Estimation of crew demand in S-tog

1. Estimation of crew demand in S-tog • Agenda • The planning process • Motivation for the model • What is the purpose of the model • Input to the model • Objectives • Experiments and conclusion • Future work Michael Folkmann Operational Researcher Production Planning, DSB S-tog

2. Draft of Product Process of the (sequential) planning Economystructure Time Table Evaluation Number of Passengers Crew plan Rolling Stock plan

3. Track Work Track Work Track Work Track Work Track Work Track Work New product and changes in the product. Planning period ≈ one year Basis plan …….. …

4. Motivation for the model • Good early estimation of crew costs in reasonable time for a plan • Crew plans were time consuming • Crew target • Train drivers • First generation • Needs Rolling Stock Plan • Duty planning with Turni integrated • Adjustment for track works • Second generation • Change the input • Other groups of personnel • No Rolling Stock Plan

5. What is the purpose of the model • Breifly: • Cover a workload with duty template in relation to a number of constraints • DayTypes • Weekdays • Saturday • Sunday • Size of time intervals; 15 minutes • Inputs • Workload • Coming from Rolling Stock Plan which needs a driver • Duty templates • Parameters for constraints • Use of the results • Not actual plan • Crew demand

6. Workload

7. Duty Templates • Working day • Amount of driving • Check In/out – work – Breaks • Six different template variations • By hand or with model • Fractionel

8. Duty Templates variants • For all six templates, i.e. three sets with six templates

9. Difference in Template Types

10. Working Rules to be modelled • Each Duty - Input • Length of break in duties • Duty length • Length of driving block • … • All Duties - Constraints • Average working time per duty • Average breaks per duty

11. Variables

12. Average Working Time per Duty • Total amount of working time divided by the number of duties • Reformulated:

13. Average Breaks per Duty • Reference solution • 241 duties • Break Average 1.722 (=AB) • Total number of breaks in duties divided by the number of duties. • Reformulated constraints with variation

14. Model Objective • Minimise the total amount of working time in the solution (Objective1) • Minimise the total number of templates used (Objective 2)

15. Adjustment and Experiments • Decision • Size of time interval • Adjustments • Importance of the average breaks • Importance of the templates types • Experiments • Two objectives • Gap - solution quality

16. Runs • One daytype for one plan – one reference solution • Two fictitious plan – relativ evaluation • Running time 6:00 hours • Zero gap tolerance • Cplex 8.1.0 (using Gams 2.0.23.10) • Windows 2000 • Pentium M 1700 MHz • 2GB ram

17. Average Breaks and Templates

18. Average Breaks and Templates

19. Quality of solutions

20. Quality of solutions

21. Gap progress • Running time for (almost) no progress in gap compared to 360 minutes • Template Type T1 • Break Average 0.1% and 1.0%

22. Results and conclusion • Decreasing in objective – as expected • Two Objectives • Average Breaks – important but not strict • Running time • Have initial parameter setting: • Minimising number of duties with T1 duty templates with 15 minutes intervals and Average Breaks variation 1.0% for a short running time

23. Future work • More reference solution from Turni • Different templates • effect of small changes • fewer/more templates • Develop of the template model • Other constraints • difference during the day • limited number of specific templates • Change the model into second generation – i.e. Public Time Table as input

24. Questions?