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routing-subtour-elimination

Subtour-elimination methods for TSP, VRP, pickup/dropoff routing, and routing MIPs with binary arc variables. Use when route-continuity constraints may permit disconnected cycles and the model needs MTZ constraints, flow-based connectivity constraints, DFJ subset cuts, or lazy/iterative subtour cuts.

tasks/bike-rebalance/environment/skills/routing-subtour-elimination/SKILL.md

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# Routing Subtour Elimination

In routing MIPs, degree and continuity constraints are not enough. A vehicle can have one depot-to-depot path and a separate closed cycle among stations. Add subtour-elimination constraints whenever binary arc variables decide routes.

Use this base notation:

```python
START = "depot_start"
END = "depot_end"
vehicles = range(K)
stations = range(n)
from_nodes = [START, *stations]
to_nodes = [*stations, END]
arcs = [(i, j) for i in from_nodes for j in to_nodes if i != j and not (i == START and j == END)]