Optimal Design of Timetables to maximize schedule reliability and minimize energy consumption, rolling stock and crew

1. Optimal Design of Timetables to maximize schedule reliabilityand minimize energy consumption,rolling stock and crew deployment DDr B.Nag,Director,RDSO

2. Timetable Design & its impact

3. Present Method of Timetable Design • done manually by feasible path construction and mapping train services • No method available for construction of optimal timetables with respect to energy consumption, schedule reliability or crew & rolling stock deployment STATIONS TIME

4. Problems of Timetable Design • Large number of trains • Large number of sections • Many constraints • No metrics developed for schedule reliability, energy consumption, rolling stock & crew requirements • Mathematical model not solvable because of size

5. Resources for Train Services • Energy • Sectional capacity • Rolling Stock • Crew

6. route 1 k m Minimum Headway Time Slack Time

7. delayed on route 1 by will be delayed on route 1 by will be delayed on route 2 by

8. Resources for Train Services • Energy • Sectional capacity • Rolling Stock • Crew

10. m 1 k route Energy Consumption depends on train speed, section terrain (ruling gradient & curvature), rolling stock resistance & locomotive efficiency, and regeneration.

11. Resources for Train Services • Energy • Sectional capacity • Rolling Stock • Crew

12. Rolling Stock Maintenance Primary Maintenance Station A Secondary Maintenance Station B

13. Rolling Stock Deployment The number of rakes required for a train service depends on the following factors: • the cycle time • maintenance requirements, mp hours for primary maintenance and ms hours for secondary maintenance • running time of a trip, say ug hours each way • scheduled lie-over of say lp,g hours at the primary maintenance station and ls,g hours at the secondary maintenance station;

14. Resources for Train Services • Energy • Sectional capacity • Rolling Stock • Crew

15. Labour Regulations • Maximum duty of 8 –10 hours • Out-station Rest for minimum of 8 hours • Base-station Rest for minimum of 16 hours

16. 0900 Hrs Crew Requirements Min 16 Hrs Rest Train 1 0830 Hrs 1630 Hrs Train 11 Min 8 Hrs Rest 0100 Hrs

17. Crew Deployment Index (CDI)

18. Objective Functions • Minimize Total Consumption of Energy (TCE) • Maximize Total Slack Index (TSI) • Minimize Rolling Stock Deployment Index (RSDI) • Minimize Crew Deployment Index (CDI) Multi-criteria Decision Making Problem

19. Mathematical Model- Constraints • Minimum section traversal time • Cycle Time • Bounds on departure times, slack times, total running time

20. Solution Methodology • Analytic Hierarchy Process (AHP) to determine relative weights of each objective • Compute distance functions for distance from PIS, NIS & Closeness Rating(CR) • Global Criteria Approach (GCA) to Minimize dPIS or • Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to Maximize CR

21. Relative Importance of Objective Functions for the Decision Maker • Schedule Reliability • Customer Perception • Line Capacity creation • Energy Consumption • Rolling Stock • cost of rake • lead time for new rake procurement • Creation of facilities for maintenance • Crew • Cost of crew recruitment, training and operation • lead time for recruitment & training

22. Analytic Hierarchy Process(AHP))

23. Solution Methodology • Analytic Hierarchy Process (AHP) to determine relative weights of each objective • Compute distance functions for distance from PIS, NIS & Closeness Rating(CR) • Global Criteria Approach (GCA) to Minimize dPIS or • Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to Maximize CR

24. Distance Functions Global Criteria Approach (GCA) Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)

25. Test Problem GAMS Program of 9083 equations & 9123 variables required 6 sec compilation and execution time on a 600 Mhz computer

26. Test Case Results

27. Cost Benefits • Will vary on the section, train density, rolling stock characteristics, operating & maintenance practices, crew management • Results for the test case indicate 10% savings in energy, 2% less requirement of crew and 12% less requirement of rolling stock when comparing the best & worst scenarios

28. Summary • Identification of decision variables for time table design- slack times and minimum headways • Developing the concept of route to reduce problem size • Developing metrics for robustness & rolling stock deployment • Exploring the aspects of speed differentials and throughput • Formulation and Demonstration of mathematical model to optimally design timetables

29. Applications • Formulation of timetables which are robust to disturbances • Formulation of timetables which maximize resource utilization and minimize energy consumption • Identification of bottleneck sections • Compare timetables for robustness • Analysis of implications of speed changes: CBA • Analysis of resource augmentations : CBA • Identify optimal timetables for maintenance blocks • Can be integrated with Driving Advice System for pacing of trains

30. Strategic opportunities offered byoptimal timetable design • Take advantage of new technologies such as regenerative braking • Use optimal pacing of trains • Reduce capital investment on new lines and rolling stock • Methodologies can be applied for on-line scheduling and integration with on-board driving advice systems

31. Thank You