A Multiperiodic Optimization Formulation for the Operation Planning of Free-Floating Shared Bike in China

Table 1

Notations used in this paper.

Subscripts and Sets
	The set of stations in region 1.
	The set of stations in region 2.
	The set of studied period.
	Any given station in region 1, .
	Any given station in region 2, .
	Any given time period, .
Input Parameters
	The number of bicycle travel demand in period , with station in region 1 as start point, and station in region 2 as terminal point. (Meaning that demand of bicycles traveling from station to station during time period ).
	The number of bicycle travel demand in period , with site in region 2 as start point, and site in region 1 as terminal point. (Meaning that demand of bicycles traveling from site to site ).
	The unit bike inventory holding cost.
	The capacity threshold of each station (overload is allowed, but will be punished).
	The penalty cost per unit at flexible station when the capacity is above the threshold.
	The maximum number of times for dispatching in the system planning horizon.
	The maximum number of bikes the dispatching truck capable to load at one time.
	The fixed cost of dispatching for one time.
	The penalty cost per unit for unmet demand in each time period.
	The transporting cost per empty bike (between two sites).
	The purchasing cost per bike per day (the purchasing cost per day per bike is converted according to the service life of bikes).
	The rental income per bike between two stations.
	A big positive constant.
Other Parameters
	The number of bikes which are rented at station in time period , with station in region 1 as start point, and station in region 2 as terminal point.
	The number of bikes which are rented at station in time period , with station in region 2 as start point, and station in region 1 as terminal point.
	The unsatisfied demand (characterized as the number of bikes) at the end of the time period , with site in region 1 as start point, and site in region 2 as terminal point.
	The unsatisfied demand (characterized as the number of bikes) at the end of the time period , with site in region 2 as start point, and site in region 1 as terminal point.
Decision Variables
	Whether the unutilized bikes at station in region 1 are dispatched at the beginning of period (1 for “Yes”, 0 for “No”).
	Whether the unutilized bikes at station in region 2 are dispatched at the beginning of period (1 for “Yes”, 0 for “No”).
	The number of unutilized bikes which are moved from station in region 1 to station in region 2 in time period .
	The number of unutilized bikes which are moved from site in region 2 to site in region 1 in time period .
	The initial allotment of bikes (initial bicycle inventory position) to site in region 1 at the beginning of period .
	The initial allotment of bikes (initial bicycle inventory position) to site in region 2 at the beginning of period .