the variable labor cost $c^C_w$ of $m_\tau^C(\omega)$ couriers.\
Again, since the nominal routing cost (with no detours) is a sunk cost incurred regardless of the capacity deployment, the marginal cost is sufficient to inform the tactical decision of the impact of recourse actions.The marginal cost of the detours induced by the tactical decisions, or the difference between the courier routing cost with detours and the nominal courier routing cost is: $$\Delta C^C_{l}(\tau, \omega) = \sum_{a \in A_{pool}(l)} (2 n_{a}^C(\tau, \omega) d_a) c^C_{v_0}) + \Delta T^C_{l}(\tau, \omega) c^C_w$$ where the time associated with performing detours is: $$\Delta T^C_{l}(\tau, \omega) = \sum_{a \in A_{pool}(l)} n_{a}^C(\tau, \omega)(\frac{2 d_a}{s^C_0} + t^C_a)$$

### Operations Synchronization {#operations-synchronization .unnumbered}

Recall that a key objective of integrating routing operations with the capacity deployment problem is to guarantee the synchronisation of the operations between couriers and riders at each location. To do so, this subsection proposes to develop time-based synchronisation constraints based on the travel time approximations (\[rider time cumulative\]) and (\[courier time cumulative\]), developed above.

Parcels transshipped from riders to couriers and couriers to riders through access hubs must be transshipped during the period of time the parcels are within the network. That is, the length of a 