Table 1 Three-echelon urban freight on transit system model notations

P:

Initial set of all parcels to be delivered.

R:

Set of all train stations.

H:

Set of potential candidate hubs.

S:

Set of potential candidate satellites.

Dist:

Distance matrix on the road network.

T_rail:

Travel time matrix on the rail network.

N:

Number of initial candidate satellites.

Q₁:

Vehicle capacity of the fleet in the first echelon.

D₁:

Maximum route duration for the vehicle in the first echelon.

Q₂:

Vehicle capacity of the fleet in the third echelon.

D₂:

Maximum route duration for the vehicle in the third echelon.

T_max:

Maximum travel time between the hub to other satellites on the rail network.

x_h:

If h ∈ H is selected as a hub, it is 1, otherwise, it is 0.

y_s:

If s ∈ S is selected as a satellite, it is 1, otherwise, it is 0.