Bike-Sharing Static Rebalancing by Considering the Collection of Bicycles in Need of Repair

Table 1

Summary of the characteristics of the static BRP in the literature.

References	Bicycle demand	Formulations	Objective	Damaged bicycles	Solution
Benchimol et al.; J. H. Lin et al.	Given	Single-vehicle 1-PDTSP	Minimize total travel cost	Without Consideration	Approximation algorithm
Raviv et al.	A decision variable	Extends the 1-PDTSP	Minimize the weighted sum of total travel time and penalty cost	Without Consideration	A two-stage heuristic
Chemla et al. Dell’Amico et al.	Given	Extends the 1-PDTSP	Minimize total travel cost	Without consideration	Branch-and-cut algorithm
Ho and Szeto.	A decision variable	A single-vehicle MIP	Minimize total penalty cost	Without consideration	Iterated tabu search heuristic
Angeloudis et al.	Determined by the history net flow data	m-TSP	Minimize the total duration of travel	Without Consideration.	Approximation algorithm
Forma et al.	A decision variable	3-step mathematical programming-based heuristic	Minimize total cost, consisting of the sum of penalties and the operating costs.	Without Consideration.	3-step math heuristic
Alvarez-Valdes et al.	A decision variable	Multi-commodity PDTSP	Minimize the weighted sum of the total service time and the coefficient of variations of the duration of all routes	Yes, but the impact of the damaged bicycles to the vehicle’s; capacity constraint is not considered	A heuristic algorithm based on minimum cost flow problem and an insertion algorithm
Szeto et al.	Given	Single-vehicle 1-PDTSP	Minimize the weighted sum of unmet customer demand and operational time on the vehicle route.	Without Consideration	Enhanced Chemical Reaction Optimization
Li et al.	Given	MIP	Minimize total cost	Without Consideration.	A combined hybrid genetic algorithm
Kadri et al.	Given	TSP	Minimize the total waiting time of the stations	Without consideration	Branch and bound algorithm
Cruz et al.	Given	1-PDTSP	Minimize the traveling cost	Without Consideration.	Iterated Local Research-based heuristic.
Ho and Szeto.	Given	1-VRPSPD	Minimize the sum of penalty cost	Without Consideration.	A hybrid large neighborhood search combined with a tabu search.
Schuijbroek et al.	Determine service level requirements at each station	A Clustered MIP	Minimize maximum tour length	Without consideration	Cluster-first route-second heuristic
Szeto and Shui.	Given	MIP	Minimize the total demand dissatisfaction (TDD) and total service time	Without consideration	An enhanced artificial bee colony algorithm
Bulhões et al.	Given	MIP	Minimize the total travel time	Without consideration	Branch-and-cut algorithm combined with local search metaheuristic
This study	Present a predict method using the operating data	Multi-commodity VRPSPD	Minimize the traveling cost	Yes, the vehicle’s; capacity constraint to the damaged bicycles is considered	A hybrid DPSO-VNS