Applying a single fixed cost per “physical” vehicle when modelling multiple shifts in OR‑Tools

[Steffenctrl]

Hello everyone,

To model multiple shifts per vehicle, I duplicate each real vehicle into as many "virtual" vehicles as there are shifts. This way each shift has its own time window in the solver. I'm then modelling a pick-up and delivery problem with time windows in OR-Tools. The reason I have modelled it this way is that I sometimes have to deliver to a customer several times in my planning horizon. However, this cannot be done during the same shift. Otherwise, the option of creating dummy depot nodes with a breakpoint would probably also work. However, the solution would then tell me to deliver to the same customer one after the other:

(depot -> customer A -> customer A -> depot -> depot) instead of (depot -> customer A -> depot -> customer A -> depot).

With the current approach, I can add a constraint that the same customer cannot be delivered by the same vehicle. The challenge I'm facing now is how to deal with the fixed costs:

Current issue: OR‑Tools charges the fixed‑cost parameter for every virtual vehicle that is used. If a single real vehicle covers three shifts, the fixed cost is counted three times.
Desired behaviour: I need the fixed cost to apply once per real vehicle, regardless of how many of its shifts are utilized.

Question:

• What’s the best way in OR‑Tools to group those shift‑vehicles so that the solver only incurs the fixed cost once per group?