Dutch railway quantities 1.000.000 passengers per workday 14.000.000.000 passenger kilometers per year 5000 timetabled trains per workday 2800 kilometers of tracks 380 stations 2650 wagons 3000 train drivers 4000 conductors (and assistants) 29 depots for drivers/conductors

Lines in the “Randstad”

Hourly Pattern for the track Rotterdam - Utrecht Rtd Rtn Rta Cps Nwk Mda Gd Gdg Wd Hmla Vtn Ut 500 10 10 21700 8800 9700 20 20 4000 2800 2000 30 30 1700 2000 2800 40 40 14000 8800 20500 9700 50 50 2800 2000 60 60

Platform Occupation Chart for Utrecht Central

Koploper with 3 or 4 wagons Double decker with 3 or 4 wagons Mat’64 with 2 or 4 wagons q/.r

Gvc Rtd Ut Amf Dv Es 9:00 10:00 11:00 12:00 9:30 10:30 11:30 1731 21731 1636 1640 1738 1734 1632 1730 20533 21735 20537 21739 20541 529 533 1735 537 1739 1629 1727 1633 1637 524 1726 528 532 Gvc 541 9:00 10:00 11:00 12:00 9:30 10:30 11:30

Maintenance Routing Input: Problem: Objectives: Duties for rolling stock units Status quo of rolling stock units Location (time / space) of maintenance facilities Details of infrastructure Problem: Connect duties for critical rolling stock units such that these arrive in time in a maintenance facility Objectives: Feasibility Simplicity of solution Efficient use of rolling stock units

12 11 10 9 8 7 6 5 4 3 2 1 Maintenance Gvc Rtd Ut

12 11 10 9 8 7 6 5 4 3 2 1 Maintenance Gvc Rtd Ut

12 11 10 9 8 7 6 5 4 3 2 1 Maintenance Gvc Rtd Ut

12 11 10 9 8 7 6 5 4 3 2 1 Maintenance Gvc Rtd Ut

12 11 10 9 8 7 6 5 4 3 2 1 Maintenance Maintenance path Gvc Rtd Ut

Maintenance Maintenance path Train unit path Gvc Rtd Ut 12 11 10 9 8 7 6 5 4 3 2 1 Maintenance Maintenance path Train unit path Gvc Rtd Ut

12 11 10 9 8 7 6 5 4 3 2 1 Maintenance Train unit path Gvc Rtd Ut

Ldd Rtd Gvc Ut Amr Hlm Wgm Asd Llso maandag dinsdag woensdag donderdag vrijdag zaterdag zondag 6 2 5 3 10 4 8 7 9 12

Maintenance Routing Complexity of a connection depends on: arrival time arrival platform position in arriving train departure time departure platform position in departing train difficult: 3 4* 3 4 4 3 easier: 3 4* 3 4 4 3

Shunting Input: Problem: Objectives: Arrivals: arrival time, inbound route, platform track, composition, Departures:departure time, outbound route, platform track, composition Connections of (compositions of) arriving and departing trains Details of the infrastructure Initial occupation of the infrastructure Problem: Find a simple and feasible shunting and storage plan including efficient duties for the shunting employees Objectives: Feasibility and simplicity of the solution

Shunting Example 2 tracks 3 train types 4 arrivals 4 departures 1 Arrivals: Departures: 4 3

Shunting Example 2 1 Arrivals: 4 3 Dep . (reverse): Solution: 1/4 2/3

Shunting Arrivals: Departures: Plan Realisation

Shunting Arrivals: Departures: Plan Realisation

Robustness and Stability robustness stability

Redesign project order: desire or necessity to change the plan management of the plan. process structural changes in hour pattern structural changes in day pattern incidental changes in day pattern completing the plan Allocation of train units BUP/BSO Basic day Specific day 9 months 3 months 4 weeks 3 days Throughput time of the planning process