A Bilevel Programming Model and Algorithm for the Static Bike Repositioning Problem

Table 3

Notations for the bi-level model.

N	Set of stations
No	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 pick-up stations, i.e.,
D	Set of drop-off 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 upper-level decision variables,
	The vector of the lower-level decision variables,