Table 3: Notations for the bi-level model.

NSet of stations

NoSet of nodes, including the stations and the depot (indexed by 0)

i, jIndices of stations

Initial inventory level at station i before the repositioning operation

Final inventory level at station i after the repositioning operation

Convex penalty function of for station i

The target optimal inventory at station i, ,i.e., the optimal number of bikes at station i

PSet of pick-up stations, i.e.,

DSet of drop-off stations, i.e.,

QTruck capacity

Capacity of station i

TRepositioning time

LTime required to load a bike from a station onto the truck

UTime required to unload a bike from the truck to a station

MA very large number

Traveling time from station i to station j

Binary variable that equals 1 if the truck travels directly from station i to station j, and 0 otherwise

Number of bikes on the truck when it travels directly from station i to station j

The loading quantities at station i,  

The unloading quantitiesat station i,  

The vector of the upper-level decision variables,  

The vector of the lower-level decision variables,