The document discusses operational planning for railroad yards. It introduces how inbound trains are disassembled by hump engines and railcars are classified, then outbound trains are assembled by pullback engines. It describes challenges around scheduling hump and pullback engines given arrival times and train compositions. Solutions proposed include longest-first humping sequences and considering waiting for longer trains to arrive to reduce idle time.

1. 1/39
Session C3: 排程理論2013/10/19 15:00 ~ 16:20 @ 管理一館301 室
Effective Heuristics for
Scheduling Hump & Pullback Engines
in Railroad Yard Operational Plans
I-Lin Wang (Associate Professor)
Wei Lee (Junior)
Chiao-Yu Liao (Junior)
Dept of Industrial & Information Management
National Cheng Kung University

2. 2/39
Railroad Yard
Team NCKU lead by I-Lin Wang

3. 4/39
Introduction
Hump engine Pullback engine
Team NCKU lead by I-Lin Wang
10 tracks; 185 cars
42 tracks;
60 cars
7 tracks; 207 cars

4. 5/39
Introduction
Hump engine Pullback engine
Team NCKU lead by I-Lin Wang
10 tracks; 185 cars
42 tracks;
60 cars
7 tracks; 207 cars

5. 6/39
Introduction
• The inbound trains in receiving area are disassembled and
humped to classification area by hump engine.
Hump engine Pullback engine
Team NCKU lead by I-Lin Wang
10 tracks; 185 cars
42 tracks;
60 cars
7 tracks; 207 cars

6. 7/39
Introduction
• The inbound trains in receiving area are disassembled and
humped to classification area by hump engine.
Hump engine Pullback engine
Team NCKU lead by I-Lin Wang
10 tracks; 185 cars
42 tracks;
60 cars
7 tracks; 207 cars

7. 8/39
Introduction
• The inbound trains in receiving area are disassembled and
humped to classification area by hump engine.
Hump engine Pullback engine
Team NCKU lead by I-Lin Wang
10 tracks; 185 cars
42 tracks;
60 cars
7 tracks; 207 cars

8. 9/39
Introduction
• The inbound trains in receiving area are disassembled and
humped to classification area by hump engine.
Hump engine Pullback engine
Team NCKU lead by I-Lin Wang
10 tracks; 185 cars
42 tracks;
60 cars
7 tracks; 207 cars

9. 10/39
Introduction
• The inbound trains in receiving area are disassembled and
humped to classification area by hump engine.
Hump engine Pullback engine
Team NCKU lead by I-Lin Wang
10 tracks; 185 cars
42 tracks;
60 cars
7 tracks; 207 cars

10. 11/39
Introduction
• The inbound trains in receiving area are disassembled and
humped to classification area by hump engine.
• The railcars in classification tracks are assembled by
pullback engine to generate the desired outbound train.
Hump engine Pullback engine
Team NCKU lead by I-Lin Wang
10 tracks; 185 cars
42 tracks;
60 cars
7 tracks; 207 cars

11. 12/39
Introduction
• The inbound trains in receiving area are disassembled and
humped to classification area by hump engine.
• The railcars in classification tracks are assembled by
pullback engine to generate the desired outbound train.
Hump engine Pullback engine
Team NCKU lead by I-Lin Wang
10 tracks; 185 cars
42 tracks;
60 cars
7 tracks; 207 cars

12. 13/39
Introduction
• The inbound trains in receiving area are disassembled and
humped to classification area by hump engine.
• The railcars in classification tracks are assembled by
pullback engine to generate the desired outbound train.
Hump engine Pullback engine
Team NCKU lead by I-Lin Wang
10 tracks; 185 cars
42 tracks;
60 cars
7 tracks; 207 cars

13. 14/39
Introduction
• The inbound trains in receiving area are disassembled and
humped to classification area by hump engine.
• The railcars in classification tracks are assembled by
pullback engine to generate the desired outbound train.
Hump engine Pullback engine
Team NCKU lead by I-Lin Wang
10 tracks; 185 cars
42 tracks;
60 cars
7 tracks; 207 cars

14. 15/39
Introduction
• The inbound trains in receiving area are disassembled and
humped to classification area by hump engine.
• The railcars in classification tracks are assembled by
pullback engine to generate the desired outbound train.
Hump engine Pullback engine
Team NCKU lead by I-Lin Wang
10 tracks; 185 cars
42 tracks;
60 cars
7 tracks; 207 cars

