Two-Phase Optimization Models for Liner Shipping Network Based on Hub Ports Cooperation: From the Perspective of Supply-Side Reform in China

Table 1

Notations of model in NA phase.

Sets
N	Set of all nodes in the LSNs
H	Set of all traditional hub ports (THP)
R	Set of all emerging hub ports (EHP)
O	Set of all origin ports of demands
D	Set of all destination ports of demands
V	Set of all available legs in the LSNs
Parameters
π	Capacity of any deployed containership
	Voyage expense of operating on leg (i1, i2) ∊ V
	Transit time of operating on leg (i1, i2) ∊ V
Ω	Maximum containership capacity for a voyage circle controlled by the government
Qod	Quantity of demand between origin port o ∊ O ⊆ N and destination port d ∊ D ⊆ N
eod	Freight rate of transporting unit demand between origin port o ∊ O ⊆ N and destination port d ∊ D ⊆ N
E	Expected total revenue, which can be calculated as
W	Fixed transit time for the total legs in a voyage cycle
Decision variables
	(Binary) 1 iff the leg (i1, i2) exists
	The number of containers to be transported on leg (i1, i2) ∊ V
z	The number of deployed containerships