Presenting a Multi-Start Hybrid Heuristic for Solving the Problem of Two-Echelon Location-Routing Problem with Simultaneous Pickup and Delivery (2E-LRPSPD)

Table 1

Summary of related studies.

Paper	Number of echelons in the network	Location decision	Customer demand	Whether the vehicle delivery and pickup	Other constraints considered	Model	Solution method
Karaoglan et al. [34]	One	Depot	Pickup and delivery demands	√	×	Two-index flow-based formulation	Branch and cut algorithm
Yu and Lin [35]	One	Depot	Pickup and delivery demands	√	×	×	Multistart simulated annealing
Karaoglan and Altiparmak [36]	One	Depot	Pickup and delivery demands	√	×	Flow-based formulation	Memetic algorithm
Zhang et al. [37]	One	Depot	Pickup and delivery demands	√	×	Three-index formulation	Variable neighbourhood scatter search algorithm
Karaoglan et al. [38]	One	Depot	Pickup and delivery demands	√	×	Node-based formulation and flow-based formulation	A two-phase heuristic based on simulated annealing
Wang et al. [39]	One	Depot and courier transceiver point	Pickup and delivery demands	√	Fuzzy time windows constraints	Formulation with two objective function: minimize distribution operation cost and maximize service level	A hybrid heuristic algorithm combining tabu search and efficient procedures
Crainic et al. [41]	Two	Platform (depot) and satellite	Delivery demand	×	×	Three formulations, differing by the type and the number of routing variables	×
Vidović et al. [42]	Two	Depot and satellite	Pickup demand	×	×	MILP model	A heuristic solution approach
Contardo et al. [45]	Two	Platform (depot) and satellite	Delivery demand	×	×	Two-index vehicle-flow formulation	Branch and cut algorithm
Boccia et al. [46]	Two	Satellite	Delivery demand	×	×	×	TS heuristic is based on the integration of the nested approach and the two-phase iterative approach
Li et al. [48]	Two	Satellite	Delivery demand	×	×	Mixed integer linear programming model	Genetic algorithm
Dalfard et al. [47]	Two	Satellite	Delivery demand	×	Maximum route length	Mathematical model regarding the constraints of the vehicle fleet capacity and the maximum route distance	Hybrid genetic algorithm and simulated annealing
Nguyen et al. [3, 4]	Two	Satellite	Delivery demand	×	×	Two-index integer linear program and three-index integer linear program	GRASP reinforced by a learning process and path relinking, multistart iterated local search with tabu list and path relinking
Govindan et al. [56]	Two	Satellite	Delivery demand	×	Soft-time windows constraint	Multi-objective optimisation model	A multi-objective hybrid approach called MHPV, a hybrid of two known multi-objective algorithms: multi-objective particle swarm optimisation (MOPSO) and adapted multiobjective variable neighbourhood search (AMOVNS)
Wang et al. [58]	Two	Satellite	Delivery demand	×	Time windows constraint	Biobjective model minimizing costs and maximizing customer satisfaction	A three-step customer clustering based approach
Ouhader and Elkyal [59]	Two	Satellite	Delivery demand	×	Multisourcing and multiproducts	Mixed integer linear programming formulation	×
Pichka et al. [60]	Two	Satellite	Delivery demand	×	Open route	Three mixed-integer linear programming models	A two-phase hybrid heuristic
Zhao et al.[61]	Two	Satellite	Delivery demand	×	Working hours and traffic restrictions	Mathematical formulation	The cooperative approximation heuristic algorithm
Dai et al. [2]	One, two, three, and four	Depot and satellite	Delivery demand	×	Maximum route length	One-echelon, two-echelon, three-echelon, and four echelon models	A two-phase method based on improved Clarke and Wright saving algorithm
Rahmani et al. [62]	Two	Satellite	Delivery demand	√	×	×	Local search methods
Demircan-Yildiz et al. [63]	Two	Satellite	Pickup and delivery demands	√	×	Node-based formulation and flow-based formulation	×
Ghatreh and Hosseini-Motlagh [64]	Two	Satellite	Pickup and delivery demands	√	Fuzzy demand	Mixed integer linear programming model	A combined heuristic method based on simulated annealing algorithm and genetic algorithm