15 min of shunting time is added) respectively. Similarly, the maintenance starting time and ending time of the new 3041C+3075C are 22:57 and 2:29 respectively. After these two reconnections, we need only 7 tracks in the maintenance yard for the resulting 12 EMUs. After being reconnected, EMU 3041C is pulled out to the temporary storage yard at 2:29, which is 9 minutes later compared to the schedule in Table 2 but can still depart on time for daily service. This method is applicable if there are some short EMUs that arrive at the maintenance yard with a short time interval. Since this method will increase shunting work, the trim end of the depot may become a bottleneck. (2) Reschedule the maintenance starting and ending times of some EMUs. If the arrival and departure times of two short EMUs follow the policy of arrival earlier and departure later as shown in scenario (e) and (f) in Figure 2, those two short EMUs can share the same track. For example, if we change the departure time of EMUs 3027C and 3041C to 23:25 and 2:30 and change the arrival time and departure time of 3033C to 21:56 and 1:30, one track will be saved for all 14 EMUs. In other words, we can use 7 tracks to accommodate all maintenance tasks. Three pairs of short EMUs can share the same track, such as 3027C and 3026C, 3033C and 3051C, and 3041C and 3075C. However, this method may lead to longer dwell time on the maintenance track for some short EMUs. 4.2 Capacity of Stub-end Yard vs. Through Yard The service capacity of different yard types in an EMU depot depends on the maintenance schedule. If most of the short EMUs follow the first-in first-out rule at a yard, it is more suitable to design this yard with the through type. Otherwise, it may be more suitable to design it with the stub-end yard type. For this case study, short EMUs in general follow the first-in first-out rule so the service capacity of a through yard is larger than a stub-end yard. If the maintenance yard is turned into the through type so that EMUs moves from left to right, the computational time for CPLEX to solve the ETT with the same data in Table 2 is the same as that for the stub-end yard. The results show that only 6 tracks are needed in the maintenance yard for accommodating all 14 EMUs, as shown in Table 5. Compared to the 14
stub-end yard, 2 tracks are saved for serving the same number of EMUs. The track utilization rate is improved to 80.83%, much higher than the rate of 60.62% with the stub-end type.
TABLE 5: EMU-to-track Assignment of the Maintenance Area of Through Type Track No. 1 2 3 4 5 6
Makeup S L S L S L S L S L S L
Section I 3075C
Section II 3022C, 3038C
3051C
3033C
3043C
3041C 3533L
3026C
3027C 2564L 2566L 3534L, 2559L
TABLE 6: EMU-to-track Assignment of the Temporary Storage Area of Through Type Track No. 1 2 3 4 5 6 7 8 9
Makeup S L S L S L S L S L S L S L S L S L
Section I
Section II
3534L, 2564L, 3534L 3033C 3051C, 3043C 2559L 3041C 3022C, 3075C, 3027C 3533L 3026C, 3041C, 3038C, 3075C 3051C 2566L 3033C 3043C 2559L 3027C, 2566L 3022C 3026C, 3038C
2564L 3533L 15
Similarly, the number of tracks at the temporary storage yard could be reduced by one (i.e., we need only 9 tracks to accommodate all 14 EMUs twice) if we convert it into the through type, as shown in Table 6. In other words, the track utilization rate could be improved from 61.84% to 68.71% through the conversion. However, compared to the maintenance yard, the utilization improvement is smaller for the temporary storage yard in this case study. A possible reason for the smaller improvement is that the storage tasks span 16 hours and 48 minutes. 5. CONCLUSIONS This paper proposes an optimization model called ETT for the EMU-to-track assignment problem at high-speed rail EMU depots. This simple model, whose computational burden is very trivial, can be used for both stub-end yards and through yards and for any combinations of long and short EMUs. The time conflict constraints for stub-end yards and through yards are formulated through defining a set of EMUs that cannot share the same track with any given EMU. The set definition depends on the EMU type (long or short) and yard type (stub-end or through). A case study based on data from a Chinese Class-II EMU depot was conducted. The results show that the proposed method can help to generate an optimal EMU-to-track assignment with the highest track utilization. Furthermore, we found that the maintenance area is more suitable to be designed as through type with the maintenance times fixed for most of the EMUs, which in general follow the first-in first-out rule currently. Reconnecting two short EMUs to be maintained together as one long EMU or postponing the departure time of some short EMUs can help to improve the track utilization rate for a maintenance yard with the stub-end type. A possible future research direction is to schedule the dispatching plan of an EMU depot, which includes track assignment of different yards as well as detailed arrival and departure times of each EMU in each area based on the maintenance schedule of all EMUs. When we consider all areas in an integrated way and adjust the number of tracks assigned to each area, computational complexity is expected to be a challenge. Furthermore, the proposed ETT does not consider the time conflict at the trim end. It may be worthwhile to incorporate switch time conflicts to make the dispatching plan more executable. 16
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APPENDIX
Appendix A. Interface of the Daily Dispatching Application for Class II EMUs Depot
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Optimal Track Utilization in Electric Multiple Unit Maintenance Depots Highlights
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Build a simple model for improving the maintenance efficiency of electric multiple units in Chinese high-speed rails.
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The solution method yields the optimal track utilization in a small amount of computational time.
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A case is presented to show the real application of the method and discuss the difference caused by the track layout.
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