The empty wagons adjustment algorithm of Chinese heavy-haul railway

1

The empty wagons adjustment algorithm of Chinese heavy-

haul railway

ZHANG Jinchuan, YANG Hao, WEI Yuguang, SHANG Pan

School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China

Abstract: The paper studied the problem of empty wagons adjustment of Chinese heavy-haul

railway. Firstly, based on the existing study of the empty wagons adjustment of heavy-haul

railway in the world, Chinese heavy-haul railway was analyzed, especially the mode of

transportation organization and characteristics of empty wagons adjustment. Secondly, the

optimization model was set up to solve the empty wagons adjustment of heavy-haul railway and

the model took the minimum idling period as the function goal. Finally, through application and

solution of one case, validity and practicability of model and algorithm had been proved. So, the

model could offer decision support to transport enterprises on adjusting empty wagons.

Key words: empty wagons adjustment; dynamic planning; heavy-haul railway; idling period;

transportation organization

1 Introduction

Because of the quick development of CRH in recent years, part of passenger traffic volume of

existing railways has been transferred to the high-speed railways. So, the ability of freight

transportation of existing railways gets enhanced, and optimization of transportation

organization of existing railways becomes more possible. The developing direction of Chinese

railway freight are logistics for high valued freight and heavy-haul transportation for mass freight

at present[1].

The heavy-haul transportation can enhance the traffic ability and labor productivity, and also

reduce transport cost notably. According to the analysis of BNSF, organizing the heavy-haul

trains of 120 wagons loaded 112.5t, which will save5.2% of transport cost every year, can obtain

the best economic benefits. The heavy-haul railway mode is different between different countries.

There are mostly unit heavy-haul trains on American heavy-haul railway and combined trains

on Chinese heavy-haul railway, therefore, organization means have nothing in common with

each other in transportation of heavy-haul railway.

The heavy-haul railway is a dynamic complicated system, and the adjustment of empty

wagons is an important link. In order to guarantee the continuity of transport course, it is very

important to organize the empty wagons sent to loading areas from unloading areas continually.

The adjustment of empty wagons is a method of traffic flow adjustment to rationally distribute

the serviceable wagons to meet the need of wagons loading.

As to the issue of empty wagons adjustment, the past researches mostly direct against on

complexity of network structure and dynamic changes of transportation and production of

2

railway, the purpose is to improve models in order to realize abstract description of actual

adjustment and try hard to narrow the scale of the model constantly[2-10].Special literature is still

few that study empty wagons adjustment according to the characteristics of heavy-haul railway.

Firstly, the foreign heavily-haul railway mainly relies on the new and high technology and

equipment. The apparatus has abundant maintenance time. Transportation organization

(including empty wagons adjustment) is simpler instead; Secondly, Chinese transportation

system of heavy-haul railway lack of special further investigation, the related mode and method

of transportation organization are not systematized, which need further investigated.

The issue of empty wagons adjustment differ from each other between different modes of

heavy-haul railway. The issue need be studied according to the corresponding particularity. So,

the paper based on the thought optimizing the issue of empty wagons adjustment, set up a model

of that for Chinese heavy-haul railway.

2 Analysis of empty wagons adjustment of Chinese heavy-haul railway

2.1 Mode of Chinese heavy-haul railway

The mode of Chinese heavy-haul railway, of which both ends connecting relevant lines in the

railway network, is relatively independent in the railway network. In this mode, the source and

destination of traffic flow are relatively more complicated, and the majority of traffic flow need

make-up or break-up of trains in technical station in either ends of railway, thus form the mode

of Chinese heavy-haul railway, shown in Fig.1.

Technical Station

Heavy-haul Railway Ordinary Railway

Heavy-haul Empty

Train Flow

Ordinary Empty

Train Flow

Heavy-haul Loaded

Train Flow

Ordinary Loaded

Train Flow

Fig.1 Traffic flow organization of Chinese heavy-haul railway

In the empty wagons flow direction of the heavy-haul railway, on the influence of the

unloading apparatus, most heavy-haul train sets (long trains) arriving at unloading stations

should be disassembled to unload the freight, thus, one train set unloaded became several trains

(short trains). So, in Chinese heavy-haul railway, the technical stations combining or

disassembling train are called combination station or disassembly station. The train sets (long

3

trains) combined by some trains (short trains) called combination trains.

