t^R_a)$$

### Couriers operations {#couriers-operations .unnumbered}

Couriers operate in unit zones, which are clusters of pickup and delivery points served by access hub(s). Couriers leave their reference access hubs to visit customers and perform pickups/deliveries before returning to their access hub. When a courier arrives at the courier’s access hub with picked parcels, if the courier observes a lack of capacity, the courier can be immediately directed to available capacity in some neighboring access hub. Then, the courier will perform a detour (out and back) to the assigned neighbour access hub before starting their next tour from their reference access hub. Figure \[fig: Courier\] illustrates a courier’s tour and a detour as described.

Since access hubs are located in the same area as pickup/delivery locations, the line-haul distance at this echelon is negligible, which eliminates the first term of approximation (\[VRPDaganzo\]). If the number of detours performed by couriers on arc $a \in A_{pool}(l)= \{a=(l,j), \forall j: (l,j) \in A_{pool}\}$ of length $d_a$ in period $\tau$ under scenario $\omega$ is $n_{a}^C(\tau, \omega)$, the route length estimation with detours of couriers’ operations is: $$\label{VRPCouriers}
VRP^C_{l}(\tau, \omega) = (\rho_{l}^P(\tau,\omega) + \rho_{l}^D(\tau,\omega))k^C(\delta_{l})^{-\frac{1}{2}} + \sum_{a \in A_{pool}(l)} (2 n_{a}^C(\tau, \omega) d_a)$$ where the first 