ERASMUS CENTER OF OPTIMIZATION IN PUBLIC TRANSPORT
MAINTENANCE IN
RAILWAY ROLLING
STOCK RESCHEDULING
FOR PASSENGER
RAILWAYS
OUTLINE
1. Introduction
2. Models
Extra Unit Type Model
Shadow Account Model
Job-Composition Model
Introduction
1. Introduction
2. Models
Extra Unit Type Model
Shadow Account Model
Job-Composition Model
3. Results
Introduction
SCHEDULING THE ROLLING STOCK
•
Rolling stock circulation is made before the operations take
place.
•
Limited number of rolling stock units require maintenance.
•
Regular maintenance check
•
Broken door
•
Broken coupling mechanism
Introduction
DISRUPTION MANAGEMENT
Problem during operations:
Unexpected events make the planned resource schedules
infeasible.
→
Disruption
Disruption management consists of:
•
Handling disruptions if they occur
Introduction
ROLLING STOCK RESCHEDULING
Given:
•
The planned timetable
•
The planned rolling stock circulation
•
The rescheduled timetable
Output:
•
A rescheduled rolling stock circulation that serves the
Introduction
MAINTENANCE
•
Disruption causes infeasibilities in the current rolling stock
schedule.
•
Current rescheduling models do not take maintenance
appointments into account.
Introduction
EXAMPLE
•
Two units require maintenance.
•
Alkmaar, 16:00 at Nijmegen lasting 2 hours.
Introduction
Introduction
Models
1. Introduction
2. Models
Extra Unit Type Model
Shadow Account Model
Job-Composition Model
3. Results
Models
MODELS
Three novel models developed:
1. Extra Unit Type model.
2. Shadow Account model.
3. Job-Composition model.
Models Extra Unit Type Model
1. Introduction
2. Models
Extra Unit Type Model
Shadow Account Model
Job-Composition Model
3. Results
Models Extra Unit Type Model
EXTRA UNIT TYPE MODEL
•
New rolling stock type for every unit with a maintenance
appointment.
•
Example:
•
10 units of type
a
and 10 units of type
b
.
•
1 unit of type
a
has a maintenance appointment at 16:00 at
Nijmegen.
•
1 unit of type
a
has a maintenance appointment at 22:00 at
Nijmegen.
Models Extra Unit Type Model
COMPOSITIONS
•
Coupled units form a composition (e.g.
aab
,
bba
).
Models Extra Unit Type Model
IMPORTANT CONSTRAINTS
•
Appoint exactly one composition to every trip
•
Composition changes match with appointed compositions
•
Inventory always non-negative
•
Units have to be present at the right location and time of
Models Extra Unit Type Model
OBJECTIVE
Minimize:
•
Number of additional cancelled trains.
•
Total capacity shortage.
•
Carriage kilometers.
•
Deviations from original shunting plan.
•
Deviations from end of day balance.
Models Extra Unit Type Model
SUMMARY
•
Advantage: very easy and intuitive approach.
•
Disadvantage: the additional number of compositions is
large and therefore the number of additional composition
changes is even larger.
Models Shadow Account Model
1. Introduction
2. Models
Extra Unit Type Model
Shadow Account Model
Job-Composition Model
3. Results
Models Shadow Account Model
SHADOW ACCOUNT MODEL
•
Split the model in three parts
•
Composition model part
•
Shadow account part
•
Linking part
•
The same constraints and variables are used in
Models Shadow Account Model
SHADOW ACCOUNT PART
•
Introduce additional RS types 0
,
1
, ...,
x
, called shadow
types.
•
Shadow type 0 represents units without maintenance
appointment.
Models Shadow Account Model
SHADOW ACCOUNT PART
Example:
•
10 units of type
a
and 10 units of type
b
.
•
1 unit of type
a
has a maintenance appointment at 16:00 at
Nijmegen.
•
1 unit of type
a
has a maintenance appointment at 22:00 at
Nijmegen.
•
10 type
a
, 10 type
b
in normal part.