15. 16/39
Introduction
• The inbound trains in receiving area are disassembled and
humped to classification area by hump engine.
• The railcars in classification tracks are assembled by
pullback engine to generate the desired outbound train.
Hump engine Pullback engine
Team NCKU lead by I-Lin Wang
10 tracks; 185 cars
42 tracks;
60 cars
7 tracks; 207 cars

16. 17/39
Introduction
• The inbound trains in receiving area are disassembled and
humped to classification area by hump engine.
• The railcars in classification tracks are assembled by
pullback engine to generate the desired outbound train.
Hump engine Pullback engine
Team NCKU lead by I-Lin Wang
10 tracks; 185 cars
42 tracks;
60 cars
7 tracks; 207 cars

17. 18/39
Operational Planning
Team NCKU lead by I-Lin Wang
• Given
– Arrival time, numbers & types of railcars for each train
– # tracks in receiving, classification, departure areas
– Time of processing, transporting, inspection a railcar or train
• Objective
• Decisions

18. 19/39
Operational Planning
Team NCKU lead by I-Lin Wang
• Given
– Arrival time, numbers & types of railcars for each train
– # tracks in receiving, classification, departure areas
– Time of processing, transporting, inspection a railcar or train
• Objective
– Give a schedule that minimizes the total waiting time
• Decisions

19. 20/39
Operational Planning
Team NCKU lead by I-Lin Wang
• Given
– Arrival time, numbers & types of railcars for each train
– # tracks in receiving, classification, departure areas
– Time of processing, transporting, inspection a railcar or train
• Objective
– Give a schedule that minimizes the total waiting time
• Decisions
– When to pull which train from waiting area to receiving area
– When to hump which train in receiving area
– Which railcars to be assigned to which classification track
– When to assemble how many railcars
from which classification tracks to which departure track by
which pull-back engine

20. 21/39
Bottlenecks
• Too many possible assembly combinations
• Humping sequence
• Timing for humping & pulling back operations
Team NCKU lead by I-Lin Wang

21. 22/39
Bottlenecks
• Too many possible assembly combinations
– A train may have up to 7 railcar types
– A train of k railcar types can have 2k-1 subsets
– For each subset, too many possible number of
railcar combinations
• E.g. a 200-car train by 3 car types, with x, y, & z cars,
then x+y+z=200, x,y,z≥1 has a lot of feasible solutions
• Humping sequence
• Timing for humping & pulling back operations
Team NCKU lead by I-Lin Wang

22. 23/39
Solution Methods
• Integer Programming
• Meta-Heuristics
• Greedy Heuristics
• Key operations in our solution:
Team NCKU lead by I-Lin Wang

23. 24/39
Solution Methods
• Integer Programming
 Too much time/storage
– Can only deal with small-scale problems
– Too many variables
– Nonlinear objective function
• Meta-Heuristics
• Greedy Heuristics
• Key operations in our solution:
Team NCKU lead by I-Lin Wang

24. 25/39
Solution Methods
• Integer Programming
 Too much time/storage
– Can only deal with small-scale problems
– Too many variables
– Nonlinear objective function
• Meta-Heuristics
 Not intuitive
– Genetic Algorithm, Tabu Search,….etc.
• Greedy Heuristics
• Key operations in our solution:
Team NCKU lead by I-Lin Wang

25. 26/39
Solution Methods
• Integer Programming
 Too much time/storage
– Can only deal with small-scale problems
– Too many variables
– Nonlinear objective function
• Meta-Heuristics
 Not intuitive
– Genetic Algorithm, Tabu Search,….etc.
• Greedy Heuristics
– FIFO? SPT? EDD?
 How & When ?
E.g. Longest Track First
• Key operations in our solution:
Team NCKU lead by I-Lin Wang

26. 27/39
Solution Methods
• Integer Programming
 Too much time/storage
– Can only deal with small-scale problems
– Too many variables
– Nonlinear objective function
• Meta-Heuristics
 Not intuitive
– Genetic Algorithm, Tabu Search,….etc.
• Greedy Heuristics
– FIFO? SPT? EDD?
 How & When ?
E.g. Longest Track First
• Key operations in our solution:
– How and when to conduct a hump process?
– How and when to conduct a pullback process?
Team NCKU lead by I-Lin Wang

27. 28/39
Waiting Time in Humping
• Hump time of a train=
Humping interval + Hump Rate * length of train
Constant Constant
Team NCKU lead by I-Lin Wang