The main types of trains operated in the railway are combination and unit heavy-haul trains,

and direction of loaded or empty trains is generally fixed. Loading and unloading stations are

separately arranged in each end of heavy-haul railway. Therefore, combination stations and

disassembly stations are set up separately in each end. In unloading end, unloading stations link

to the combination stations (for the train with empty wagons). If the trains with empty wagons

from one unloading station need to be combined, they will generally be connected corresponding

to the loaded trains, shown in Fig.2.

Unloading End Loading End

Unloading

Station

Loading

Station

Heavy-haul Railway

Technical

StationTechnical

Station

Fig.2 Topological diagram of Chinese heavy-haul railway system

For example, Datong-Qinhuangdao railway is a closed ring system, but both ends of the

railway connect many other lines among the railway network, thus form the heavy-haul railway

system. In loading end, there are many loading stations located in Shanxi province, Shaanxi

province and Inner Mongolia. When the trains are loaded by freight, mainly coal, they are

transported through Datong-Qinhuangdao railway to the unloading stations in unloading end

located in Hebei province and Northeast China Region. Datong-Qinhuangdao railway is a

typical Chinese heavy-haul railway.

2.2 Characteristics of empty wagons adjustment of Chinese heavy-haul railway

The wagons of Chinese heavy-haul railway are attached to certain stations hence empty wagons

adjustment has certain particularity. The directions of empty wagons flow, according to which

empty wagons are concentrated and transported, have often been fixed. Compared to empty

wagons adjustment on ordinary railway, the particularities of heavy-haul railway mainly include

the following.

(1) Generally, empty wagons of heavy-haul railway are distributed in the form of a train.

According to weight and wagon type, the train sets of empty wagons can be divided into several

types.

(2) Because of the difference of the cycle of capital repair and interval time between trains,

the transport capacity of the direction of empty wagons is more abundant than that of the

direction of loaded wagons; hence, the train diagram of heavy-haul railway can be arranged as

train diagram not in pairs.

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(3) The empty wagons flow has basically been fixed and will not show convection.

(4) The wagons used in heavy-haul railway are expensive specialized vehicles of heavy axles,

so the turnaround of the wagons needs to be accelerated. Some specialized vehicles need

corresponding handling facilities in loading and unloading stations.

2.3 Questions considered by the model of empty wagons adjustment of heavy haul railway

Apparently, the combination and disassembling work for trains increase the work nodes and

reduce the vehicle turnover velocity, thus, it is very uneconomical. However, the work can reduce

the quantity of trains and is the main measure to improve transport capacity. When designing the

traffic program, the combination and disassembling work for trains should be reduced as much

as possible according to the limitation of transport capacity. From feedback of empty wagons,

not all trains with empty wagons need to be combined to be delivered; some trains with empty

wagons can directly be delivered if transport capacity is enough.

In the unloading end of the heavy haul railway, the problem, feedback of empty wagons mainly

concerned, is to reduce the times of combination and disassembling work for trains, decrease

work nodes, and accelerate vehicle turnaround.

When Analyzing and carrying on modeling on empty wagons adjustment of heavy haul

railway, the following questions should be considered.

(1)The proportion of the trains that transported directly from unloading end to loading end should

be tried hard to increase.

Basically, the number of wagons in a long train is 2 or 4 times than that in a small train. If the

adjustment of empty wagons is carried out totally according to the train structure of the loaded

train direction, it will certainly be influenced that the turn-round time of the rolling stock greatly.

Because the loaded wagons are basically made up at one single station, and the continuing time

between trains is shorter, meanwhile, the makeup of empty wagons should be carried out at

several stations because of the disperse whereabouts, which will certainly increase continuing

time between the trains, and then influence turn-round time of the rolling stocks.

The proportion of empty trains (small trains) directly transported from unloading station to

loading station should be increased. Thus, the train density increases. So certain measures must

be taken to increase the carrying capacity of the railway. That is, it is to reduce accumulation

time of rolling stocks by improving the carrying capacity of railway, and then reducing the turn-

round time of rolling stocks.

(2)Carrying capacity has great influence on the numbers of loaded trains and empty trains

When carrying capacity of the railway is relatively more than need, with the increase of traffic

flow, it is to increase the loaded train quantity in order to meet the request of traffic capacity at

first. Meanwhile, the empty train quantity will correspondingly increase. So, the ratio between

empty trains and loaded trains does not change much finally.

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When carrying capacity of the railway is meet the request, with the increase of traffic flow, it

is to operate the trains with increasing number of wagons in a train to load more freight to meet

the request of traffic capacity at first, but the loaded train quantity will not change greatly.

