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

Timetable Design & its impact

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 TIME STATIONSSTATIONS

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

Resources for Train Services Energy Sectional capacity Rolling Stock Crew

Minimum Headway Time 1mk Slack Time route

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

Resources for Train Services Energy Sectional capacity Rolling Stock Crew

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

Resources for Train Services Energy Sectional capacity Rolling Stock Crew

Rolling Stock Maintenance Primary Maintenance Station A Secondary Maintenance Station B

Rolling Stock Deployment The number of rakes required for a train service depends on the following factors: the cycle time maintenance requirements, m p hours for primary maintenance and m s hours for secondary maintenance running time of a trip, say u g hours each way scheduled lie-over of say l p,g hours at the primary maintenance station and l s,g hours at the secondary maintenance station;

Resources for Train Services Energy Sectional capacity Rolling Stock Crew

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

Crew Requirements 0900 Hrs 1630 Hrs 0100 Hrs 0830 Hrs Train 1 Train 11

Crew Deployment Index (CDI)

Objective Functions Minimize Total Consumption of Energy (TCE) Maximize Total Slack Index (TSI) Minimize Rolling Stock Deployment Index (RSDI) Minimize Crew Deployment Index (CDI)

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

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 d PIS or Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to Maximize CR

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

Analytic Hierarchy Process(AHP)) Energy Consumed Schedule Reliability Rolling Stock Deployment Crew Deployment Raw weight RW Normalized weight NW Energy Consumed Schedule Reliability 1/ Rolling Stock Deployment 1/51/ Crew Deployment 1/61/ Column Total

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 d PIS or Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to Maximize CR

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

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

Test Case Results

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

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

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

Strategic opportunities offered by optimal 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

Thank You