28. 29/39
Waiting Time in Humping
• Hump time of a train=
Humping interval + Hump Rate * length of train
Constant Constant
E.g. Trains a & b are to be humped with lengths na > nb.
Hump a first, then b.
Team NCKU lead by I-Lin Wang

29. 30/39
Waiting Time in Humping
• Hump time of a train=
Humping interval + Hump Rate * length of train
Constant Constant
E.g. Trains a & b are to be humped with lengths na > nb.
Hump a first, then b.
Train a Train b
Team NCKU lead by I-Lin Wang

30. 31/39
Waiting Time in Humping
• Hump time of a train=
Humping interval + Hump Rate * length of train
E.g. Trains a & b are to be humped with lengths na > nb.
Hump a first, then b.
Train a Train b
Team NCKU lead by I-Lin Wang
nb
na
Constant Constant

31. 32/39
Waiting Time in Humping
• Hump time of a train=
Humping interval + Hump Rate * length of train
E.g. Trains a & b are to be humped with lengths na > nb.
Hump a first, then b.
– Total waiting time = the shaded area
Train a Train b
Team NCKU lead by I-Lin Wang
nb
na
Constant Constant

32. 33/39
Humping Sequence
Team NCKU lead by I-Lin Wang
• Longest-first
• Shortest-first

33. 34/39
Humping Sequence
Team NCKU lead by I-Lin Wang
n4
Train 1 Train 2 Train 3 Train 4
n3
n2
n1
n1
n2
n3
n4
Train 4 Train 3 Train 2 Train 1
• Longest-first
• Shortest-first

34. 35/39
Humping Sequence
Team NCKU lead by I-Lin Wang
n4
Train 1 Train 2 Train 3 Train 4
n3
n2
n1
n1
n2
n3
n4
Train 4 Train 3 Train 2 Train 1
• Longest-first
• Shortest-first

35. 36/39
Humping Sequence
Team NCKU lead by I-Lin Wang
n4
Train 1 Train 2 Train 3 Train 4
n3
n2
n1
n1
n2
n3
n4
Train 4 Train 3 Train 2 Train 1
• Longest-first
• Shortest-first

36. 37/39
Humping Sequence
Team NCKU lead by I-Lin Wang
n4
Train 1 Train 2 Train 3 Train 4
n3
n2
n1
n1
n2
n3
n4
Train 4 Train 3 Train 2 Train 1
• Longest-first
• Shortest-first

37. 38/39
Humping Sequence
Team NCKU lead by I-Lin Wang
n4
Train 1 Train 2 Train 3 Train 4
n3
n2
n1
n1
n2
n3
n4
Train 4 Train 3 Train 2 Train 1
• Longest-first
• Shortest-first
Extra area

38. 39/39
Should We Wait? For How Long?
• Suppose 3 trains a, b, and c to be humped with na>nb>nc,
and a longer train d will arrive in x min.
 No wait for d : humping order a-d-b-c
 Wait for d : humping order d-a-b-c
Team NCKU lead by I-Lin Wang

39. 40/39
Should We Wait? For How Long?
• Suppose 3 trains a, b, and c to be humped with na>nb>nc,
and a longer train d will arrive in x min.
 No wait for d : humping order a-d-b-c
Train a Train d Train b Train c
 Wait for d : humping order d-a-b-c
Team NCKU lead by I-Lin Wang
nc
nb
nd
na
x

40. 41/39
Should We Wait? For How Long?
• Suppose 3 trains a, b, and c to be humped with na>nb>nc,
and a longer train d will arrive in x min.
 No wait for d : humping order a-d-b-c
Train a Train d Train b Train c
 Wait for d : humping order d-a-b-c
Team NCKU lead by I-Lin Wang
nc
nb
nd
na
x
Train d Train a Train b Train c
nc
nb
na
nd
x

41. 42/39
Should We Wait? For How Long?
• Suppose 3 trains a, b, and c to be humped with na>nb>nc,
and a longer train d will arrive in x min.
 No wait for d : humping order a-d-b-c
Train a Train d Train b Train c
 Wait for d : humping order d-a-b-c
Team NCKU lead by I-Lin Wang
nc
nb
nd
na
x
Train d Train a Train b Train c
nc
nb
na
nd
x

42. 43/39
Single Pull
engine
Team NCKU lead by I-Lin Wang
……
Classification tracks Departure tracks

43. 44/39
Single Pull
engine
Team NCKU lead by I-Lin Wang
……
Classification tracks Departure tracks