Meanwhile, the empty train quantity will vary greatly because the empty trains will be

disassembled and directly transported with less number of wagons considering carrying capacity

and turn-round time of rolling stocks. So, the ratio between empty trains and loaded trains

changes greatly.

3 Model of empty wagons adjustment of heavy-haul railway

3.1 Variables Declaration for model of empty wagons adjustment

Based on the analysis of empty wagons adjustment of heavy-haul railway, the paper, considering

the load end and unload end of the heavy-haul railway as a whole, taking it as the function goal

that minimizing the idling period of empty wagons, sets up the model of empty wagons

adjustment giving consideration to the load end and unload end of the heavy-haul railway.

The meaning of variables and the relation among variables should be defined when setting up

the model. The variables of the model are stated as following Tab.1.

Tab.1 Variables Declaration for model of empty wagons adjustment

Variables Meanings

S ( s S ) Set of unloading stations

D ( d D ) Set of combination stations

F ( f F ) Set of disassembly stations

E ( e E ) Set of loading stations

K ( k K ) Set of types of empty trains e

kw Function of idling period

k Influence coefficient

e

kg Earliest expected arrival time of empty trains permitted by loading station

e

kl Latest expected arrival time of empty trains permitted by loading station

e

kt Arrival time of empty trains to loading station

s

kt Departure time of empty trains from unloading station

sdT Running time of empty trains from unloading station s to combination station d sd

kZH 0-1 Variable for combination of empty trains in combination station

'

ZH

kkT Combination time of combination of empty trains

'

FJ

kkT Disassembly time of empty trains

TDT Running time of empty trains on heavy-haul railway

feT Running time of empty trains from disassembly station f to loading station e

s

k Quantity of k type of empty trains from unloading station s

e

kq Quantity of k type of empty trains requested by loading station e

sd

kx Quantity of k type of empty trains running from unloading station s to combination

station d

6

sd

kM Carrying capacity of railway from unloading station s to combination station d

fe

kx Quantity of k type of empty trains from disassembly station f to loading station e

fe

kM Carrying capacity of railway from disassembly station f to loading station e

sd

ky Quantity of empty trains for combination from unloading station s to combination

station d fARR

kt Arrival time of empty trains to disassembly station

fDEP

kt Departure time of empty trains from disassembly station

RECI Time interval between receiving trains

DEPI Time interval between departure trains

TDM Carrying capacity of heavy-haul railway

sd

k Combination coefficient of empty trains for combination

In Chinese heavy-haul railway, the variable k representing types of empty trains generally

include unit train made-up by 50 empty wagons and unit train made-up by 100 empty wagons.

Because the numbers of empty wagons in the trains are different, the value of idling periods are

different for different trains. So the variable of influence coefficient k is value according to

the types of empty trains. The value of k in Chinese heavy-haul railway is shown as following.

when the train made-up by 50 empty wagons

when the train made-up by 100 empty wagons

1

2k

3.2 Model of empty wagons adjustment

Based on the above defined variables, the model of empty wagons adjustment of heavy-haul is

to be introduced.

The objective of the model is to minimize the idling period of empty wagons, so the calculation

method of idling period need discussed. Because the time is wasted when the empty trains arrive

the loading station earlier or later than the stations expect, so the paper introduces the expected

arrival time space of empty trains shown as Fig.3.

TimeExpected

arrival time

Idli

ng

per

iod

45°45°

Earlier Later

Fig.3 Description of expected arrival time space of empty trains

And also, the following formula[19] is given

7

( ) max[ ,0] max[ ,0]e e e e e e

k k k k k k

k K e E k K e E

w t g t t l

（1）

The function of idling period took e

kt as independent variable, aim to meet the request to

transport the empty trains to loading station in times of need. And, arrival time of empty trains

to loading station is given

' '( )e s sd sd ZH FJ fe

k k kZH TDkk kkt t T T T T T （2）

Traffic equilibrium condition between loading station and unloading station is

s e

k k

s S k K e E k K

q

（3）

Traffic equilibrium condition between loading station and combination station is

sd s

k k

d D

x

（4）

Traffic equilibrium condition between unloading station and disassembly station is

fe e

k k

f F

x q

（5）

Constraint of carrying capacity of route between loading station and combination station is

sd sd

k kx M （6）

Constraint of carrying capacity of route between unloading station and disassembly station is

fe fe

k kx M （7）

Constraint of number of combination trains

sd sd

k ky x （8）

Constraint of quantitative relation between sd

ky and sd

kZH is

sd sd

kk

s S d D

y

组（9）

Constraint of time interval between receiving trains

'fARR fARR

k k RECt t I （10）

Constraint of time interval between departure trains

'fDEP fDEP

k k DEPt t I （11）

The formula calculating arrival time of empty trains to disassembly station is

'

fARR s sd sd ZH

k k kZH TDkkt t T T T （12）

The formula calculating departure time of empty trains from disassembly station is

