ERASMUS CENTER OF OPTIMIZATION IN PUBLIC TRANSPORT MAINTENANCE IN RAILWAY ROLLING STOCK RESCHEDULING FOR PASSENGER RAILWAYS J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 1 / 39
OUTLINE 1. Introduction 2. Models Extra Unit Type Model Shadow Account Model Job-Composition Model 3. Results 4. Conclusions and further research J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 2 / 39
Introduction 1. Introduction 2. Models Extra Unit Type Model Shadow Account Model Job-Composition Model 3. Results 4. Conclusions and further research J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 3 / 39
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 Maintenance appointment at one of the stations. J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 4 / 39
Introduction DISRUPTION MANAGEMENT Problem during operations: Unexpected events make the planned resource schedules infeasible. Disruption Disruption management consists of: Handling disruptions if they occur And not preventing disruptions to occur J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 5 / 39
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 adapted timetable Literature: Fioole et al (2006), Nielsen et al (2012) J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 6 / 39
Introduction MAINTENANCE Disruption causes infeasibilities in the current rolling stock schedule. Current rescheduling models do not take maintenance appointments into account. As a result, maintenance appointments are missed. J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 7 / 39
Introduction EXAMPLE Two units require maintenance. Alkmaar, 16:00 at Nijmegen lasting 2 hours. Den Helder, 22:00 at Nijmegen lasting 2 hours. J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 8 / 39
Introduction EXAMPLE: SCHEDULED CIRCULATION WITH DISRUPTION J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 9 / 39
Introduction EXAMPLE: AFTER RESCHEDULING J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 10 / 39
1. Introduction 2. Models Extra Unit Type Model Shadow Account Model Job-Composition Model 3. Results 4. Conclusions and further research J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 11 / 39
MODELS Three novel models developed: 1. Extra Unit Type model. 2. Shadow Account model. 3. Job-Composition model. Based on Composition Model, created by Fioole et al. (2006). J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 12 / 39
Extra Unit Type Model 1. Introduction 2. Models Extra Unit Type Model Shadow Account Model Job-Composition Model 3. Results 4. Conclusions and further research J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 13 / 39
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. 8 type a, 10 type b, 1 type c and 1 type d J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 14 / 39
Extra Unit Type Model COMPOSITIONS Coupled units form a composition (e.g. aab, bba). Compositions can be changed at stations J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 15 / 39
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 their appointment. J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 16 / 39
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. Minimize number of missed maintenance appointments J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 17 / 39
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. J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 18 / 39
Shadow Account Model 1. Introduction 2. Models Extra Unit Type Model Shadow Account Model Job-Composition Model 3. Results 4. Conclusions and further research J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 19 / 39
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 composition model part as in the Extra Unit Type model. J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 20 / 39
Shadow Account Model SHADOW ACCOUNT PART Introduce additional RS types 0, 1,..., x, called shadow types. Shadow type 0 represents units without maintenance appointment. Shadow types 1,..., x represent units with an appointment. J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 21 / 39
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 All the constraints of the composition part are used for the shadow types as well. J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 22 / 39
Shadow Account Model EXAMPLE J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 23 / 39
Shadow Account Model EXAMPLE J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 24 / 39
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. J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 25 / 39
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 appointment, then trip 1: 001, trip 2: 0010. J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 25 / 39
Shadow Account Model SUMMARY Advantage: Less additional compositions, so less possible composition changes. Disadvantage: More constraints. J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 26 / 39
Job-Composition Model 1. Introduction 2. Models Extra Unit Type Model Shadow Account Model Job-Composition Model 3. Results 4. Conclusions and further research J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 27 / 39
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 has a composition. J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 28 / 39
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 denotes whether job j is performed by a rolling stock unit with a specific maintenance appointment m 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 1 unit of type m 1 and 1 unit of type m 2 in M J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 29 / 39
Job-Composition Model SUMMARY Advantage: no additional compositions, so no additional composition changes Disadvantage: list of jobs can become large J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 30 / 39
Results 1. Introduction 2. Models Extra Unit Type Model Shadow Account Model Job-Composition Model 3. Results 4. Conclusions and further research J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 31 / 39
Results INSTANCES Hdr Amr Hlm Asd Dv Ledn Gv Rtd Ddr Bd Ut Amf Ah Ed Nm In total 1095 trips. J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 32 / 39
Results 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 2 RS types 31 compositions, 356 composition changes. 3 RS types 72 compositions, 884 composition changes. J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 33 / 39
Results INSTANCES 20 different time slots for disruptions. Between 1 and 6 units require maintenance. In total 960 cases per model. Maximum computation time of 500 seconds. J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 34 / 39
Results RESULTS TURNAROUND TIME 10 MINUTES Two types: Computation time 500 400 300 200 100 EUT SA JC Computation time 500 400 300 200 100 EUT SA JC 0 1 2 3 4 5 6 # Maintenance units 1 2 3 4 5 6 # Maintenance units (a) Ut-Asd Three types: Computation time 500 400 300 200 EUT SA JC Computation time 500 400 300 200 (b) Rtd-Gv EUT SA JC 100 100 1 2 3 4 5 6 # Maintenance units 1 2 3 4 5 6 # Maintenance units (a) Ut-Asd (b) Rtd-Gv J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 35 / 39
Results RESULTS TURNAROUND TIME 30 MINUTES Two types: Computation time 500 400 300 200 100 EUT SA JC Computation time 500 400 300 200 100 EUT SA JC 0 1 2 3 4 5 6 # Maintenance units 0 1 2 3 4 5 6 # Maintenance units (a) Ut-Asd Three types: Computation time 500 400 300 200 EUT SA JC Computation time 500 400 300 200 (b) Rtd-Gv EUT SA JC 100 100 1 2 3 4 5 6 # Maintenance units 1 2 3 4 5 6 # Maintenance units (a) Ut-Asd (b) Rtd-Gv J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 36 / 39
Conclusions and further research 1. Introduction 2. Models Extra Unit Type Model Shadow Account Model Job-Composition Model 3. Results 4. Conclusions and further research J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 37 / 39
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 as dead-heading trips, robustness, station routing. J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 38 / 39
Conclusions and further research END OF PRESENTATION Thank you for your attention! J.C. Wagenaar & L.G. Kroon (jwagenaar@rsm.nl) Rotterdam School of Management, Erasmus University November 6, 2014 39 / 39