44. 45/39
Single Pull
engine
10 minute
Team NCKU lead by I-Lin Wang
……
Classification tracks Departure tracks

45. 46/39
Multi-Pull
engine
Team NCKU lead by I-Lin Wang
……
Classification tracks Departure tracks

46. 47/39
Multi-Pull
engine
Team NCKU lead by I-Lin Wang
……
Classification tracks Departure tracks

47. 48/39
Multi-Pull
engine
10 minute
Team NCKU lead by I-Lin Wang
……
Classification tracks Departure tracks

48. 49/39
Multi-Pull
engine
10+ 1 5 + 1 5 minute
Team NCKU lead by I-Lin Wang
……
Classification tracks Departure tracks

49. 50/39
Pullback Decision
• To assemble a departure train of the same
size, single pull takes less time than multi-pull
 If possible, conduct single pull (on longest track)
 Sometimes it pays to wait longer
 multi-pull may be beneficial to avoid congestion
Team NCKU lead by I-Lin Wang

50. 51/39
Pullback Decision
• To assemble a departure train of the same
size, single pull takes less time than multi-pull
 If possible, conduct single pull (on longest track)
• Too frequent fast pulling back might cause
congestion by outbound interval
 Sometimes it pays to wait longer
 multi-pull may be beneficial to avoid congestion
Team NCKU lead by I-Lin Wang

51. 52/39
Outbound Train Interval
ready
ready
Ready
Departure tracks
Team NCKU lead by I-Lin Wang

52. 53/39
Outbound Train Interval
ready
Ready
Departure tracks
Team NCKU lead by I-Lin Wang

53. 54/39
Outbound Train Interval
ready
Departure tracks
Team NCKU lead by I-Lin Wang
10 minute later
Ready

54. 55/39
Outbound Train Interval
Departure tracks
Team NCKU lead by I-Lin Wang
10 minute later
Ready

55. 56/39
Outbound Train Interval
Ready
Departure tracks
Team NCKU lead by I-Lin Wang

56. 57/39
Outbound Train Interval
Ready
Departure tracks
10 minute later
Team NCKU lead by I-Lin Wang

57. 58/39
Outbound Train Interval
Departure tracks
10 minute later
Team NCKU lead by I-Lin Wang

58. 59/39
Outbound Train Interval
Departure tracks
Team NCKU lead by I-Lin Wang

59. 60/39
Outbound Train Interval
Wait for another 20 minute !!!
Departure tracks
Team NCKU lead by I-Lin Wang

60. 61/39
Timing for multi-pull
engine
Team NCKU lead by I-Lin Wang
……

61. 62/39
Timing for multi-pull
engine
Team NCKU lead by I-Lin Wang
……

62. 63/39
Timing for multi-pull
engine
Team NCKU lead by I-Lin Wang
……
10

63. 64/39
Timing for multi-pull
engine
Team NCKU lead by I-Lin Wang
……
10 + 45

64. 65/39
Timing for multi-pull
engine
Team NCKU lead by I-Lin Wang
……
10 + 45 + x

65. 66/39
Timing for multi-pull
If x ≧ 15
10 + 45 + x ≧ 10 + 45 + 15
Team NCKU lead by I-Lin Wang

66. 67/39
Timing for multi-pull
If x ≧ 15
10 + 45 + x ≧ 10 + 45 + 15
larger than multi-pull one more
track
Team NCKU lead by I-Lin Wang

67. 68/39
Timing for multi-pull
If x ≧ 30
10 + 45 + x ≧ 10 + 45 + 30
Team NCKU lead by I-Lin Wang

68. 69/39
Timing for multi-pull
If x ≧ 30
10 + 45 + x ≧ 10 + 45 + 30
larger than multi-pull two more
tracks
Team NCKU lead by I-Lin Wang

69. 70/39
Timing for multi-pull
If x = 23
10 + 45 + x ≧ 10 + 45 + 15
multi-pull one more track
Team NCKU lead by I-Lin Wang

70. 71/39
Timing for multi-pull
If x = 23
10 + 45 + x ≧ 10 + 45 + 15
multi-pull one more track
≒ 10 + 45 +30
multi-pull two more tracks
Team NCKU lead by I-Lin Wang

71. 72/39
Timing for multi-pull
Multi-Pull 1 or 2 ???
Team NCKU lead by I-Lin Wang

72. 73/39
How many tracks to multi-pull
1. Flooring (x/15)
2. Ceiling (x/15)
Team NCKU lead by I-Lin Wang