' '( )fDEP s sd sd ZH FJ

k k kZH kk kkt t T T T （13）

8

Constraint of carrying capacity of heavy-haul railway is

sd sd sd sd

k k k k TDx y y M （14）

So, the model of empty wagons adjustment of heavy-haul railway is set up as follows:

Min ( )e e

k k k

k K f F

w t

（15）

St. Eq. (1) – Eq. (14)

3.3 Algorithm for the model - dynamic programming

The key thought of dynamic planning is optimization principle put forward by American

mathematician Richard Bellman. The principle has caused the decision method stage by stage,

which is based on the fact of overall optimization to seek the optimal solution at a certain stage.

Dynamic planning handles a complicated problem with n-dimensional variables stage by stage.

The method turns the problem with n-dimensional variables into solving a single variable

problem. It will simplify the solution procedure and save enormous calculation amount, which

is impossible for the classical methods solving extreme value.

There is extensive application of dynamic planning algorithm in the field of transportation

organization of railway, such as railway location design and phased construction, optimization

of development scheme for marshalling stations, design of passenger flow line in terminal

stations[11-18], and so on.

In the paper, the dynamic programming algorithm for the model of empty wagons adjustment

was designed as following.

Stages: Considering the particularities of the empty wagons adjustment model of heavy-haul

railway, division stages need defined. The paper sequenced the arrival times of every empty train

consist of 50 wagons, which was taken as basic unit, to combination stations. The No. of empty

trains were regarded as the stages in the dynamic planning algorithm, as shown in Tab.2.

Tab. 2 Departure time of empty trains from unloading stations

No. of empty trains Departure time of empty trains

1 xx:xx

2 xx:xx

3 xx:xx

…… ……

n xx:xx

Status: It is named status that the objective condition at the beginning of every stages. In the

issue, the situation is considered that the present empty trains were only combined with the empty

trains of later stages, other situations were left out of account. So, when the situation of the nth

9

empty train was considered at present, if the train need combined with the previous empty trains,

the situation of n-2 stage was called to be calculated; if the train need not combined with the

previous empty trains, the situation of n-1 stage was called to be calculated;

Decision: After the status of every stages were confirmed definitely, the different decides can

be made, thus the status of the next stage was confirmed, and this kind of operation is called

decision. In the problem, except the first empty train with only one decision of non-combination,

there were two types of decisions that the present empty trains combined with the previous trains

or not at other stages.

Status transition: The status at this stage is often a decision result on last stage in dynamic

planning. In this algorithm, because decision at this stage was correlated with the status of the

preceding one or two stages, so the definition of status transition was the same as the definition

of status.

Dynamic programming calculation table: The dynamic planning computation sheet that the

paper designed is as shown in Tab. 3.

Tab. 3 Calculation table of dynamic programming for the model

1 2 3 4 5 6 No. of

empty

trains

Idling period if

combination

Idling period if

non- combination

Time

difference

Decision-making(No.

of trains combined)

Result of idling

period

1

2

3

……

n

The first column is filled with No. of empty trains, which is the stage in the dynamic planning

algorithm as discussed above. The second column is filled with the total idling period which is

the sum of present idling period and idling period of the previous n-2 stage, if the present empty

trains will be combined with the empty trains at previous stages. The third column is filled with

the total idling period which is the sum of present idling period and idling period of the previous

n-1 stage, if the present empty trains will not be combined with the empty trains at previous

stages. The fourth column is filled with the difference between the second and third column, as

the essential to choose more combination trains under the constraints of carrying capacity of

railway. The fifth column is filled with the decision-making of combination of the empty trains.

The fifth column is filled with the minimum value of the second and third column, as the idling

period under the optimal decision.

When the optimal solution was obtained, but the constraints of carrying capacity became more

stringent, so more empty trains need combined. Thus, the trains will be chosen to be combined,

whose value in the sixth column is positive and minimum.

