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Table 1 Description of parameters and variables

From: Optimization of multi- period empty container repositioning and renting in CHINA RAILWAY Express based on container sharing strategy

parameters description
I Collection of all sites (i, j  I), I1 represents a collection of Chinese sites, I2 represents a collection of European sites.
I1 Collection of train companies (k, g  I1).As the train company is based on the Chinese city, it is represented by the collection of Chinese stations.
T Decision period length, weeks.
\( {\mathrm{b}}_{\mathrm{ik}}^{\mathrm{t}} \) The initial volume of k company’s containers at station i at the end of t period, FEU.
\( {\mathrm{d}}_{\mathrm{ijk}}^{\mathrm{t}} \) The demand of k company’s container transportation from station i to station j in t period, FEU.
cij Single case transportation cost from station i to station j, USD / FEU.
cj Rental of single container and single time cost of CRCT, USD / FEU.
cy Single case and single time cost of COSCO Shipping Group, USD / FEU.
cjoutlast Rental of overdue single container of CRCT, USD / FEU * week.
cyoutlast Rental of COSCO Shipping Group’s single case overdue cost, USD / FEU * week.
\( c{j}_i^{trans} \) Transportation cost of single container from station i to the nearest rental and return point of CRCT, USD / FEU.
\( \mathrm{c}{\mathrm{y}}_{\mathrm{i}}^{\mathrm{trans}} \) Transportation cost of single container from station i to the nearest rental and return point of COSCO Shipping Group, USD / FEU.
\( {\mathrm{c}}_{\mathrm{i}}^{\mathrm{store}} \) Single container and single cycle storage cost of site i, USD / FEU * week.
hj Leasing the container of CRCT for a single time, week.
hy Lease the container of COSCO Shipping Group for a single time, week.
\( {\mathrm{x}}_{\mathrm{ijkg}}^{\mathrm{t}} \) In t period, K company calls the number of containers from G company at site i to site j, FEU.
\( \mathrm{l}{\mathrm{j}}_{\mathrm{ik}}^{\mathrm{t}} \) In t period, K company rented the container volume of CRCT at site i, FEU.
\( \mathrm{l}{\mathrm{y}}_{\mathrm{ik}}^{\mathrm{t}} \) In t period, K company rented COSCO Shipping Company’s container volume at site i, FEU.
\( \mathrm{h}{\mathrm{j}}_{\mathrm{ik}}^{\mathrm{t}} \) In t period, K company returns the container quantity of CRCT at site i, FEU.
\( \mathrm{h}{\mathrm{y}}_{\mathrm{ik}}^{\mathrm{t}} \) In t period, K company returns the container quantity of COSCO Shipping Company at site i, FEU.
hjot The container quantity of China Railway Container Co., Ltd. not returned due to overdue period in t period, FEU.
\( \mathrm{hy}{\mathrm{o}}_{\mathrm{dom}}^{\mathrm{t}} \) Container volume of COSCO Shipping Company in t period due to overdue return in China, FEU.