
N  Set of stations 

N_{o}  Set of nodes, including the stations and the depot (indexed by 0) 

i, j  Indices 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 

P  Set of pickup stations, i.e., 

D  Set of dropoff stations, i.e., 

Q  Truck capacity 

 Capacity of station i 

T  Repositioning time 

L  Time required to load a bike from a station onto the truck 

U  Time required to unload a bike from the truck to a station 

M  A 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 upperlevel decision variables, 

 The vector of the lowerlevel decision variables, 