•
18 type 0, 1 type 1 and 1 type 2 in shadow part
Models Shadow Account Model
Models Shadow Account Model
Models Shadow Account Model
LINKING PART
•
Two rolling stock schedules, one for the original types and
one for the shadow types.
•
Both schedules have to be linked to each other.
•
Normal schedule: Trip 1:
aab
, trip 2:
aaba
.
•
Shadow schedule: If all units do not have a maintenance
appointment, then trip 1: 000, trip 2: 0000.
•
Shadow schedule: If unit
b
has a maintenance
Models Shadow Account Model
LINKING PART
•
Two rolling stock schedules, one for the original types and
one for the shadow types.
•
Both schedules have to be linked to each other.
•
Normal schedule: Trip 1:
aab
, trip 2:
aaba
.
•
Shadow schedule: If all units do not have a maintenance
appointment, then trip 1: 000, trip 2: 0000.
Models Shadow Account Model
SUMMARY
•
Advantage: Less additional compositions, so less possible
composition changes.
Models Job-Composition Model
1. Introduction
2. Models
Extra Unit Type Model
Shadow Account Model
Job-Composition Model
3. Results
Models Job-Composition Model
JOB-COMPOSITION MODEL
•
A job is a sequence of successive trips between coupling
and uncoupling.
•
List of all possible jobs is created.
•
Appoint units to jobs instead of trips, such that every trip
Models Job-Composition Model
JOB-COMPOSITION MODEL
•
Y
j
,
m
denotes whether job
j
is performed by a rolling stock
unit
m
or not
•
Q
j
,
m
0denotes whether job
j
is performed by a rolling stock
unit with a specific maintenance appointment
m
0
•
10 units of type
a
and 10 units of type
b
.
•
1 unit of type
a
has a maintenance appointment at 16:00 at
Nijmegen.
•
1 unit of type
a
has a maintenance appointment at 22:00 at
Nijmegen.
Models Job-Composition Model
SUMMARY
•
Advantage: no additional compositions, so no additional
composition changes
Results
1. Introduction
2. Models
Extra Unit Type Model
Shadow Account Model
Job-Composition Model
3. Results
Results
INSTANCES
Hdr Amr Asd Ut Ed Ah Nm Hlm Ledn Gv Rtd Ddr Bd Amf DvResults
RESULTS
#RS types
Turnaround time
Disrupted area
2
10
Gv-Rtd
2
10
Ut-Asd
3
10
Gv-Rtd
3
10
Ut-Asd
2
30
Gv-Rtd
2
30
Ut-Asd
3
30
Gv-Rtd
3
30
Ut-Asd
Results
INSTANCES
•
20 different time slots for disruptions.
•
Between 1 and 6 units require maintenance.
•
In total 960 cases per model.
Results
RESULTS TURNAROUND TIME 10 MINUTES
Two types:
1 2 3 4 5 6 0 100 200 300 400 500 # Maintenance units Computation time EU T SA JC (a) Ut-Asd 1 2 3 4 5 6 100 200 300 400 500 # Maintenance units Computation time EU T SA JC (b) Rtd-GvThree types:
300 400 500 time EU T SA JC 300 400 500 time EU T SA JCResults
RESULTS TURNAROUND TIME 30 MINUTES
Two types:
1 2 3 4 5 6 0 100 200 300 400 500 # Maintenance units Computation time EU T SA JC (a) Ut-Asd 1 2 3 4 5 6 0 100 200 300 400 500 # Maintenance units Computation time EU T SA JC (b) Rtd-GvThree types:
200 300 400 500 Computation time EU T SA JC 200 300 400 500 Computation time EU T SA JCConclusions and further research
1. Introduction
2. Models
Extra Unit Type Model
Shadow Account Model
Job-Composition Model
3. Results
Conclusions and further research
CONCLUSIONS AND FURTHER RESEARCH
•
3 novel models to take maintenance appointments into
account in the RSRP.
•
JC model performs best with a turnaround time of 10
minutes.
•
SA model performs best with a turnaround time of 30
minutes.
•
Future research: inclusion of other practical aspects, such
Conclusions and further research
