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

Table 2

Parameters and variables used in the mathematical formulation.

Sets
	Set of nodes,
	Subset of one main depot (node 0)
	Subset of candidate satellites,
	Subset of customers,
	Set of vehicles,
	Subset of primary vehicles
	Subset of secondary vehicles
	Set of valid arcs,
	Subsets of valid arcs for first-level trips,
	Subsets of valid arcs for second-level trips,
Indicators
	Node in primary network,
	Node in secondary network,
	Vehicle,
Parameters
	Nonnegative travelling cost of arc
	Nonnegative travelling cost of arc
	Capacity of primary vehicle
	Capacity of secondary vehicle
	Fixed cost of primary vehicle
	Fixed cost of secondary vehicle
	Capacity of satellite
	Opening cost of satellite
	Pickup demand of customer
	Delivery demand of customer
Additional variables
	Dynamic load of primary vehicle in arc
	Dynamic load of secondary vehicle in arc
	Pickup demand of opened satellite
	Delivery demand of opened satellite
Decision variables
	Binary variable with a value of 1 when primary vehicle travels directly from node to node ,
	Binary variable with a value of 1 when secondary vehicle travels directly from node to node ,
	Binary variable with a value of 1 when customer is allocated to satellite
	Status of satellite with a value of 1 when satellite is open