Skip to main content

Table 1 The parameter values adopted for the model

From: Holistic tactical-level planning in liner shipping: an exact optimization approach

Parameter

Value

Number of port rotations: n1 (port rotations)

3

Number of ports of call under port rotation r: \( {n}_r^2,r\in R \) (ports)

6

Number of available vessel types: n3 (vessel types)

2

Number of available TWs at port p of port rotation r: \( {n}_{rp}^4,r\in R,p\in {P}_r \) (TWs)

3

Number of available HRs at port p of port rotation r during TW t: \( {n}_{rp t}^5,r\in R,p\in {P}_r,t\in {T}_{rp} \) (HRs)

4

Maximum port service frequency: Ï•max (days)

14

Number of vessels of type v available in company’s own fleet for deployment: \( {q}_v^{own-m},v\in V \) (vessels)

[3; 4]

Number of vessels of type v available for chartering: \( {q}_v^{\mathit{\operatorname{char}}-m},v\in V \) (vessels)

[5; 6]

Maximum sailing speed: Ï‘max (knots)

25

Minimum sailing speed: Ï‘min (knots)

15

Fuel consumption coefficient: αv, v ∈ V

[3; 3.2]

Fuel consumption coefficient: γv, v ∈ V

[0.012; 0.014]

Coefficient of the container demand sensitivity to the vessel sailing speed at port p of port rotation r: \( {\alpha}_{rp}^{dem},r\in R,p\in {P}_r \)

U[400; 1,800]

Coefficient of the container demand sensitivity to the vessel sailing speed at port p of port rotation r: \( {\beta}_{rp}^{dem},r\in R,p\in {P}_r \)

U[1,250; 3,000]

Portion of import containers at port p of port rotation r: Importrp, r ∈ R, p ∈ Pr (%)

U[40; 60]

Total quantity of containers on board a vessel before it is moored at the first port of call under port rotation r: \( {QC}_r^{SEA-0},r\in R \) (TEUs)

U[4,000; 7,000]

Handling productivity under HR h during TW t at port p of port rotation r for vessels of type v: phrpthv, r ∈ R, p ∈ Pr, t ∈ Trp, h ∈ Hrpt, v ∈ V (TEUs/hour)

U[50; 125]

Average weight of cargo inside a standard 20-ft container: AWC (tons)

11

Empty weight of a vessel of type v: LWTv, v ∈ V (tons)

[48,000; 50,000]

Total cargo carrying capacity of a vessel of type v: TWCv, v ∈ V (tons)

[144,000; 150,000]

Arrival TW duration: \( \left[{\tau}_{rp t}^{end}-{\tau}_{rp t}^{st}\right]\forall r\in R,p\in {P}_r,t\in {T}_{rp} \) (hours)

U[12; 24]

Emission factor in sea: EFSEA (tons of emissions/ton of fuel)

3.082

Emission factor at port p of port rotation r under HR h for vessel type v: \( {EF}_{rphv}^{PORT},r\in R,p\in {P}_r,h\in {H}_{rpt},v\in V \) (tons of emissions/TEU)

0.01729 for h = 180

Unit vessel operational cost for vessel type v: \( {c}_v^{oper},v\in V \) (USD/day)

[39,000; 43,000]

Unit chartering cost for vessel type v: \( {c}_v^{char},v\in V \) (USD/day)

[59,000; 65,000]

Unit handling cost for vessel type v at port p of port rotation r during TW t under HR h: \( {c}_{rp t hv}^{hand},r\in R,p\in {P}_r,t\in {T}_{rp},h\in {H}_{rp t},v\in V \) (USD/TEU)

U[200; 500]

Unit late arrival cost for port p of port rotation r: \( {c}_{rp}^{late},r\in R,p\in {P}_r \) (USD/hour)

U[5,000; 8,000]

Unit fuel cost: cfuel (USD/ton)

200

Unit inventory cost: cinv (USD/TEU/hour)

0.25

Unit emission cost: cemis (USD/ton)

32

Unit freight rate for delivery to port p of port rotation r: \( {c}_{rp}^{rev},r\in R,p\in {P}_r \) (USD/TEU)

U[1,000; 2,500]