10

4 Case study on model of empty wagons adjustment of heavy-haul railway

4.1 Basic situation introduction of the case

In order to prove validity and practicability of the model, a heavy-haul railway system will be

introduced which consists of 3 loading stations, 3 unloading stations, 1 combination station and

1 disassembly station, shown as Fig.4.

1

2

3

4

5

6

Combination

Station

Disassembly

Station

Unloading End Loading EndHeavy-haul

Railway

Fig.4 Network of heavy-haul railway system of the case

The serial number is 1, 2, and 3 to the unloading stations, and 4, 5, and 6 to the loading stations

sequentially. The unloading stations linked to the combination station directly, and the loading

stations linked to the disassembly station directly. The combination station and the disassembly

station were joined by the heavy-haul railway.

4.2 Introduction to known conditions of the model

The departure times and quantity of empty trains of all unloading stations are shown from

Tab.4 to Tab.6. The empty trains were to be ranked and numbered according to the time, which

was taken as the stage of dynamic planning algorithm.

Tab.4 Departure time and quantity of empty trains of No.1 unloading station

No. of empty trains 1 2 3 4 5

Departure time 6:50 7:10 7:30 8:10 8:30



Departure time 6:55 7:15 7:45 8:15 8:55



Departure time 9:00 9:20 9:30 9:40 9:40

The arrival times and quantity of empty trains requested by all loading stations are shown from

Tab.7 to Tab9.

Tab.7 Arrival time and quantity of empty trains requested by N0.4 loading station


Arrival time requested 12:40 12:50 12:50 13:10 13:20

11







It is shown as Tab.10 that the running time from unloading stations to the combination station.

Tab.10 Running time of empty trains from unloading stations to the combination station

No. of unloading station 1 2 3

sdT （min） 10 15 20

It is shown as Tab.11 that the running time from loading stations to the disassembly station.

Tab.11 Running time of empty trains from loading stations to the disassembly station

No. of loading station 4 5 6

feT （min） 20 15 10

There are other known conditions shown as following.

TDT =270min， '

ZH

kkT =30min， '

FJ

kkT =30min,

RECI =10min, DEPI =10min。

4.3 Solution procedures of the model

According to known terms, the arrival time of empty trains to combination station and the

requested time of empty trains by disassembly station were to be calculated at first, as shown

Tab.12 and Tab.13.

Tab.12 Arrival time of empty trains to combination station


Arrival time to combination station 7:00 7:10 7:20 7:30 7:40





Tab.13 Requested time of empty trains by disassembly station


Requested time of disassembly station 12:20 12:30 12:30 12:30 12:40





The model was solved according to the known conditions by use dynamic planning algorithm,

and process are shown in Tab.14.

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Tab.14 Solution procedures without constraint of carrying capacity

No. of

empty

trains

Idling period if

combination

Idling period if

non- combination

Time

difference

Decision-making(No. of

trains combined)

Result of

idling

period

1 / 5

6 / / /

2 0+2

6+

1

6=

3

6

5

6+

1

6=

6

6 -

3

6 1 and 2

3

6

3 5

6+

2

6+

2

6=

9

6

3

6+

4

6=

7

6

2

6 1 and 2

7

6

4 3

6+

3

6+

3

6=

9

6

7

6+

3

6=

10

6 -

1

6 1 and 2, 3 and 4

9

6

5 7

6+

4

6+

5

6=

16

6

9

6+

2

6=

11

6

15

6 1 and 2, 3 and 4

11

6

6 9

6+

5

6+

5

6=

19

6

11

6+

1

6=

12

6

7

6 1 and 2, 3 and 4

12

6

7 11

6+

6

6+

7

6=

24

6

12

6+0=

12

6

12

6 1 and 2, 3 and 4

12

6

8 12

6+

6

6+

7

6=

25

6

12

6+0=

12

6

12

6 1 and 2, 3 and 4

12

6

9 12

6+

7

6+

7

6=

26

6

12

6+

1

6=

13

6

13

6 1 and 2, 3 and 4

13

6

10 12

6+

7

6+

10

6=

29

6

13

6+

1

6=

14

6

15

6 1 and 2, 3 and 4

14

6

11 13

6+

7

6+

8

6=

28

6

15

6+0=

15

6

13

6 1 and 2, 3 and 4

15

6

12 14

6+

6

6+

9

6=

29

6

15

6+0=

15

6

14

6 1 and 2, 3 and 4

15

6

13 15

6+

6

6+

7

6=

28

6

15

6+0=

15

6

13

6 1 and 2, 3 and 4

15

6

14 15

6+

5

6+

7

6=

27

6

15

6+

1

6=

16

6

11

6 1 and 2, 3 and 4

16

6

15 15

6+

2

6+

5

6=

22

6

16

6+

8

6=

24

6 -

2

6

1 and 2, 3 and 4, 14 and

15

22

6

Through calculation of the model, the optimum scheme is that No.1 train combined with No.2

train, No.3 train combined with No.4 train, No.14 train combined with No.15 train, and other

trains are not combined. The idling period is 3.67 hour under the optimal solution.