73. 74/39
Flooring
engine
Team NCKU lead by I-Lin Wang
……

74. 75/39
Flooring
engine
Team NCKU lead by I-Lin Wang
……
10:00 11:20

75. 76/39
Flooring
engine
Team NCKU lead by I-Lin Wang
……
10:00 10:25 11:20
10+15
Pullback time

76. 77/39
Flooring
engine
10+15 45
Team NCKU lead by I-Lin Wang
……
10:00 10:25 11:20
Pullback time Technical inspection

77. 78/39
Flooring
engine
10+15 45
Team NCKU lead by I-Lin Wang
……
10:00 10:25 11:10 11:20
Pullback time Technical inspection

78. 79/39
Flooring
engine
10+15 45 X=10
Team NCKU lead by I-Lin Wang
……
10:00 10:25 11:10 11:20
Pullback time Technical inspection Waiting time

79. 80/39
Flooring
engine
Team NCKU lead by I-Lin Wang
……
( T can outbound – T currnet )*N

80. 81/39
Ceiling
engine
Team NCKU lead by I-Lin Wang
……

81. 82/39
Ceiling
engine
Team NCKU lead by I-Lin Wang
……
10:00 11:20

82. 83/39
Ceiling
engine
10+15+15
Team NCKU lead by I-Lin Wang
……
10:00 11:20
Pullback time

83. 84/39
Ceiling
engine
10+15+15
Team NCKU lead by I-Lin Wang
……
10:00 11:20
Pullback time

84. 85/39
Ceiling
engine
10+15+15
Team NCKU lead by I-Lin Wang
……
10:00 11:20
Pullback time
10:40

85. 86/39
Ceiling
engine
10+15+15
10:40 11:25
45
Team NCKU lead by I-Lin Wang
……
10:00 11:20
Pullback time Technical inspection

86. 87/39
Ceiling
engine
10+15+15
10:40 11:25
45
Team NCKU lead by I-Lin Wang
……
10:00
Pullback time Technical inspection

87. 88/39
Ceiling
engine
Team NCKU lead by I-Lin Wang
……

88. 89/39
Ceiling
engine
Team NCKU lead by I-Lin Wang
……
( T pullback + T inspection )*(N+N’)

89. 90/39
Pullback Model
( T can outbound – T currnet )*N
( T pullback + T inspection )*(N+N’)
Team NCKU lead by I-Lin Wang
1.Flooring
2.Ceiling

90. 91/39
Pullback Model
( T can outbound – T currnet )
( T pullback + T inspection )*(1+N’/N)
Team NCKU lead by I-Lin Wang
1.Flooring
2.Ceiling

91. 92/39
Pullback Model
( T can outbound – T currnet )
( T pullback + T inspection )*(1+N’/N)
Team NCKU lead by I-Lin Wang
1.Flooring
2.Ceiling

92. 93/39
Pullback Model
( T can outbound – T currnet )
( T pullback + T inspection )*(1+N’/N)
Team NCKU lead by I-Lin Wang
1.Flooring
2.Ceiling

93. 94/39
Pullback Model
( T can outbound – T currnet )
( T pullback + T inspection )*(1+N’/N)
Team NCKU lead by I-Lin Wang
1.Flooring
2.Ceiling

94. 95/39
Pullback Model
( T can outbound – T currnet )
( T pullback + T inspection )*(1+N’/N)
Team NCKU lead by I-Lin Wang
1.Flooring
2.Ceiling

95. 96/39
Computational Result
Team NCKU lead by I-Lin Wang
1. Original
2. Original + Hump model
3. Original + Pullback model
4. Original + Hump model + Pullback Model

96. 97/39
Data characteristics
combination
Small (33) Large (247)
Team NCKU lead by I-Lin Wang
Number
of data
(blocks)
Small
(24330)
Data 2 Data 3
Large
(34130)
Data 4 Data 5

97. 98/39
Computation Result
Team NCKU lead by I-Lin Wang

98. 99/39
Conclusions & Future Research
• Give a simulation-based greedy mechanism.
– Simple dispatching rules
• Longest first rule
• Timing for humping & pulling back operations
– Efficient, with flexibility to adjust
• Future research
– Integer Programming Model
• Difficulty: cannot model waiting time in linear way
too many variables and constraints
Team NCKU lead by I-Lin Wang

99. 100/3
9
Q&A
王逸琳副教授
李唯、廖巧鈺
成功大學工業與資訊管理學系