Assgm 02 - DMTM

Timetabling and Rolling Stock scheduling.

Timetabling

For the headway at arrival, do we do the same considerations that we do at departure? ✅ 2025-12-13
- No need. headway at arrival is already gartanteed
In Std (Sittard), there are 3 tracks leaving the station. There are 2 lines: to Mt and to Hrl. One of the 3 tracks is shared between the 2 lines. How should we treat it? Are the line contrasting? Do they always need headways? ✅ 2025-12-13
- Pretend it's not a problem
[[Screenshot 2025-12-10 at 18.34.42.png]]: should we keep both transfer opportunities? How would we select only the best? ✅ 2025-12-13
- Think about it. If you do, it makes it infeasible

Abbink 2004:

train classes: power-driven, diesel-drive, locomotive-driven, locomotive-hauled carriages
- Train types: Koplopers (intercity), Mat'64 (regional)
  - Train subtypes: Koplopers 3 cars; Koplopers 4 cars... Mat'64 2 cars and MAt'64 4 cars...
  - Train units of same type can be combined. Train units of different types cannot.
Train unit: certain number of carriages that cannot be split during operation

In our case, we have

We can minimise shortages or cost

$S :$ shortages = number of paxs without a seat

Variables:

constraints:

S_{t} \geq P_{t} - \sum_{u} C_{u} \cdot N_{u, t} \forall t \in T

\begin{aligned} \sum_{u} N_{u, t} & \geq 1 \forall t \in T \\ \sum_{u} λ_{u} N_{u, t} & \leq L_{t} \forall t \in T \\ \sum_{t} N_{1, t} & \leq 1.25 \cdot \sum_{t} N_{2, t} \\ \sum_{t} N_{2, t} & \leq 1.25 \cdot \sum_{t} N_{1, t} \end{aligned}

\begin{aligned} S & \geq P - \sum C N \\ S & \geq 0 \end{aligned}