If carrying ability of the route is busy at 13:00 - 14:00, transporting only 3 trains, the further

solution was to be chased because it needed transport 4 trains under present optimal solution.

It was to find the empty train with the positive and minimum value in the sixth column in

Tab4-11, which was to be combined with the previous train. In the case, the ones are No.9 and

No.11train. Anyone of the two could be chosen, and No.9 train chosen for instance. The No.9

train was combined with No.8 train, and seeking the optimal solution under constraint of carrying

13

capacity. Solution process are shown in Tab.15.

Tab.15 Solution procedures with constraint of carrying capacity

No. of

empty

trains

Idling period if

combination

Idling period if

non-combination

Time

difference

Decision-

making(No. of trains

combined)

Result of idling period

1 / 5

6 / / /

2 0+2

6+

1

6=

3

6

5

6+

1

6=

6

6 -

3

6 1 and 2

3

6

3 5

6+

2

6+

2

6=

9

6

3

6+

4

6=

7

6

2

6 1 and 2

7

6

4 3

6+

3

6+

3

6=

9

6

7

6+

3

6=

10

6 -

1

6 1 and 2, 3 and 4

9

6

5 7

6+

4

6+

5

6=

16

6

9

6+

2

6=

11

6

15

6 1 and 2, 3 and 4

11

6

6 9

6+

5

6+

5

6=

19

6

11

6+

1

6=

12

6

7

6 1 and 2, 3 and 4

12

6

7 11

6+

6

6+

7

6=

24

6

12

6+0=

12

6

12

6 1 and 2, 3 and 4

12

6

8 12

6+

6

6+

7

6=

25

6

12

6+0=

12

6

12

6 1 and 2, 3 and 4

12

6

9 12

6+

7

6+

7

6=

26

6

12

6+

1

6=

13

6 /

1 and 2, 3 and 4, 8

and 9

26

6

10 12

6+

7

6+

10

6=

29

6

26

6+

1

6=

27

6

2

6

1 and 2, 3 and 4, 8

and 9

27

6

11 26

6+

7

6+

8

6=

41

6

27

6+0=

27

6

14

6

1 and 2, 3 and 4, 8

and 9

27

6

12 27

6+

6

6+

9

6=

42

6

27

6+0=

27

6

15

6

1 and 2, 3 and 4, 8

and 9

27

6

13 27

6+

6

6+

7

6=

40

6

27

6+0=

27

6

13

6

1 and 2, 3 and 4, 8

and 9

27

6

14 27

6+

5

6+

7

6=

39

6

27

6+

1

6=

28

6

11

6

1 and 2, 3 and 4, 8

and 9

28

6

15 27

6+

2

6+

5

6=

34

6

28

6+

8

6=

36

6 -

2

6

1 and 2, 3 and 4, 8

and 9, 14 and 15

22

6

The optimum scheme under constraint of carrying capacity is that No.1 train combined with

No.2 train, No.3 train combined with No.4 train, No.8 train combined with No.9 train, No.14

train combined with No.15 train, and other trains are not combined. The idling period is 5.67

hour under the optimal solution.

5 conclusion

Empty wagons adjustment of heavy-haul railway was a complicated and dynamic problem.

The paper, based on the thought optimizing the issue by considering the loading end and

14

unloading at the same time, set up a model taking the minimum idling period as the function goal

and used dynamic planning to solve the problem. But there are a lot of details needed further

researched. Firstly, extension of number of combination and disassembly stations. There will be

several combination and disassembly stations, and there will be exchanged empty trains among

them. The paper just considered one combination station and one disassembly station. Secondly,

extension of types of empty trains. There will be several kinds of empty train in the heavy-haul

trains, unit trains made-up by 50 or 100 empty wagons, and combination trains made-up by 100,

150, or 200 empty wagons. The paper just considered the unit empty trains, and more groups of

kinds of empty trains could be studied.

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The empty wagons adjustment algorithm of Chinese heavy-haul railway

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